title: Open Shortest Path First

text: Originally designed in the 1980s, OSPF is defined for IPv4 in protocol version 2 by RFC 2328 (1998). The updates for IPv6 are specified as OSPF Version 3 in RFC 5340 (2008). OSPF supports the Classless Inter-Domain Routing (CIDR) addressing model.


title: Open Shortest Path First

text: OSPF is an interior gateway protocol (IGP) for routing Internet Protocol (IP) packets within a single routing domain, such as an autonomous system. It gathers link state information from available routers and constructs a topology map of the network. The topology is presented as a routing table to the Internet Layer which routes packets based solely on their destination IP address.


title: Open Shortest Path First

text: OSPF detects changes in the topology, such as link failures, and converges on a new loop-free routing structure within seconds. It computes the shortest-path tree for each route using a method based on Dijkstra's algorithm. The OSPF routing policies for constructing a route table are governed by link metrics associated with each routing interface. Cost factors may be the distance of a router (round-trip time), data throughput of a link, or link availability and reliability, expressed as simple unitless numbers. This provides a dynamic process of traffic load balancing between routes of equal cost.


title: Open Shortest Path First

text: OSPF divides the network into routing "areas" to simplify administration and optimize traffic and resource utilization. Areas are identified by 32-bit numbers, expressed either simply in decimal, or often in the same octet-based dot-decimal notation used for IPv4 addresses. By convention, area 0 (zero), or 0.0.0.0, represents the core or "backbone" area of an OSPF network. While the identifications of other areas may be chosen at will, administrators often select the IP address of a main router in an area as the area identifier. Each additional area must have a connection to the OSPF backbone area. Such connections are maintained by an interconnecting router, known as an area border router (ABR). An ABR maintains separate link-state databases for each area it serves and maintains summarized routes for all areas in the network.


title: Open Shortest Path First

text: OSPF runs over Internet Protocol Version 4 (IPv4) and Internet Protocol Version 6 (IPv6), but does not use a transport protocol, such as UDP or TCP. It encapsulates its data directly in IP packets with protocol number 89. This is in contrast to other routing protocols, such as the Routing Information Protocol (RIP) and the Border Gateway Protocol (BGP). OSPF implements its own transport error detection and correction functions. OSPF uses multicast addressing for distributing route information within a broadcast domain. It reserves the multicast addresses 224.0.0.5 (IPv4) and FF02::5 (IPv6) for all SPF/link state routers (AllSPFRouters) and 224.0.0.6 (IPv4) and FF02::6 (IPv6) for all Designated Routers (AllDRouters). For non-broadcast networks, special provisions for configuration facilitate neighbor discovery. OSPF multicast IP packets never traverse IP routers, they never travel more than one hop. The protocol may therefore be considered a link layer protocol, but is often also attributed to the application layer in the TCP/IP model. It has a virtual link feature that can be used to create an adjacency tunnel across multiple hops. OSPF over IPv4 can operate securely between routers, optionally using a variety of authentication methods to allow only trusted routers to participate in routing. OSPFv3 (IPv6) relies on standard IPv6 protocol security (IPsec), and has no internal authentication methods.


title: Open Shortest Path First

text: For routing IP multicast traffic, OSPF supports the Multicast Open Shortest Path First (MOSPF) protocol. Cisco does not include MOSPF in their OSPF implementations. Protocol Independent Multicast (PIM) in conjunction with OSPF or other IGPs, is widely deployed.


title: Open Shortest Path First

text: OSPF version 3 introduces modifications to the IPv4 implementation of the protocol. Except for virtual links, all neighbor exchanges use IPv6 link-local addressing exclusively. The IPv6 protocol runs per link, rather than based on the subnet. All IP prefix information has been removed from the link-state advertisements and from the "hello" discovery packet making OSPFv3 essentially protocol-independent. Despite the expanded IP addressing to 128 bits in IPv6, area and router Identifications are still based on 32-bit numbers.


title: Open Shortest Path First

text: OSPF supports complex networks with multiple routers, including backup routers, to balance traffic load on multiple links to other subnets. Neighboring routers in the same broadcast domain or at each end of a point-to-point link communicate with each other via the OSPF protocol. Routers form "adjacencies" when they have detected each other. This detection is initiated when a router identifies itself in a "hello" protocol packet. Upon acknowledgment, this establishes a "two-way state" and the most basic relationship. The routers in an Ethernet or Frame Relay network select a "designated router" (DR) and a "backup designated router" (BDR) which act as a hub to reduce traffic between routers. OSPF uses both unicast and multicast transmission modes to send "hello" packets and link-state updates.


title: Open Shortest Path First

text: As a link-state routing protocol, OSPF establishes and maintains neighbor relationships for exchanging routing updates with other routers. The neighbor relationship table is called an "adjacency database". Two OSPF routers are neighbors if they are members of the same subnet and share the same area ID, subnet mask, timers and authentication. In essence, OSPF neighborship is a relationship between two routers that allow them to see and understand each other but nothing more. OSPF neighbors do not exchange any routing information – the only packets they exchange are hello packets. OSPF adjacencies are formed between selected neighbors and allow them to exchange routing information. Two routers must first be neighbors and only then, can they become adjacent. Two routers become adjacent if at least one of them is designated router or backup designated router (on multiaccess-type networks), or they are interconnected by a point-to-point or point-to-multipoint network type. For forming a neighbor relationship between, the interfaces used to form the relationship must be in the same OSPF area. While an interface may be configured to belong to multiple areas, this is generally not practiced. When configured in a second area, an interface must be configured as a secondary interface.


title: Open Shortest Path First

text: Virtual link over Virtual links, Tunneling and shamelinks, are a form of connections, that goes over the routing engine. And is not a direct connection to the remote host.


title: Open Shortest Path First

text: Each OSPF router within a network communicates with other neighboring routers on each connecting interface to establish the states of all adjacencies. Every such communication sequence is a separate "conversation" identified by the pair of router IDs of the communicating neighbors. RFC 2328 specifies the protocol for initiating these conversations ("Hello Protocol") and for establishing full adjacencies ("database description packets", "link-state request packets"). During its course, each router conversation transitions through a maximum of eight conditions defined by a state machine:


title: Open Shortest Path First

text: In broadcast multiple-access networks, neighbor adjacency is formed dynamically using multicast hello packets to .


title: Open Shortest Path First

text: In non-broadcast multiple-access network(NBMA), neighbor adjacency is formed with unicast packets to remote host. A network may have more than two routers, but is no broadcast support.


title: Open Shortest Path First

text: A network is divided into OSPF "areas" that are logical groupings of hosts and networks. An area includes its connecting router having an interface for each connected network link. Each router maintains a separate link-state database for the area whose information may be summarized towards the rest of the network by the connecting router. Thus, the topology of an area is unknown outside the area. This reduces the routing traffic between parts of an autonomous system.


title: Open Shortest Path First

text: OSPF can handle thousands of routers with more a concern of reaching capacity of the forwarding information base (FIB) table when the network contains lots of routes and lower-end devices. Modern low-end routers have a full gigabyte of RAM, which allows them to handle many routers in an area 0. Many resources refer to OSPF guides from over 20 years ago where it was impressive to have 64 MB of RAM.


title: Open Shortest Path First

text: Areas are uniquely identified with 32-bit numbers. The area identifiers are commonly written in the dot-decimal notation, familiar from IPv4 addressing. However, they are not IP addresses and may duplicate, without conflict, any IPv4 address. The area identifiers for IPv6 implementations (OSPFv3) also use 32-bit identifiers written in the same notation. When dotted formatting is omitted, most implementations expand area "1" to the area identifier "0.0.0.1", but some have been known to expand it as "1.0.0.0".


title: Open Shortest Path First

text: Several vendors (Cisco, Allied Telesis, Juniper, Alcatel-Lucent, Huawei, Quagga), implement "totally stubby" and "NSSA totally stubby area" for stub and not-so-stubby areas. Although not covered by RFC standards, they are considered by many to be standard features in OSPF implementations.


title: Open Shortest Path First

text: The backbone area (also known as "area 0" or "area 0.0.0.0") forms the core of an OSPF network. All other areas are connected to it, either directly or through other routers. OSPF requires this to prevent routing loops. Inter-area routing happens via routers connected to the backbone area and to their own associated areas. It is the logical and physical structure for the 'OSPF domain' and is attached to all nonzero areas in the OSPF domain. In OSPF the term "autonomous system boundary router" (ASBR) is historic, in the sense that many OSPF domains can coexist in the same Internet-visible autonomous system, RFC 1996.


title: Open Shortest Path First

text: All OSPF areas must connect to the backbone area. This connection, however, can be through a virtual link. For example, assume area 0.0.0.1 has a physical connection to area 0.0.0.0. Further assume that area 0.0.0.2 has no direct connection to the backbone, but this area does have a connection to area 0.0.0.1. Area 0.0.0.2 can use a virtual link through the "transit area" 0.0.0.1 to reach the backbone. To be a transit area, an area has to have the transit attribute, so it cannot be stubby in any way.


title: Open Shortest Path First

text: A regular area is just a non-backbone (nonzero) area without specific feature, generating and receiving summary and external LSAs. The backbone area is a special type of such area.


title: Open Shortest Path First

text: A stub area is an area that does not receive route advertisements external to the AS and routing from within the area is based entirely on a default route. An ABR deletes type 4 and 5 LSAs from internal routers, sends them a default route of 0.0.0.0 and turns itself into a default gateway. This reduces LSDB and routing table size for internal routers.


title: Open Shortest Path First

text: Modifications to the basic concept of stub area have been implemented by systems vendors, such as the "totally stubby area" (TSA) and the "not-so-stubby area" (NSSA), both an extension in Cisco Systems routing equipment.


title: Open Shortest Path First

text: A "totally stubby area" is similar to a stub area. However, this area does not allow "summary" routes in addition to not having "external" routes, that is, "inter-area" (IA) routes are not summarized into totally stubby areas. The only way for traffic to get routed outside the area is a default route which is the only Type-3 LSA advertised into the area. When there is only one route out of the area, fewer routing decisions have to be made by the route processor, which lowers system resource utilization.


title: Open Shortest Path First

text: A "not-so-stubby area" (NSSA) is a type of stub area that can import autonomous system external routes and send them to other areas, but still cannot receive AS-external routes from other areas.


