<jupyter_start><jupyter_text>$\def\Arc1{\buildrel\frown\over{1}}$$\def\Between123{1\!-\!2\!-\!3}$$\def\Degrees{^{\tt o}}$$\def\Frac1/2{{^{1}/_{2}}}$$\def\Line1{\buildrel\longleftrightarrow\over{1}}$$\def\Ray1{\kern-.1em\vec{\kern.1em 1}}$$\def\Segment1{\overline{1}}$ PrefaceThis project began as a personal review of an old geometry textbook and ended up with a deeper dive into the amazing SciPy software.  Unless you are a beginning geometry student or someone who draws triangles for a living, it may have a high boringness level, like eight or nine.  The table of contents is helpful for finding or remembering things, there are a few matplotlib programs.[Jump to table of contents](Contents.ipynb). ConventionsTo simplify command line searching, the following heading conventions are used:     Chapter 11 - Parallel Lines     Axiom 2 - Segments and Lines     Postulate 8 - Congruent Angles     Definition - Transversal     Theorem 10-1     Corollary 10-1.1     ProofTo avoid mixing in comments from python code, python comments at beginning of line can use '-' or '%' or any other second character besides hash '' or space ' ',    - This is a matplotlib python comment.Then searching is easier,    bash> egrep '"(| )' Chapter* | grep ParallelTo distinguish text of a definition or theorem from comments by the author, block quotes are used for indentation:     Theorem 10-2        > Large triangles are especially pointy.        That is an excellent theorem. NotationTextbook notation is used whenever possible to ease comparison with this notebook.  Plain $\rm\TeX$ macros defined here use Pascal case (yes, [that's a thing](https://en.wikipedia.org/wiki/Camel_case)) to avoid most collisions.  Examples below may be copy/pasted as needed.    $\def\Arc1{\buildrel\frown\over{1}}$If $\angle ACB$ is a central angle and points $A$ and $B$ lie on the circle, then the **minor arc** $\Arc{AB}$ is the union of $A$, $B$, and all points of the circle which lie in the interior of $\angle ABC$.  The **major arc** $\Arc{AB}$ is the union of $A$, $B$, and all points of the circle which lie in the exterior of $\angle ABC$.  (See [Chapter 16](Chapter16_CirclesAndMeasures.ipynbDefinition---Arc).)    $\def\Between123{1\!-\!2\!-\!3}$This reduces space around binary '$-$' operator improving appearance of the book's "between" notation.  You get $\Between A B C$ rather than $A-B-C$.    $\def\Degrees{^{\tt o}}$Knuth's `\circ` is too small for author's eye; this macro raises the temperature to $120\Degrees$.    $\def\Frac1/2{{^{1}/_{2}}}$Can anything rational be said about $\Frac1/2$?    $\def\Line1{\buildrel\longleftrightarrow\over{1}}$Line $\Line{AB}$ is parallel to line $\Line{CD}$ but, if you love typing, go right ahead and spell it out.    $\def\Ray1{\kern-.1em\vec{\kern.1em 1}}$For some reason, MathJax `\vec` looks awful with one symbol but works nominally with two or more.  The following display shows `$\vec{A}$`, `$\vec{AB}$`, `$\Ray{A}$`, `$\Ray{AB}$` in that order:$$ \vec{A} \qquad \vec{AB} \qquad \Ray{A} \qquad \Ray{AB} $$    $\def\Segment1{\overline{1}}$Segment $\Segment{AB}$ has two endpoints, namely $A$ and $B$.  The *distance* from $A$ to $B$, the segment length, is written simply as $AB$.Negation syntax *~p* is changed to **$\neg p$** (i.e., `$\neg p$`).  The tilde symbol appears to be reserved for binary *similarity* operator (`\sim`) in both old and new $\rm\TeX$ usage.And finally, images are centered with snippet from another author, copied below for easy retrieval.![alt text](triangle-01.png)<jupyter_code>#- For centering plots, this is borrowed from the lovely creation of
#- <NAME> at https://stackoverflow.com/questions/18380168.
from IPython.core.display import HTML
HTML("""
<style>
.output_png {
    display: table-cell;
    text-align: center;
    vertical-align: middle;
}
</style>
""")<jupyter_output><empty_output>
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