Geometric Model by A. Harry Wheeler, Spherical Polar Triangles
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Harry Wheeler, Spherical Polar Triangles"}, "metadata_usage": {"access": "CC0"}, "data_source": "National Museum of American History"}, "indexedStructured": {"geoLocation": [{"Other": {"type": "Place", "content": "United States"}}, {"Other": {"type": "Place", "content": "Massachusetts"}}, {"Other": {"type": "Place", "content": "Worcester"}}, {"points": {"point": {"latitude": {"type": "decimal", "content": "42.25"}, "longitude": {"type": "decimal", "content": "-71.8"}}}}], "object_type": ["Models"], "name": ["Wheeler, Albert Harry"], "topic": ["Spherical Trigonometry", "Science", "Mathematics", "Trigonometry"], "place": ["United States", "Worcester", "Massachusetts"], "online_media_type": ["Images"]}, "freetext": {"setName": [{"label": "See more items in", "content": "Medicine and Science: Mathematics"}, {"label": "See more items in", "content": "Trigonometry"}, {"label": "See more items in", "content": "Science & Mathematics"}, {"label": "See more items in", "content": "Spherical Trigonometry"}], "identifier": [{"label": "ID Number", "content": "MA.304723.169"}, {"label": "accession number", "content": "304723"}, {"label": "catalog number", "content": "304723.169"}], "notes": [{"label": "Description", "content": "This cut and folded tan paper model is one of several in which A. Harry Wheeler illustrated properties of polar spherical triangles. A line perpendicular to the plane of a great circle of a sphere intersects the sphere in two points called poles (for example, on the earth, the great circle of the equator has poles the North Pole and South Pole). In the model, the outer spherical triangle has vertices labeled A, B, and C. Sides a, b, and c are opposite the corresponding vertices. Vertices of the inner spherical triangle are A<sub>2</sub>, B<sub>2</sub>, and C<sub>2</sub>, with sides a <sub>2</sub>, b<sub>2</sub>, and c<sub>2</sub>. A is the pole nearest A<sub>2</sub> of the great circle of the sphere that includes the arc B<sub>2</sub> C<sub>2</sub>. B is the pole nearest B<sub>2</sub> of the great circle that includes the arc A<sub>2</sub>C<sub>2</sub>. C is the pole nearest C<sub>2</sub> of the great circle that includes arc A<sub>2</sub>B<sub>2</sub>. Also, spherical triangle A<sub>2</sub>B<sub>2</sub>C<sub>2</sub> is the polar triangle of spherical triangle ABC (A<sub>2</sub> is the pole nearest A of a great circle through BC and so forth)."}, {"label": "Description", "content": "In this model, the point C moves along the arc AC and the point B<sub>2</sub> along the arc B<sub>2</sub>C<sub>2</sub>."}, {"label": "Description", "content": "The model is among those Wheeler dubbed collapsible."}, {"label": "Description", "content": "Reference:"}, {"label": "Description", "content": "G. van Brummelen, <I>Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry</I>, Princeton: Princeton University Press, 2013."}, {"label": "Location", "content": "Currently not on view"}], "creditLine": [{"label": "Credit Line", "content": "Gift of Helen M. Wheeler"}], "name": [{"label": "maker", "content": "Wheeler, Albert Harry"}], "topic": [{"label": "subject", "content": "Mathematics"}], "place": [{"label": "place made", "content": "United States: Massachusetts, Worcester"}], "physicalDescription": [{"label": "Physical Description", "content": "paper (overall material)"}, {"label": "Physical Description", "content": "tan (overall color)"}, {"label": "Physical Description", "content": "cut and folded (overall production method/technique)"}, {"label": "Measurements", "content": "average spatial: 7 cm x 9 cm x 5 cm; 2 3/4 in x 3 17/32 in x 1 31/32 in"}], "dataSource": [{"label": "Data Source", "content": "National Museum of American History"}], "objectType": [{"label": "Object Name", "content": "Geometric Model"}]}}, "url": "edanmdm:nmah_1066624", "hash": "813d92d79e665327f1173ec1c6bd0669a9336b2a", "docSignature": "e80a4666da5dbbc6b6bf0c914a459675", "timestamp": 1663781938, "lastTimeUpdated": 1655973454, "title": "Geometric Model by A. Harry Wheeler, Spherical Polar Triangles"}