title: Open Shortest Path First

text: NSSA is an extension of the stub area feature that allows the injection of external routes in a limited fashion into the stub area. A case study simulates an NSSA getting around the stub-area problem of not being able to import external addresses. It visualizes the following activities: the ASBR imports external addresses with a type 7 LSA, the ABR converts a type 7 LSA to type 5 and floods it to other areas, the ABR acts as an "ASBR" for other areas.


title: Open Shortest Path First

text: An addition to the standard functionality of an NSSA, the "totally stubby NSSA" is an NSSA that takes on the attributes of a TSA, meaning that type 3 and 4 summary routes are not flooded into this type of area. It is also possible to declare an area both totally stubby and not-so-stubby, which means that the area will receive only the default route from area 0.0.0.0, but can also contain an autonomous system boundary router (ASBR) that accepts external routing information and injects it into the local area, and from the local area into area 0.0.0.0.


title: Open Shortest Path First

text: A newly acquired subsidiary is one example of where it might be suitable for an area to be simultaneously not-so-stubby and totally stubby if the practical place to put an ASBR is on the edge of a totally stubby area. In such a case, the ASBR does send externals into the totally stubby area, and they are available to OSPF speakers within that area. In Cisco's implementation, the external routes can be summarized before injecting them into the totally stubby area. In general, the ASBR should not advertise default into the TSA-NSSA, although this can work with extremely careful design and operation, for the limited special cases in which such an advertisement makes sense.


title: Open Shortest Path First

text: By declaring the totally stubby area as NSSA, no external routes from the backbone, except the default route, enter the area being discussed. The externals do reach area 0.0.0.0 via the TSA-NSSA, but no routes other than the default route enter the TSA-NSSA. Routers in the TSA-NSSA send all traffic to the ABR, except to routes advertised by the ASBR.


title: Open Shortest Path First

text: The router type is an attribute of an OSPF process. A given physical router may have one or more OSPF processes. For example, a router that is connected to more than one area, and which receives routes from a BGP process connected to another AS, is both an area border router and an autonomous system boundary router.


title: Open Shortest Path First

text: Each router has an identifier, customarily written in the dotted-decimal format (e.g., 1.2.3.4) of an IP address. This identifier must be established in every OSPF instance. If not explicitly configured, the highest logical IP address will be duplicated as the router identifier. However, since the router identifier is not an IP address, it does not have to be a part of any routable subnet in the network, and often isn't to avoid confusion.


title: Open Shortest Path First

text: A system of "designated router" (DR) and "backup designated router" (BDR), is used to reducing network traffic by providing a source for routing updates.


title: Open Shortest Path First

text: The DR and BDR maintains a complete topology table of the network and sends the updates to the other routers via multicast. All routers in a multi-access network segment will form a slave/master relationship with the DR and BDR. They will form adjacencies with the DR and BDR only. Every time a router sends an update, it sends it to the DR and BDR on the multicast address . The DR will then send the update out to all other routers in the area, to the multicast address . This way all the routers do not have to constantly update each other, and can rather get all their updates from a single source. The use of multicasting further reduces the network load. DRs and BDRs are always setup/elected on OSPF broadcast networks. DR's can also be elected on NBMA (Non-Broadcast Multi-Access) networks such as Frame Relay or ATM. DRs or BDRs are not elected on point-to-point links (such as a point-to-point WAN connection) because the two routers on either side of the link must become fully adjacent and the bandwidth between them cannot be further optimized. DR and non-DR routers evolve from 2-way to full adjacency relationships by exchanging DD, Request, and Update.


title: Open Shortest Path First

text: A "designated router" (DR) is the router interface elected among all routers on a particular multiaccess network segment, generally assumed to be broadcast multiaccess. Special techniques, often vendor-dependent, may be needed to support the DR function on non-broadcast multiaccess (NBMA) media. It is usually wise to configure the individual virtual circuits of an NBMA subnet as individual point-to-point lines; the techniques used are implementation-dependent.


title: Open Shortest Path First

text: A "backup designated router" (BDR) is a router that becomes the designated router if the current designated router has a problem or fails. The BDR is the OSPF router with the second-highest priority at the time of the last election.


title: Open Shortest Path First

text: A given router can have some interfaces that are designated (DR) and others that are backup designated (BDR), and others that are non-designated. If no router is a DR or a BDR on a given subnet, the BDR is first elected, and then a second election is held for the DR.


title: Open Shortest Path First

text: A router that has not been selected to be "designated router" (DR) or "backup designated router" (BDR).


title: Open Shortest Path First

text: Router forms adjacency to both the "designated router" (DR) and the "backup designated router" (BDR).


title: Open Shortest Path First

text: Unlike other routing protocols, OSPF does not carry data via a transport protocol, such as the User Datagram Protocol (UDP) or the Transmission Control Protocol (TCP). Instead, OSPF forms IP datagrams directly, packaging them using protocol number 89 for the IP Protocol field. OSPF defines five different message types, for various types of communication. Multiple packets can be sent per frame.


title: Open Shortest Path First

text: OSPF's Hello messages are used as a form of greeting, to allow a router to discover other adjacent routers on its local links and networks. The messages establish relationships between neighboring devices (called adjacencies) and communicate key parameters about how OSPF is to be used in the autonomous system or area. During normal operation, routers send hello messages to their neighbors at regular intervals (the "hello interval"); if a router stops receiving hello messages from a neighbor, after a set period (the "dead interval") the router will assume the neighbor has gone down.


title: Open Shortest Path First

text: "Database description" messages contain descriptions of the topology of the autonomous system or area. They convey the contents of the link-state database (LSDB) for the area from one router to another. Communicating a large LSDB may require several messages to be sent by having the sending device designated as a master device and sending messages in sequence, with the slave (recipient of the LSDB information) responding with acknowledgments.


title: Open Shortest Path First

text: OSPF uses "path cost" as its basic routing metric, which was defined by the standard not to equate to any standard value such as speed, so the network designer could pick a metric important to the design. In practice, it is determined by comparing the speed of the interface to a reference-bandwidth for the OSPF process. The cost is determined by dividing the reference bandwidth by the interface speed (although the cost for any interface can be manually overridden). If a reference bandwidth is set to '10000', then a 10 Gbit/s link will have a cost of 1. Any speeds less than 1 are rounded up to 1. Here is an example table that shows the routing metric or 'cost calculation' on an interface.


title: Open Shortest Path First

text: OSPF is a layer 3 protocol: if a layer 2 switch is between the two devices running OSPF, one side may negotiate a speed different from the other side. This can create an asymmetric routing on the link (Router 1 to Router 2 could cost '1' and the return path could cost '10'), which may lead to unintended consequences.


title: Open Shortest Path First

text: Metrics, however, are only directly comparable when of the same type. Four types of metrics are recognized. In decreasing preference, these types are (for example, an intra-area route is always preferred to an external route regardless of metric):


title: Open Shortest Path First

text: Despite the expansion of addresses to 128 bits in IPv6, area and router identifications are still 32-bit numbers.


title: Open Shortest Path First

text: A customer can use OSPF over a MPLS-VPN, where the service provider uses BGP or RIP as their interior gateway protocol.


title: Open Shortest Path First

text: When using OSPF over MPLS-VPN, the VPN backbone becomes part of the OSPF backbone area 0. In all areas, isolated copies of the IGP are run.


title: Open Shortest Path First

text: To achieve this, a non-standard OSPF-BGP redistribution is used. All OSPF routes retain the source LSA type and metric.


title: Open Shortest Path First

text: To prevent loops, an optional DN bit is used in LSAs to indicate that a route has already been sent from the provider edge to the customer's equipment.


title: Open Shortest Path First

text: OSPF-TE is an extension to OSPF extending the expressivity to allow for traffic engineering and use on non-IP networks. Using OSPF-TE, more information about the topology can be exchanged using opaque LSA carrying type–length–value elements. These extensions allow OSPF-TE to run completely out of band of the data plane network. This means that it can also be used on non-IP networks, such as optical networks.


title: Open Shortest Path First

text: OSPF-TE is used in GMPLS networks as a means to describe the topology over which GMPLS paths can be established. GMPLS uses its own path setup and forwarding protocols, once it has the full network map.


title: Open Shortest Path First

text: In the Resource Reservation Protocol (RSVP), OSPF-TE is used for recording and flooding RSVP signaled bandwidth reservations for label switched paths within the link-state database.


title: Open Shortest Path First

text: The Multicast Open Shortest Path First (MOSPF) protocol is an extension to OSPF to support multicast routing. MOSPF allows routers to share information about group memberships.


title: Open Shortest Path First

text: OSPF is a widely deployed routing protocol that can converge a network in a few seconds and guarantee loop-free paths. It has many features that allow the imposition of policies about the propagation of routes that it may be appropriate to keep local, for load sharing, and for selective route importing. IS-IS, in contrast, can be tuned for lower overhead in a stable network, the sort more common in ISP than enterprise networks. There are some historical accidents that made IS-IS the preferred IGP for ISPs, but ISPs today may well choose to use the features of the now-efficient implementations of OSPF, after first considering the pros and cons of IS-IS in service provider environments.


title: Open Shortest Path First

text: OSPF can provide better load-sharing on external links than other IGPs. When the default route to an ISP is injected into OSPF from multiple ASBRs as a Type I external route and the same external cost specified, other routers will go to the ASBR with the least path cost from its location. This can be tuned further by adjusting the external cost. If the default route from different ISPs is injected with different external costs, as a Type II external route, the lower-cost default becomes the primary exit and the higher-cost becomes the backup only.


title: Tiber

text: The Tiber ( ; ; ) is the third-longest river in Italy and the longest in Central Italy, rising in the Apennine Mountains in Emilia-Romagna and flowing through Tuscany, Umbria, and Lazio, where it is joined by the River Aniene, to the Tyrrhenian Sea, between Ostia and Fiumicino. It drains a basin estimated at . The river has achieved lasting fame as the main watercourse of the city of Rome, which was founded on its eastern banks.


title: Tiber

text: The river rises at Mount Fumaiolo in central Italy and flows in a generally southerly direction past Perugia and Rome to meet the sea at Ostia. Known in ancient times (in Latin) as "" ("the blond"), in reference to the yellowish colour of its water, the Tiber has advanced significantly at its mouth, by about , since Roman times, leaving the ancient port of Ostia Antica inland. However, it does not form a proportional delta, owing to a strong north-flowing sea current close to the shore, to the steep shelving of the coast, and to slow tectonic subsidence.


title: Tiber

text: The source of the Tiber consists of two springs away from each other on Mount Fumaiolo. These springs are called "le Vene". The springs are in a beech forest above sea level. During the 1930s, Benito Mussolini had an antique marble Roman column built at the point where the river rises, inscribed ("Here is born the river / sacred to the destinies of Rome"). An eagle is on the top of the column, part of its fascist symbolism. The first miles of the Tiber run through Valtiberina before entering Umbria.


title: Tiber

text: The genesis of the name "Tiber" probably was pre-Latin, like the Roman name of Tibur (modern Tivoli), and may be specifically Italic in origin. The same root is found in the Latin "praenomen" "Tiberius". Also, Etruscan variants of this praenomen are in "Thefarie" (borrowed from Faliscan "*Tiferios", lit. '(He) from the Tiber' < "*Tiferis" 'Tiber') and "Teperie" (via the Latin hydronym "Tiber").


title: Tiber

text: Legendary king Tiberinus, ninth in the king-list of Alba Longa, was said to have drowned in the River Albula, which was afterward called "Tiberis". The myth may have explained a memory of an earlier, perhaps pre-Indo-European name for the river, "white" ("alba") with sediment, or "from the mountains" from pre-Indo-European word "alba, albion" mount, elevated area. "Tiberis/Tifernus" may be a pre-Indo-European substrate word related to Aegean "tifos" "still water", Greek phytonym "τύφη" a kind of swamp and river bank weed ("Typha angustifolia"), Iberian hydronyms "Tibilis, Tebro" and Numidian "Aquae Tibilitanae". Yet another etymology is from *dubri-, water, considered by Alessio as Sicel, whence the form Θύβρις later Tiberis. This root *dubri- is widespread in Western Europe e.g. Dover, Portus Dubris.


title: Tiber

text: According to legend, the city of Rome was founded in 753 BC on the banks of the Tiber about from the sea at Ostia. Tiber Island, in the center of the river between Trastevere and the ancient city center, was the site of an important ancient ford and was later bridged. Legend says Rome's founders, the twin brothers Romulus and Remus, were abandoned on its waters, where they were rescued by the she-wolf, Lupa.


title: Tiber

text: The river marked the boundary between the lands of the Etruscans to the west, the Sabines to the east and the Latins to the south. Benito Mussolini, born in Romagna, adjusted the boundary between Tuscany and Emilia-Romagna, so that the springs of the Tiber would lie in Romagna.


title: Tiber

text: The Tiber was critically important to Roman trade and commerce, as ships could reach as far as upriver; some evidence indicates that it was used to ship grain from the Val Teverina as long ago as the fifth century BC. It was later used to ship stone, timber, and foodstuffs to Rome.


title: Tiber

text: During the Punic Wars of the third century BC, the harbour at Ostia became a key naval base. It later became Rome's most important port, where wheat, olive oil, and wine were imported from Rome's colonies around the Mediterranean. Wharves were also built along the riverside in Rome itself, lining the riverbanks around the Campus Martius area. The Romans connected the river with a sewer system (the "Cloaca Maxima") and with an underground network of tunnels and other channels, to bring its water into the middle of the city.


title: Tiber

text: Wealthy Romans had garden-parks or "horti" on the banks of the river in Rome through the first century BC. These may have been sold and developed about a century later.


title: Tiber

text: The heavy sedimentation of the river made maintaining Ostia difficult, prompting the emperors Claudius and Trajan to establish a new port on the Fiumicino in the first century AD. They built a new road, the "Via Portuensis", to connect Rome with Fiumicino, leaving the city by Porta Portese (the port gate). Both ports were eventually abandoned due to silting.


title: Tiber

text: Several popes attempted to improve navigation on the Tiber in the 17th and 18th centuries, with extensive dredging continuing into the 19th century. Trade was boosted for a while, but by the 20th century, silting had resulted in the river only being navigable as far as Rome.


title: Tiber

text: The Tiber was once known for its floods — the Campus Martius is a flood plain and would regularly flood to a depth of . The river is now confined between high stone embankments, which were begun in 1876. Within the city, the riverbanks are lined by boulevards known as "lungoteveri", streets "along the Tiber".


title: Tiber

text: Because the river is identified with Rome, the terms "swimming the Tiber" or "crossing the Tiber" have come to be the shorthand term for converting to Roman Catholicism. A Catholic who converts to Protestantism, in particular Anglicanism, is referred to as "swimming the Thames" or "crossing the Thames".


title: Tiber

text: In ancient Rome, executed criminals were thrown into the Tiber. People executed at the Gemonian stairs were thrown in the Tiber during the later part of the reign of the emperor Tiberius. This practice continued over the centuries. For example, the corpse of Pope Formosus was thrown into the Tiber after the infamous Cadaver Synod held in 897.


title: Tiber

text: In addition to the numerous modern bridges over the Tiber in Rome, there remain a few ancient bridges (now mostly pedestrian-only) that have survived in part (e.g., the Ponte Milvio and the Ponte Sant'Angelo), or in whole (Pons Fabricius).


title: Tiber

text: Following the standard Roman depiction of rivers as powerfully built reclining male gods, the Tiber, also interpreted as a god named Tiberinus, is shown with streams of water flowing from his hair and beard.


title: Tiber

text: In the "Command & Conquer" video game series, the alien mineral the game revolves around, Tiberium, was first discovered by, and named after, the Tiber River.


title: Tiber

text: In Part 5 of the manga series JoJo's Bizarre Adventure, the final conflict between the characters occurs on a street adjacent to the Tiber River, and ends with Diavolo's body flying into it.


title: Tiber

text: In 2022, there was a big heatwave in Europe. As a result of these, the water levels dropped and a number of objects emerged. Some of these objects include world war 2 shipwrecks, bombs and a 2000 year old bridge.


title: Men Without Women (Haruki Murakami short story collection)

text: Kafuku, a veteran and widowed actor, hires twenty-four year old driver Misaki Watari to chauffeur him around Tokyo due to his license being revoked due to a D.U.I. and glaucoma. During their trips, Kafuku occasionally tells her about his life as an actor and his late wife's extramarital affairs. One tale includes how he befriended her lover, Takatsuki, with the intention of harming him. However, over the course of their six month friendship which was spent mostly binge drinking at local bars, he was never able to find any damning information and instead sympathizes with Takatsuki's observations. He also never learns of his wife's motives, calling it a "blind spot" in his knowledge of her. After hearing his story, Misaki notes that perhaps his wife having affairs had had nothing to do with love and that was a good enough reason to do so. After contemplating this propositions, he falls asleep as she continues driving. Dealing with actors and the world of theatre, "Drive My Car" could be considered as an example of what Graham Wolfe calls "theatre-fiction".


text: Tanimura remembers a time in his early twenties when he worked in a restaurant with his friend Kitaru. Kitaru has a few idiosyncrasies that cause his girlfriend Erika to feel uneasy about their relationship; he speaks in a Kansai dialect despite living all his life in Tokyo, does not want to study hard despite having university aspirations, and seems to be asexual around her. One day, Kitaru proposes that Tanimura go on a "date" with Erika to which Tanimura reluctantly agrees. On their date, both talk about their personal lives. Tanimura's girlfriend could not commit to him while Erika admits that she is seeing another man because of Kitaru's apathy. Despite her "unfaithfulness," she admits that Kitaru holds a special place in her heart, and has vivid dreams of them as a couple. Tanimura retells his experience with her to Kitaru during their next shift, omitting certain details. A week later, Kitaru quits and Tanimura loses contact with both Kitaru and Erika.


text: Sixteen years later, in his thirties, Tanimura sees Erika at a wine tasting event. He reveals that he is married, but Erika is still single. As far as she knows, Kitaru is a sushi chef in Denver and is also still single. He goes on to ask whether she had sex with the man she mentioned on their date years ago; she replies yes, but that it did not lead to anything and that she still thinks about Kitaru on occasion.


text: The title of the story comes from The Beatles' "Yesterday" and how, upon hearing it, Tanimura is reminded of Kitaru's playful mistranslation of the lyrics into "Kansai Japanese."


text: Tanimura tells of a time in his life when he regularly played squash with Dr. Tokai, a fifty-two year old cosmetic surgeon and bachelor who has never lived long-term or fallen into a serious relationship with anyone. However, Tokai falls in love with a thirty-six year old married mother and asks Tanimura for advice. During their conversation, Tokai mentions how he is struggling with the question, "Who in the world am I?" and retells a story of a Jewish doctor who lost everything but his life at Auschwitz and how that could have been him. Tokai also notes that for the first time in his life, he feels rage.


text: Tokai suddenly stops coming to the gym soon after and it is not until two months later that Tanimura learns of his death from Tokai's office assistant Goto; they arrange to meet and discuss Tokai. Goto tells of how the doctor suddenly changed his habits at work: he gave off a different aura than before. After Tokai stopped showing up at work, Goto grows concerned and goes to Tokai's apartment and finds him bedridden and feeble. He learns that Tokai has given up on life after the woman Tokai loves abandoned both him and her husband for a third lover. Tokai, lovesick and heartbroken, condemns himself to a slow death by anorexia. Goto concludes by giving Tanimura a squash racket Tokai wanted him to have and asks Tanimura to not forget Tokai.


text: The title of the story comes from Tanimura's memory of Tokai's observation that women have "an independent organ" that allows them to lie with a clear conscience.


text: Unable to go outside of his apartment, Habara relies on a female nurse he dubs "Scheherazade" for his provisions. Despite being married with children, she visits him regularly to have sex with him; after each session, she tells him a story. She also notes that she was a lamprey in her previous life and can sometimes access those memories of being in the sea.


text: Over the course of several encounters, Scheherazade tells of how she was madly in love with a boy from high school, so much so that she discreetly broke into his house several times with a hidden doormat key during school hours. While inside, she surveys his stuff, lies on his bed, and "exchanges" her stuff for his, too afraid to be a burglar. On her first two visits, she trades a tampon for a pencil and then three strands of her own hair for a small soccer badge. On her third visit, she finally steals one of his worn shirts. Upon remembering how infatuated she was with him at the time, she asks Habara to have sex with her again; he finds this session more passionate than any other.


text: Upon returning for her fourth break-in, Scheherazade notices that the locks have changed and reluctantly goes back to her regular schooling. Eventually, she begins to forget the boy, but during nursing school, she saw the boy again through the boy's mother. Noticing that evening is upon them, she tells Habara that she will tell him the circumstances during her next visit. Eager but careful, he acquiesces, but that night in bed, he worries that he will never see her again.


text: Kino, with the help of his retiring aunt, decides to open up a bar after he finds out his wife's affair with her lover, his co-worker. At first no one shows up but a cat, which he lets stay indefinitely. A week later, a mysterious man, Kamita, begins to frequent the bar because he finds the establishment a soothing place to read. Some time after, two customers cause a ruckus and Kino asks them to leave. They react threateningly, but Kamita insists and they redirect their enmity towards him. The three customers go outside, and shortly afterwards, Kamita returns and says that those men will not disturb Kino again.


text: A week later, Kino notes a particular woman who frequents the bar, but on this occasion, her male companion is absent; she interests him because of their mutual fondness of jazz. After everyone else has left, she reveals her body to him; she has many scars, the result of cigarette burns. They subsequently have sex all night in Kino's upstairs bedroom.


text: After his divorce is finalized, his wife comes to his bar to settle a few last matters. She says sorry, but Kino is unable to even understand the meaning of the apology. Some time later, the cat disappears and does not return; snakes begin to show up regularly instead. He calls his aunt for advice, and she suggests that it could be an omen. Kamita returns, and tells him that he has been working for his aunt and insists that he temporarily close the bar and go on a trip to soul search. During his trip, he sees people happy doing mundane work and wonders about his own life. During a night when he perceives there is strange knocking on his door, he comes to terms with himself, realizing that he has been living for so long in apathy.


text: Gregor Samsa wakes up in a bedroom of a two-story house, sure of who he is but unsure of his surroundings. He is hungry, so he slowly goes downstairs to the kitchen, getting accustomed to moving his body. Food is already prepared on the table, so he eats everything. He then notices that he is naked, so he searches the house until he finds a gown.


text: When the doorbell rings, he opens it to find a young, hunchbacked female locksmith who says that she is here to fix a lock in the house. Hesitant, he tells her that one of the room's lock upstairs needs fixing. As they interact, Samsa notices that he is unable to understand some of the common words she uses. When she tells him that she needs to take the lock to her family of locksmiths for further work, he asks her why she rotates her arm so often. She says that her brassiere is uncomfortable on her; while telling him this she notices that he has a visible erection. Offended, she scorns him before he says that he has no idea what he is doing. Before she leaves, he asks her if she could return so that they could talk, as he is still confused about most of the world. She says perhaps they can do so when she returns the lock, before she walks back to her family through military-occupied Prague.


text: An unnamed narrator receives a phone call in the middle of the night telling him that his former lover, who he dubs M, has committed suicide, the caller being M's husband. He is unbearably anguished upon learning of this news.


text: The narrator tells of how he imagines himself meeting M when they were fourteen and in junior high school. He asks her for an eraser in class and she breaks hers in half and gives the piece to him; this meeting warms his heart. She then breaks his heart by running off with sailors who promise to show her the world. He chases her, but is never able to catch up.


text: In reality, he knew her for only about two years in his adult life and they only saw each other a few times a month. She loves elevator music, and always plays "A Summer Place" when they have sex. He notes that because of her death, he now considers himself the second-loneliest man in the world, after her husband. He is also in a state called "Men Without Women," a period of sudden and intense misery after a man learns of the death of a beloved woman.


text: Reception for the collection has been mostly positive. Lucy Scholes, writing for "The Independent", states that the stories "strung together [a]re a sparkling strand of precious stones, the light refracted from each equally brilliant but the tones varying subtly." Heller McAlpin, writing for "The Washington Post", states that "[Murakami's] meandering, mesmerizing tales of profound alienation are driven by puzzling circumstances that neither his characters nor readers can crack — recalling existentialist Gabriel Marcel’s assertion that 'Life is not a problem to be solved but a mystery to be experienced.'"


text: The short stories "Drive My Car" and, to a lesser degree, "Scheherazade", served as the basis for the 2021 film of the same name by Ryusuke Hamaguchi.


title: George Brett

text: George Howard Brett (born May 15, 1953) is an American former professional baseball player who played all of his 21 seasons in Major League Baseball (MLB) as a third baseman for the Kansas City Royals.


title: George Brett

text: Brett's 3,154 career hits are second-most by any third baseman in major league history (after only Adrian Beltre's 3,166) and rank 18th all-time. He is one of five players in MLB history to accumulate 3,000 hits, 300 home runs, and a career .300 batting average (the others being Hank Aaron, Willie Mays, Miguel Cabrera, and Stan Musial). He was inducted into the Baseball Hall of Fame in 1999 on the first ballot and is the only player in MLB history to win a batting title in three different decades. He was also a member of the Royals' 1985 World Series victory over the St. Louis Cardinals.


title: George Brett

text: Brett was named the Royals' interim hitting coach in 2013 on May 30, but stepped down from the position on July 25 in order to resume his position of vice president of baseball operations.


title: George Brett

text: Born in Glen Dale, West Virginia, Brett was the youngest of four sons of a sports-minded family which included Ken, the second oldest, a major league pitcher who pitched in the 1967 World Series at age 19. Brothers John (eldest) and Bobby had brief careers in the minor leagues. Although his three older brothers were born in Brooklyn, George was born in the northern panhandle of West Virginia.


title: George Brett

text: Jack and Ethel Brett then moved the family to the Midwest and three years later to El Segundo, California, a suburb of Los Angeles, just south of Los Angeles International Airport. George grew up hoping to follow in the footsteps of his three older brothers. He graduated from El Segundo High School in 1971 and was selected by the Kansas City Royals in the second round (29th overall) of the baseball draft. He was high school teammates with pitcher Scott McGregor. He lived in Mission Hills, Kansas when he moved to the Midwest.


title: George Brett

text: Brett began his professional baseball career as a shortstop, but had trouble going to his right defensively and was soon shifted to third base. As a third baseman, his powerful arm remained an asset, and he remained at that spot for more than 15 years. Brett's minor league stops were with the Billings Mustangs for the Rookie-level Pioneer League in 1971, the San Jose Bees of the Class A California League in 1972, and the Omaha Royals of the Class AAA American Association in 1973, batting .291, .274, and .284, respectively.


title: George Brett

text: The Royals promoted Brett to the major leagues on August 2, 1973, when he played in 13 games and was 5 for 40 (.125) at age 20.


title: George Brett

text: Brett won the starting third base job in 1974, but struggled at the plate until he asked for help from Charley Lau, the Royals' batting coach. Spending the All-Star break working together, Lau taught Brett how to protect the entire plate and cover up some holes in his swing that experienced big-league pitchers were exploiting. Armed with this knowledge, Brett developed rapidly as a hitter, and finished the year with a .282 batting average in 113 games.


title: George Brett

text: Brett topped the .300 mark for the first time in 1975, hitting .308 and leading the league in hits and triples. He then won his first batting title in 1976 with a .333 average. The four contenders for the batting title that year were Brett and Royals teammate Hal McRae, and Minnesota Twins teammates Rod Carew and Lyman Bostock. In dramatic fashion, Brett went 2 for 4 in the final game of the season against the Twins, beating out his three rivals, all playing in the same game. His lead over second-place McRae was less than .001. Brett won the title when a fly ball dropped in front of Twins left fielder Steve Brye, bounced on the Royals Stadium AstroTurf and over Brye's head to the wall; Brett circled the bases for an inside-the-park home run. McRae, batting just behind Brett in the line up, grounded out and Brett won his first batting title.


title: George Brett

text: From May 8 through May 13, 1976, Brett had three or more hits in six consecutive games, a major league record. A month later, he was on the cover of "Sports Illustrated" for a feature article, and made his first of 13 All-Star teams. The Royals won the first of three straight American League West Division titles, beginning a great rivalry with the New York Yankees—whom they faced in the American League Championship Series each of those three years. In the fifth and final game of the 1976 ALCS, Brett hit a three-run homer in the top of the eighth inning to tie the score at six—only to see the Yankees' Chris Chambliss launch a solo shot in the bottom of the ninth to give the Yankees a 7–6 win. Brett finished second in American League MVP voting to Thurman Munson.


title: George Brett

text: A year later, Brett emerged as a power hitter, clubbing 22 home runs, as the Royals headed to another ALCS. In Game 5 of the 1977 ALCS, following an RBI triple, Brett got into an altercation with Graig Nettles which ignited a bench-clearing brawl.


title: George Brett

text: In , Brett batted .294 (the only time between 1976 and in which he did not bat at least .300) in helping the Royals win a third consecutive AL West title. However, Kansas City once again lost to the Yankees in the ALCS, but not before Brett hit three home runs off Catfish Hunter in Game Three, becoming the second player to hit three home runs in an LCS game (Bob Robertson was the first, having done so in Game two of the 1971 NLCS).


title: George Brett

text: Brett followed with a successful 1979 season, in which he finished third in AL MVP voting. He became the sixth player in league history to have at least 20 doubles, triples and homers all in one season (42–20–23) and led the league in hits, doubles and triples while batting .329, with an on-base percentage of .376 and a slugging percentage of .563.


title: George Brett

text: All these impressive statistics were just a prelude to , when Brett won the American League MVP and batted .390, a modern record for a third baseman. Brett's batting average was at or above .400 as late in the season as September 19, and the country closely followed his quest to bat .400 for an entire season, a feat which has not been accomplished since Ted Williams in .


title: George Brett

text: Brett's 1980 batting average of .390 is second only to Tony Gwynn's average of .394 (Gwynn played in 110 games and had 419 at-bats in the strike-shortened season, compared to Brett's 449 at bats in 1980) for the highest single season batting average since 1941. Brett also recorded 118 runs batted in, while appearing in just 117 games; it was the first instance of a player averaging one RBI per game (in more than 100 games) since Walt Dropo thirty seasons prior. He led the American League in both slugging and on-base percentage.


title: George Brett

text: Brett started out slowly, hitting only .259 in April. In May, he hit .329 to get his season average to .301. In June, the 27-year-old third baseman hit .472 (17–36) to raise his season average to .337, but played his last game for a month on June 10, not returning to the lineup until after the All-Star Break on July 10.


title: George Brett

text: In July, after being off for a month, he played in 21 games and hit .494 (42–85), raising his season average to .390. Brett started a 30-game hitting streak on July 18, which lasted until he went 0–3 on August 19 (the following night he went 3-for-3). During those 30 games, Brett hit .467 (57–122). His high mark for the season came a week later, when Brett's batting average was at .407 on August 26, after he went 5-for-5 on a Tuesday night in Milwaukee. He batted .430 for the month of August (30 games), and his season average was at .403 with five weeks to go. For the three hot months of June, July, and August 1980, George Brett played in 60 American League games and hit .459 (111–242), most of it after a return from a monthlong injury. For these 60 games he had 69 RBIs and 14 home runs.


title: George Brett

text: Brett missed another 10 days in early September and hit just .290 for the month. His average was at .400 as late as September 19, but he then had a 4 for 27 slump, and the average dipped to .384 on September 27, with a week to play. For the final week, Brett went 10-for-19, which included going 2 for 4 in the final regular season game on October 4. His season average ended up at .390 (175 hits in 449 at-bats = .389755), and he averaged more than one RBI per game. Brett led the league in both on-base percentage (.454) and slugging percentage (.664) on his way to capturing 17 of 28 possible first-place votes in the MVP race. Since Al Simmons also batted .390 in 1931 for the Philadelphia Athletics, the only higher averages subsequent to 1931 were by Ted Williams of the Red Sox (.406 in 1941) and Tony Gwynn of the San Diego Padres (.394 in the strike-shortened 1994 season).


title: George Brett

text: More importantly, the Royals won the American League West, and would face the Eastern champion Yankees in the ALCS.


title: George Brett

text: During the 1980 post-season, Brett led the Royals to their first American League pennant, sweeping the playoffs in three games from the rival Yankees who had beaten K.C. in the 1976, 1977 and 1978 playoffs. During Game 2 of the 1980 ALCS, Willie Randolph was on first base in the top of the eighth with two outs and the Royals up by just one run. Bob Watson hit a ball to the left field corner of Royals Stadium. The ball bounced right to Willie Wilson, but Wilson was not known for having a great arm, and third base coach Mike Ferraro waved Randolph home. Wilson overthrew U L Washington, the cut-off man, but Brett was in position behind him to catch the ball, then throw to Darrell Porter, who tagged out Randolph in a slide. TV cameras captured a furious George Steinbrenner fuming immediately after the play. The Royals won 3–2. Brett claimed after the game that he had deliberately positioned himself to cut off the throw in case Washington missed it, but Tommy John of the Yankees disagreed, thinking that if Brett had been backing up Washington, he would have been between shortstop and home plate, not over behind third base. Either way, he was in the perfect position to throw out Randolph. In Game 3, Brett hit a ball well into the third deck of Yankee Stadium off Yankees closer Goose Gossage. Gossage's previous pitch had been timed at 97 mph, leading ABC broadcaster Jim Palmer to say, "I doubt if he threw that ball 97 miles an hour." A moment later Palmer was given the actual reading of 98. "Well, I said it wasn't 97", Palmer replied. Brett then hit .375 in the 1980 World Series, but the Royals lost in six games to the Philadelphia Phillies. During the Series, Brett made headlines after leaving Game 2 in the 6th inning due to hemorrhoid pain. Brett had minor surgery the next day, and in Game 3 returned to hit a home run as the Royals won in 10 innings 4–3. After the game, Brett was famously quoted "...my problems are all behind me". In 1981 he missed two weeks of spring training to have his hemorrhoids removed.


title: George Brett

text: On July 24, 1983, with the Royals playing against the Yankees at Yankee Stadium, in the top of the ninth inning with two out, Brett hit a go-ahead two-run homer off of Goose Gossage to put the Royals up 5–4. After the home run, Yankees manager Billy Martin cited to the umpires a rule, stating that any foreign substance on a bat could extend no further than 18 inches from the knob. The umpires measured the amount of pine tar, a legal substance used by hitters to improve their grip, on Brett's bat; the pine tar extended about 24 inches. The home plate umpire, Tim McClelland, signaled Brett out, ending the game as a Yankees win. Enraged, Brett charged out of the dugout directly toward McClelland, and had to be physically restrained by two umpires and Royals manager Dick Howser.


title: George Brett

text: The Royals protested the game, which was upheld by American League president Lee MacPhail, who ruled that the bat should have been excluded from future use, but the home run should not have been nullified. Amid much controversy, the game was resumed on August 18, 1983, from the point of Brett's home run, and ended with a Royals win.


title: George Brett

text: In 1985, Brett had another brilliant season in which he helped propel the Royals to their second American League Championship. He batted .335 with 30 home runs and 112 RBI, finishing in the top 10 of the league in 10 different offensive categories. Defensively, he won his only Gold Glove, which broke Buddy Bell's six-year run of the award, and finished second in American League MVP voting to Don Mattingly. In the final week of the regular season, he went 9-for-20 at the plate with 7 runs, 5 homers, and 9 RBI in six crucial games, five of them victories, as the Royals closed the gap and won the division title at the end. He was MVP of the 1985 playoffs against the Toronto Blue Jays, with an incredible Game 3. With KC down in the series two games to none, Brett went 4-for-4, homering in his first two at bats against Doyle Alexander, and doubled to the same spot in right field in his third at bat, leading the Royals' comeback. Brett then batted .370 in the World Series against the St. Louis Cardinals, including a four-hit performance in Game 7. The Royals again rallied from a 3–1 deficit to become World Series champions for the first time in their history.


title: George Brett

text: In 1988, Brett moved across the diamond to first base in an effort to reduce his chances of injury and had another top-notch season with a .306 average, 24 homers and 103 RBI. But after batting just .282 with 12 homers the next year, it looked like his career might be slowing down. He got off to a terrible start in 1990 and at one point even considered retirement. But his manager, former teammate John Wathan, encouraged him to stick it out. Finally, in July, the slump ended and Brett batted .386 for the rest of the season. In September, he caught Rickey Henderson for the league lead, and in a battle down to the last day of the season, captured his third batting title with a .329 mark. This feat made Brett the only major league player to win batting titles in three different decades.


title: George Brett

text: Brett played three more seasons for the Royals, mostly as their designated hitter, but occasionally filling in for injured teammates at first base. He passed the 3,000-hit mark in 1992, though he was picked off by Angels first baseman Gary Gaetti after stepping off the base to start enjoying the moment. Brett retired after the 1993 season; in his final at-bat, he hit a single up the middle against Rangers closer Tom Henke and scored on a home run by now teammate Gaetti. His last game was also notable as being the final game ever played at Arlington Stadium.


title: George Brett

text: Brett was elected to the Hall of Fame in 1999, with what was then the fourth-highest voting percentage in baseball history (98.2%), trailing only Tom Seaver, Nolan Ryan, and Ty Cobb. In 2007, Cal Ripken Jr. passed Brett with 98.5% of the vote. His voting percentage was higher than all-time outfielders Babe Ruth, Hank Aaron, Willie Mays, Stan Musial, Ted Williams, and Joe DiMaggio.


title: George Brett

text: Brett's No. 5 was retired by the Royals on May 14, 1994. His number was the second number retired in Royals history, preceded by former Royals manager, Dick Howser (No. 10), in 1987. It was followed by second baseman and longtime teammate Frank White's No. 20 in 1995.


title: George Brett

text: He was voted the Hometown Hero for the Royals in a two-month fan vote. This was revealed on the night of September 27, 2006 in an hour-long telecast on ESPN. He was one of the few players to receive more than 400,000 votes.


title: George Brett

text: His 3,154 career hits are the second most by any third baseman in major league history (A. Beltre, 3166), and 18th all-time. Baseball historian Bill James regards him as the second-best third baseman of all time, trailing only his contemporary, Mike Schmidt. In 1999 he ranked Number 55 on "The Sporting News"' list of the 100 Greatest Baseball Players, and was nominated as a finalist for the Major League Baseball All-Century Team. Brett is one of five players in MLB history to accumulate 3,000 hits, 300 home runs, and a career .300 batting average (the others are Stan Musial, Willie Mays, Miguel Cabrera, and Hank Aaron). Most indicative of his hitting style, Brett is sixth on the career doubles list, with 665 (trailing Tris Speaker, Pete Rose, Stan Musial, Ty Cobb, and Craig Biggio).


title: George Brett

text: A photo in the July 1976 edition of "National Geographic" showing Brett signing baseballs for fans with his team's name emblazoned across his shirt was the inspiration for New Zealand singer-songwriter Lorde's 2013 song "Royals," which won the 2014 Grammy Award for Song of the Year.


title: George Brett

text: Brett is credited with popularizing the phrase the Mendoza Line, which is used to represent a sub-.200 batting average, and is regarded as unacceptable at the Major League level. It derives from shortstop Mario Mendoza, a career .215 hitter who finished below .200 five times in his nine seasons in the big leagues — including .198 the year the term is claimed to have been coined by a pair of his teammates.


title: George Brett

text: Brett referred to the Mendoza Line in an interview, which was picked up by ESPN baseball anchor Chris Berman and then expanded into the world of "SportsCenter".


title: George Brett

text: Following his playing career, Brett became a vice president of the Royals and has worked as a part-time coach, as a special instructor in spring training, as an interim batting coach, and as a minor league instructor dispatched to help prospects develop. He also runs a baseball equipment and glove company named Brett Bros. with Bobby and, until his death, Ken Brett. He has also lent his name to a restaurant that failed on the Country Club Plaza.


title: George Brett

text: In 1992, Brett married the former Leslie Davenport, and they reside in the Kansas City suburb of Mission Hills, Kansas. The couple has three children: Jackson (named after George's father), Dylan (named after Bob Dylan), and Robin (named after fellow Hall of Famer Robin Yount of the Milwaukee Brewers).


title: George Brett

text: Brett has continued to raise money for amyotrophic lateral sclerosis (ALS), commonly known as Lou Gehrig's disease. Brett started to raise money for the Keith Worthington Chapter during his playing career in the mid-1980s.


title: George Brett

text: He and his dog Charlie appeared in a PETA ad campaign, encouraging people not to leave their canine companions in the car during hot weather. He also threw out the ceremonial first pitch to Mike Napoli at the 2012 Major League Baseball All-Star Game.


title: George Brett

text: On May 30, 2013, the Royals announced that Brett and Pedro Grifol would serve as batting coaches for the organization. On July 25, 2013 (the day following the 30th anniversary of the pine tar incident, the Royals announced that Brett would serve as vice president of baseball operations.


title: George Brett

text: In 2015, Brett was the National Baseball Hall of Fame recipient of the Bob Feller Act of Valor Award for his support of current and former service members of the United States Military.


title: George Brett

text: Brett appeared as himself in the ABC sitcom "Modern Family" on March 28, 2018, alongside main cast member Eric Stonestreet, a Kansas City native and Royals fan, whose character on the show is also an avid fan.


title: George Brett

text: Brett appeared as himself in the "Brockmire" episode "Player to Be Named Later", in which he is dating Jules (Amanda Peet), much to Brockmire's despair; in the episode "Low and Away", Jules informs Brockmire that she and her now-husband Brett are getting a divorce. Series creator Joel Church-Cooper said in a statement, "When I created a show about a fake Kansas City legend, Jim Brockmire, I thought it only appropriate to have him worship the biggest Kansas City legend of them all — George Brett."


title: George Brett

text: In 1998, an investor group headed by Brett and his older brother, Bobby, made an unsuccessful bid to purchase the Kansas City Royals. Brett is the principal owner of the Tri-City Dust Devils, the Single-A affiliate of the Los Angeles Angels. He and his brother Bobby also co-own the Rancho Cucamonga Quakes, a Los Angeles Dodgers Single-A partner, and lead ownership groups that control the Spokane Chiefs of the Western Hockey League, the West Coast League's Bellingham Bells, and the High Desert Mavericks of the California League.


title: Endocrine gland

text: Endocrine glands are ductless glands of the endocrine system that secrete their products, hormones, directly into the blood. The major glands of the endocrine system include the pineal gland, pituitary gland, pancreas, ovaries, testes, thyroid gland, parathyroid gland, hypothalamus and adrenal glands. The hypothalamus and pituitary glands are neuroendocrine organs.


title: Endocrine gland

text: The pituitary gland hangs from the base of the brain by the pituitary stalk, and is enclosed by bone. It consists of a hormone-producing glandular portion of the anterior pituitary and a neural portion of the posterior pituitary, which is an extension of the hypothalamus. The hypothalamus regulates the hormonal output of the anterior pituitary and creates two hormones that it exports to the posterior pituitary for storage and later release.


title: Endocrine gland

text: Four of the six anterior pituitary hormones are tropic hormones that regulate the function of other endocrine organs. Most anterior pituitary hormones exhibit a diurnal rhythm of release, which is subject to modification by stimuli influencing the hypothalamus.


title: Endocrine gland

text: Somatotropic hormone or growth hormone (GH) is an anabolic hormone that stimulates the growth of all body tissues especially skeletal muscle and bone. It may act directly, or indirectly via insulin-like growth factors (IGFs). GH mobilizes fats, stimulates protein synthesis, and inhibits glucose uptake and metabolism. Secretion is regulated by growth hormone-releasing hormone (GHRH) and growth hormone-inhibiting hormone (GHIH), or somatostatin. Hypersecretion causes gigantism in children and acromegaly in adults; hyposecretion in children causes pituitary dwarfism.


title: Endocrine gland

text: Thyroid-stimulating hormone promotes normal development and activity of the thyroid gland. Thyrotropin-releasing hormone stimulates its release; negative feedback of thyroid hormone inhibits it.


title: Endocrine gland

text: Adrenocorticotropic hormone stimulates the adrenal cortex to release corticosteroids. Adrenocorticotropic hormone release is triggered by corticotropin-releasing hormone and inhibited by rising glucocorticoid levels.


title: Endocrine gland

text: The gonadotropins—follicle-stimulating hormone and luteinizing hormone regulate the functions of the gonads in both sexes. Follicle-stimulating hormone stimulates sex cell production; luteinizing hormone stimulates gonadal hormone production. Gonadotropin levels rise in response to gonadotropin-releasing hormone. Negative feedback of gonadal hormones inhibits gonadotropin release.


title: Endocrine gland

text: Prolactin promotes milk production in human females. Its secretion is prompted by prolactin-releasing hormone and inhibited by prolactin-inhibiting hormone.


title: Endocrine gland

text: The intermediate lobe of the pituitary gland secretes only one enzyme that is melanocyte stimulating hormone. It is linked with the formation of the black pigment in our skin called melanin.


title: Endocrine gland

text: The thyroid gland is located in the front of the neck, in front of the thyroid cartilage, and is shaped like a butterfly, with two wings connected by a central . Thyroid tissue consists of follicles with a stored protein called colloid, containing[thyroglobulin], a precursor to other thyroid hormones, which are manufactured within the colloid.


title: Endocrine gland

text: The thyroid hormones increase the rate of cellular metabolism, and include thyroxine (T4) and triiodothyronine (T3). Secretion is stimulated by the thyroid-stimulating hormone, secreted by the anterior pituitary. When thyroid levels are high, there is negative feedback that decreases the amount of Thyroid-stimulating hormone secreted. Most T4 is converted to T3 (a more active form) in the target tissues.


title: Endocrine gland

text: Calcitonin, produced by the parafollicular cells (C cells) of the thyroid gland in response to rising blood calcium levels, depresses blood calcium levels by inhibiting bone matrix resorption and enhancing calcium deposit in bones.


title: Endocrine gland

text: The parathyroid glands, of which there are 4–6, are found on the back of the thyroid glands, and secrete parathyroid hormone, This causes an increase in blood calcium levels by targeting bone, the intestine, and the kidneys. The parathyroid hormone is the antagonist of calcitonin. Parathyroid hormone release is triggered by falling blood calcium levels and is inhibited by rising blood calcium levels.


title: Endocrine gland

text: in front of the kidneys in other animals. The adrenal glands produce a variety of hormones including adrenaline and the steroids aldosterone cortisol and Dehydroepiandrosterone sulfate (DHEA). Adrenaline increases blood pressure, heart rate, and metabolism in reaction to stress, the aldosterone controls the body’s salt and water balance , the cortisol plays a role in stress response and the dehydroepiandrosterone sulfate (DHEA) produces aids in production of body odor and growth of body hair during puberty.


title: Endocrine gland

text: The pancreas, located in the abdomen, below and behind the stomach, is both an exocrine and an endocrine gland. The alpha and beta cells are the endocrine cells in the pancreatic islets that release insulin and glucagon and smaller amounts of other hormones into the blood. Insulin and glucagon influence blood sugar levels. Glucagon is released when the blood glucose level is low and stimulates the liver to release glucose into the blood. Insulin increases the rate of glucose uptake and metabolism by most body cells.


title: Endocrine gland

text: The ovaries of the female, located in the pelvic cavity, release two main hormones. Secretion of estrogens by the ovarian follicles begins at puberty under the influence of follicle-stimulating hormone. Estrogens stimulate the maturation of the female reproductive system and the development of secondary sexual characteristics. Progesterone is released in response to high blood levels of luteinizing hormone. It works with estrogens in establishing the menstrual cycle.


title: Endocrine gland

text: The testes of the male begin to produce testosterone at puberty in response to luteinizing hormone. Testosterone promotes maturation of the male reproductive organs, development of secondary sex characteristics such as increased muscle and bone mass, and the growth of body hair.


title: Endocrine gland

text: The pineal gland is located in the diencephalon of the brain. It primarily releases melatonin, which influences daily rhythms and may have an antigonadotropic effect in humans. It may also influence the melanotropes and melanocytes located in the skin.


title: Endocrine gland

text: Many body organs not normally considered endocrine organs contain isolated cell clusters that secrete hormones. Examples include the heart (atrial natriuretic peptide); gastrointestinal tract organs (gastrin, secretin, and others); the placenta (hormones of pregnancy—estrogen, progesterone, and others); the kidneys (erythropoietin and renin); the thymus; skin (cholecalciferol); and adipose tissue (leptin and resistin).


title: Endocrine gland

text: The natural decrease in function of the female's ovaries during late middle age results in menopause. The efficiency of all endocrine glands seems to decrease gradually as ageing occurs. This leads to a generalized increase in the incidence of diabetes mellitus and a lower metabolic rate.


title: Endocrine gland

text: Local chemical messengers, not generally considered part of the endocrine system, include autocrines, which act on the cells that secrete them, and paracrines, which act on a different cell type nearby.


title: Endocrine gland

text: The ability of a target cell to respond to a hormone depends on the presence of receptors, within the cell or on its plasma membrane, to which the hormone can bind.


title: Endocrine gland

text: Hormone receptors are dynamic structures. Changes in the number and sensitivity of hormone receptors may occur in response to high or low levels of stimulating hormones.


title: Endocrine gland

text: Blood levels of hormones reflect a balance between secretion and degradation/excretion. The liver and kidneys are the major organs that degrade hormones; breakdown products are excreted in urine and faeces.


title: Endocrine gland

text: "Permissiveness" is the situation in which a hormone cannot exert its full effects without the presence of another hormone.


title: Endocrine gland

text: "Synergism" occurs when two or more hormones produce the same effects in a target cell and their results are amplified.


title: Endocrine gland

text: The endocrine glands belong to the body's control system. The hormones which they produce help to regulate the functions of cells and tissues throughout the body. Endocrine organs are activated to release their hormones by humoral, neural, or hormonal stimuli. Negative feedback is important in regulating hormone levels in the blood.


title: Endocrine gland

text: The nervous system, acting through hypothalamic controls, can in certain cases override or modulate hormonal effects.


title: Endocrine gland

text: Diseases of the endocrine glands are common, including conditions such as diabetes mellitus, thyroid disease, and obesity.


title: Endocrine gland

text: Endocrine disease is characterized by irregulated hormone release (a productive pituitary adenoma), inappropriate response to signalling (hypothyroidism), lack of a gland (diabetes mellitus type 1, diminished erythropoiesis in chronic kidney failure), or structural enlargement in a critical site such as the thyroid (toxic multinodular goitre). Hypofunction of endocrine glands can occur as a result of the loss of reserve, hyposecretion, agenesis, atrophy, or active destruction. Hyperfunction can occur as a result of hypersecretion, loss of suppression, hyperplastic, or neoplastic change, or hyperstimulation.


title: Endocrine gland

text: Endocrinopathies are classified as primary, secondary, or tertiary. Primary endocrine disease inhibits the action of downstream glands. Secondary endocrine disease is indicative of a problem with the pituitary gland. Tertiary endocrine disease is associated with dysfunction of the hypothalamus and its releasing hormones.


title: Endocrine gland

text: As the thyroid, and hormones have been implicated in signaling distant tissues to proliferate, for example, the estrogen receptor has been shown to be involved in certain breast cancers. Endocrine, paracrine, and autocrine signaling have all been implicated in proliferation, one of the required steps of oncogenesis.


title: Endocrine gland

text: Other common diseases that result from endocrine dysfunction include Addison's disease, Cushing's disease and Grave's disease. Cushing's disease and Addison's disease are pathologies involving the dysfunction of the adrenal gland. Dysfunction in the adrenal gland could be due to primary or secondary factors and can result in hypercortisolism or hypocortisolism. Cushing's disease is characterized by the hypersecretion of the adrenocorticotropic hormone due to a pituitary adenoma that ultimately causes endogenous hypercortisolism by stimulating the adrenal glands. Some clinical signs of Cushing's disease include obesity, moon face, and hirsutism. Addison's disease is an endocrine disease that results from hypocortisolism caused by adrenal gland insufficiency. Adrenal insufficiency is significant because it is correlated with decreased ability to maintain blood pressure and blood sugar, a defect that can prove to be fatal.


title: Endocrine gland

text: Graves' disease involves the hyperactivity of the thyroid gland which produces the T3 and T4 hormones. Graves' disease effects range from excess sweating, fatigue, heat intolerance and high blood pressure to swelling of the eyes that causes redness, puffiness and in rare cases reduced or double vision.


title: Endocrine gland

text: Graves' disease is the most common cause of hyperthyroidism; hyposecretion causes cretinism in infants and myxoedema in adults.


title: Endocrine gland

text: Hyperparathyroidism results in hypercalcemia and its effects and in extreme bone wasting. Hypoparathyroidism leads to hypocalcemia, evidenced by tetany seizure and respiratory paralysis.


title: Endocrine gland

text: Hyposecretion of insulin results in diabetes mellitus; cardinal signs are polyuria, polydipsia, and polyphagia.


title: Squaring the circle

text: Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of lines and circles implied the existence of such a square.


title: Squaring the circle

text: In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi (formula_1) is a transcendental number.


title: Squaring the circle

text: That is, formula_1 is not the root of any polynomial with rational coefficients. It had been known for decades that the construction would be impossible if formula_1 were transcendental, but that fact was not proven until 1882. Approximate constructions with any given non-perfect accuracy exist, and many such constructions have been found.


title: Squaring the circle

text: Despite the proof that it is impossible, attempts to square the circle have been common in pseudomathematics (i.e. the work of mathematical cranks). The expression "squaring the circle" is sometimes used as a metaphor for trying to do the impossible. The term "quadrature of the circle" is sometimes used as a synonym for squaring the circle, but it may also refer to approximate or numerical methods for finding the area of a circle.


title: Squaring the circle

text: Methods to calculate the approximate area of a given circle, which can be thought of as a precursor problem to squaring the circle, were known already in many ancient cultures. These methods can be summarized by stating the approximation to that they produce. In around 2000 BCE, the Babylonian mathematicians used the approximation and at approximately the same time the ancient Egyptian mathematicians used Over 1000 years later, the Old Testament "Books of Kings" used the simpler approximation Ancient Indian mathematics, as recorded in the "Shatapatha Brahmana" and "Shulba Sutras", used several different approximations Archimedes proved a formula for the area of a circle, according to which formula_4. In Chinese mathematics, in the third century CE, Liu Hui found even more accurate approximations using a method similar to that of Archimedes, and in the fifth century Zu Chongzhi found formula_5, an approximation known as Milü.


title: Squaring the circle

text: The problem of constructing a square whose area is exactly that of a circle, rather than an approximation to it, comes from Greek mathematics. Greek mathematicians found compass and straightedge constructions to convert any polygon into a square of equivalent area. They used this construction to compare areas of polygons geometrically, rather than by the numerical computation of area that would be more typical in modern mathematics. As Proclus wrote many centuries later, this motivated the search for methods that would allow comparisons with non-polygonal shapes:


title: Squaring the circle

text: The first known Greek to study the problem was Anaxagoras, who worked on it while in prison. Hippocrates of Chios attacked the problem by finding a shape bounded by circular arcs, the lune of Hippocrates, that could be squared. Antiphon the Sophist believed that inscribing regular polygons within a circle and doubling the number of sides would eventually fill up the area of the circle (this is the method of exhaustion). Since any polygon can be squared, he argued, the circle can be squared. In contrast, Eudemus argued that magnitudes cannot be divided up without limit, so the area of the circle would never be used up. Contemporaneously with Antiphon, Bryson of Heraclea argued that, since larger and smaller circles both exist, there must be a circle of equal area; this principle can be seen as a form of the modern intermediate value theorem. The more general goal of carrying out all geometric constructions using only a compass and straightedge has often been attributed to Oenopides, but the evidence for this is circumstantial.


title: Squaring the circle

text: The problem of finding the area under an arbitrary curve, now known as integration in calculus, or quadrature in numerical analysis, was known as "squaring" before the invention of calculus. Since the techniques of calculus were unknown, it was generally presumed that a squaring should be done via geometric constructions, that is, by compass and straightedge. For example, Newton wrote to Oldenburg in 1676 "I believe M. Leibnitz will not dislike the theorem towards the beginning of my letter pag. 4 for squaring curve lines geometrically". In modern mathematics the terms have diverged in meaning, with quadrature generally used when methods from calculus are allowed, while squaring the curve retains the idea of using only restricted geometric methods.


title: Squaring the circle

text: James Gregory attempted a proof of the impossibility of squaring the circle in "Vera Circuli et Hyperbolae Quadratura" (The True Squaring of the Circle and of the Hyperbola) in 1667. Although his proof was faulty, it was the first paper to attempt to solve the problem using algebraic properties of formula_1. Johann Heinrich Lambert proved in 1761 that formula_1 is an irrational number. It was not until 1882 that Ferdinand von Lindemann succeeded in proving more strongly that is a transcendental number, and by doing so also proved the impossibility of squaring the circle with compass and straightedge.


title: Squaring the circle

text: After Lindemann's impossibility proof, the problem was considered to be settled by professional mathematicians, and its subsequent mathematical history is dominated by pseudomathematical attempts at circle-squaring constructions, largely by amateurs, and by the debunking of these efforts. As well, several later mathematicians including Srinivasa Ramanujan developed compass and straightedge constructions that approximate the problem accurately in few steps.


title: Squaring the circle

text: Two other classical problems of antiquity, famed for their impossibility, were doubling the cube and trisecting the angle. Like squaring the circle, these cannot be solved by compass and straightedge. However, they have a different character than squaring the circle, in that their solution involves the root of a cubic equation, rather than being transcendental. Therefore, more powerful methods than compass and straightedge constructions, such as neusis construction or mathematical paper folding, can be used to construct solutions to these problems.


title: Squaring the circle

text: The solution of the problem of squaring the circle by compass and straightedge requires the construction of the number formula_8, the length of the side of a square whose area equals that of a unit circle. If formula_8 were a constructible number, it would follow from standard compass and straightedge constructions that formula_1 would also be constructible. In 1837, Pierre Wantzel showed that lengths that could be constructed with compass and straightedge had to be solutions of certain polynomial equations with rational coefficients. Thus, constructible lengths must be algebraic numbers. If the circle could be squared using only compass and straightedge, then formula_1 would have to be an algebraic number. It was not until 1882 that Ferdinand von Lindemann proved the transcendence of formula_1 and so showed the impossibility of this construction. Lindemann's idea was to combine the proof of transcendence of Euler's number formula_13, shown by Charles Hermite in 1873, with Euler's identity


title: Squaring the circle

text: This identity immediately shows that formula_1 is an irrational number, because a rational power of a transcendental number remains transcendental. Lindemann was able to extend this argument, through the Lindemann–Weierstrass theorem on linear independence of algebraic powers of formula_13, to show that formula_1 is transcendental and therefore that squaring the circle is impossible.


title: Squaring the circle

text: Bending the rules by introducing a supplemental tool, allowing an infinite number of compass-and-straightedge operations or by performing the operations in certain non-Euclidean geometries makes squaring the circle possible in some sense. For example, Dinostratus' theorem uses the quadratrix of Hippias to square the circle, meaning that if this curve is somehow already given, then a square and circle of equal areas can be constructed from it. The Archimedean spiral can be used for another similar construction. Although the circle cannot be squared in Euclidean space, it sometimes can be in hyperbolic geometry under suitable interpretations of the terms. The hyperbolic plane does not contain squares (quadrilaterals with four right angles and four equal sides), but instead it contains "regular quadrilaterals", shapes with four equal sides and four equal angles sharper than right angles. There exist in the hyperbolic plane (countably) infinitely many pairs of constructible circles and constructible regular quadrilaterals of equal area, which, however, are constructed simultaneously. There is no method for starting with an arbitrary regular quadrilateral and constructing the circle of equal area. Symmetrically, there is no method for starting with an arbitrary circle and constructing a regular quadrilateral of equal area, and for sufficiently large circles no such quadrilateral exists.


title: Squaring the circle

text: Although squaring the circle exactly with compass and straightedge is impossible, approximations to squaring the circle can be given by constructing lengths close to formula_1.


title: Squaring the circle

text: It takes only elementary geometry to convert any given rational approximation of formula_1 into a corresponding compass and straightedge construction, but such constructions tend to be very long-winded in comparison to the accuracy they achieve. After the exact problem was proven unsolvable, some mathematicians applied their ingenuity to finding approximations to squaring the circle that are particularly simple among other imaginable constructions that give similar precision.


title: Squaring the circle

text: One of many early historical approximate compass-and-straightedge constructions is from a 1685 paper by Polish Jesuit Adam Adamandy Kochański, producing an approximation diverging from formula_1 in the 5th decimal place. Although much more precise numerical approximations to formula_1 were already known, Kochański's construction has the advantage of being quite simple. In the left diagram


title: Squaring the circle

text: This value is accurate to six decimal places and has been known in China since the 5th century as Zu Chongzhi's fraction, and in Europe since the 17th century.


title: Squaring the circle

text: In 1914, Indian mathematician Srinivasa Ramanujan gave another geometric construction for the same approximation.


title: Squaring the circle

text: An approximate construction by E. W. Hobson in 1913 is accurate to three decimal places. Hobson's construction corresponds to an approximate value of


title: Squaring the circle

text: The same approximate value appears in a 1991 construction by Robert Dixon. In 2022 Frédéric Beatrix presented a geometrographic construction in 13 steps.


title: Squaring the circle

text: In 1914, Ramanujan gave a construction which was equivalent to taking the approximate value for formula_1 to be


title: Squaring the circle

text: In his old age, the English philosopher Thomas Hobbes convinced himself that he had succeeded in squaring the circle, a claim refuted by John Wallis as part of the Hobbes–Wallis controversy. During the 18th and 19th century, the false notions that the problem of squaring the circle was somehow related to the longitude problem, and that a large reward would be given for a solution, became prevalent among would-be circle squarers. In 1851, John Parker published a book "Quadrature of the Circle" in which he claimed to have squared the circle. His method actually produced an approximation of formula_1 accurate to six digits.


title: Squaring the circle

text: The Victorian-age mathematician, logician, and writer Charles Lutwidge Dodgson, better known by his pseudonym Lewis Carroll, also expressed interest in debunking illogical circle-squaring theories. In one of his diary entries for 1855, Dodgson listed books he hoped to write, including one called "Plain Facts for Circle-Squarers". In the introduction to "A New Theory of Parallels", Dodgson recounted an attempt to demonstrate logical errors to a couple of circle-squarers, stating:


title: Squaring the circle

text: A ridiculing of circle squaring appears in Augustus De Morgan's book "A Budget of Paradoxes", published posthumously by his widow in 1872. Having originally published the work as a series of articles in "The Athenæum", he was revising it for publication at the time of his death. Circle squaring declined in popularity after the nineteenth century, and it is believed that De Morgan's work helped bring this about.


title: Squaring the circle

text: Even after it had been proved impossible, in 1894, amateur mathematician Edwin J. Goodwin claimed that he had developed a method to square the circle. The technique he developed did not accurately square the circle, and provided an incorrect area of the circle which essentially redefined formula_1 as equal to 3.2. Goodwin then proposed the Indiana Pi Bill in the Indiana state legislature allowing the state to use his method in education without paying royalties to him. The bill passed with no objections in the state house, but the bill was tabled and never voted on in the Senate, amid increasing ridicule from the press.


title: Squaring the circle

text: The mathematical crank Carl Theodore Heisel also claimed to have squared the circle in his 1934 book, "Behold! : the grand problem no longer unsolved: the circle squared beyond refutation." Paul Halmos referred to the book as a "classic crank book."


title: Squaring the circle

text: The problem of squaring the circle has been mentioned over a wide range of literary eras, with a variety of metaphorical meanings. Its literary use dates back at least to 414 BC, when the play "The Birds" by Aristophanes was first performed. In it, the character Meton of Athens mentions squaring the circle, possibly to indicate the paradoxical nature of his utopian city.


title: Squaring the circle

text: For Dante, squaring the circle represents a task beyond human comprehension, which he compares to his own inability to comprehend Paradise. Dante's image also calls to mind a passage from Vitruvius, famously illustrated later in Leonardo da Vinci's "Vitruvian Man", of a man simultaneously inscribed in a circle and a square. Dante uses the circle as a symbol for God, and may have mentioned this combination of shapes in reference to the simultaneous divine and human nature of Jesus. Earlier, in canto XIII, Dante calls out Greek circle-squarer Bryson as having sought knowledge instead of wisdom.


title: Squaring the circle

text: Several works of 17th-century poet Margaret Cavendish elaborate on the circle-squaring problem and its metaphorical meanings, including a contrast between unity of truth and factionalism, and the impossibility of rationalizing "fancy and female nature". By 1742, when Alexander Pope published the fourth book of his "Dunciad", attempts at circle-squaring had come to be seen as "wild and fruitless":


title: Squaring the circle

text: Similarly, the Gilbert and Sullivan comic opera "Princess Ida" features a song which satirically lists the impossible goals of the women's university run by the title character, such as finding perpetual motion. One of these goals is "And the circle – they will square it/Some fine day."


title: Squaring the circle

text: The sestina, a poetic form first used in the 12th century by Arnaut Daniel, has been said to metaphorically square the circle in its use of a square number of lines (six stanzas of six lines each) with a circular scheme of six repeated words. writes that this form invokes a symbolic meaning in which the circle stands for heaven and the square stands for the earth. A similar metaphor was used in "Squaring the Circle", a 1908 short story by O. Henry, about a long-running family feud. In the title of this story, the circle represents the natural world, while the square represents the city, the world of man.


title: Squaring the circle

text: In later works, circle-squarers such as Leopold Bloom in James Joyce's novel "Ulysses" and Lawyer Paravant in Thomas Mann's "The Magic Mountain" are seen as sadly deluded or as unworldly dreamers, unaware of its mathematical impossibility and making grandiose plans for a result they will never attain.


title: Stefanie Scott

text: Stefanie Noelle Scott (born December 6, 1996) is an American actress and singer. Scott began acting with the comedy film "Beethoven's Big Break" (2008), and thereafter released her debut extended play "New Girl in Town" (2009). This was followed by a supporting role in the romance film "Flipped" (2010), which won her a Young Artist Award. She played the role of Lexi Reed on Disney Channel's "A.N.T. Farm" (2011–2014), which won her a second Young Artist Award and introduced her to a wider audience. While on Disney, she recorded a number of Disney Channel promotional singles, which were released between 2008 and 2012.


title: Stefanie Scott

text: Scott made her foray into mainstream film and television with a voice role in the animated film "Wreck-It Ralph" (2012), for which she won a BTVA Award. She then played the leading role of Quinn Brenner in the horror film "" (2015)—her highest-grossing film—and co-starred in the musical film "Jem and the Holograms" (2015), for which she additionally contributed to its soundtrack. Her subsequent film roles have consisted of independent features, such as the neo-noir "Small Town Crime" (2017), the biopic "Beautiful Boy" (2018), the high-school drama "Good Girls Get High" (2018) and the thriller "Mary" (2019). She currently leads the Peacock original series "The Girl in the Woods" (2021–present).


title: Stefanie Scott

text: Scott was born in Chicago, Illinois and has two older brothers. She lived in Indialantic, Florida and attended Holy Trinity Episcopal Academy, before becoming home schooled in 2010.


title: Stefanie Scott

text: Scott was first a California Discovery Girl in the 2009 August/September issue of "Discovery Girls" magazine. She appeared in the role of Katie in "Beethoven's Big Break". She appeared in the feature film "Flipped" directed by Rob Reiner as well as in the film titled "No Strings Attached" where she played a young version of the main character.


title: Stefanie Scott

text: Scott was the voice of Emma on the Disney animated TV series "Special Agent Oso" premiering in April 2009 on Disney Channel. Scott had a guest-starring role in the Fox series "Sons of Tucson" as well as on NBC series "Chuck" playing the 12-year-old Sarah Walker. Scott released her second song entitled, "Shoulda Woulda Coulda".


title: Stefanie Scott

text: In 2011 she starred in the Disney Channel Original Series "A.N.T. Farm" as one of the main characters, Lexi Reed. She also served as second assistant director in the show's first season. Scott released a song entitled, "Girl I Used to Know" in the same year. The official music video for the song premiered on October 26, the music video features an appearance by Orlando based band Before You Exit portraying as her band.


title: Stefanie Scott

text: In 2013 Scott was a guest star on the fifteenth season of "" as Clare Wilson. Scott provided the voice of Moppet Girl in "Wreck-It Ralph". Scott also guest-starred on the Disney Channel show "Jessie", as Maybelle. From 2013, Scott has sponsored girls through Shoeboxes for Haiti, and is a cookie ambassador with the organization Cookies for Kids Cancer.


title: Stefanie Scott

text: In 2014, Scott began to film four films, "" (released in June 2015), "Jem and the Holograms", "1 Mile to You", and "Caught". "Caught" was screened at the premiere of the 2015 Los Angeles Film Festival on June 12, 2015. Also in 2015, Scott appeared in Hayley Kiyoko's music video for "Girls Like Girls". In 2015, Scott appeared as the daughter of Pierce Brosnan and Anna Friel, in crime thriller film "I.T." (2016), directed by John Moore.


title: Stefanie Scott

text: In August 2016, it was announced that Scott would play the lead role in the independent sci-fi feature film "At First Light" (2018), directed by Jason Stone. In February 2021, Scott appeared as the main character Sara Cody in the Lifetime movie "Girl In The Basement", based on the infamous Fritzl kidnapping case. In May 2021, she played the lead as Warrior Carrie in the Crypt TV supernatural drama series "The Girl in the Woods".


title: Lake Placid, New York

text: Lake Placid is a village in the Adirondack Mountains in Essex County, New York, United States. As of the 2020 census, the population was 2,303.


title: Lake Placid, New York

text: The village of Lake Placid is near the center of the town of North Elba, southwest of Plattsburgh. Lake Placid, along with nearby Saranac Lake and Tupper Lake, comprise what is known as the Tri-Lakes region. Lake Placid hosted the 1932 and the 1980 Winter Olympics. Lake Placid also hosted the 1972 Winter Universiade, the 2000 Goodwill Games, and will host the 2023 Winter Universiade.


title: Lake Placid, New York

text: Lake Placid was founded in the early 19th century to develop an iron ore mining operation. By 1840, the population of "North Elba" (four miles southeast of the present village, near where the road to the Adirondak Loj crosses the Ausable River), was six families. In 1845, the philanthropist Gerrit Smith arrived in North Elba and not only bought a great deal of land around the village but granted large tracts to former slaves. He reformed the land law and demonstrated his support of abolitionism.


title: Lake Placid, New York

text: The abolitionist John Brown heard about Smith's reforms, and left his anti-slavery activities in Kansas to buy of land in North Elba. This parcel later became known as the "Freed Slave Utopian Experiment," "Timbuctoo". Shortly before his execution in 1859, John Brown asked to be buried on his farm, preserved as the John Brown Farm State Historic Site.