Geometric Model by A. Harry Wheeler, Spherical Polar Triangles
name: label: maker
content: Wheeler, Albert Harry
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
place: label: place made
content: United States: Massachusetts, Worcester
topic: label: Subject
content: Mathematics
setName: label: See more items in
content: Medicine and Science: Mathematics
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content: Trigonometry
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content: Science & Mathematics
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content: Spherical Trigonometry
creditLine: label: Credit Line
content: Gift of Helen M. Wheeler
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: MA.304723.169
label: accession number
content: 304723
label: catalog number
content: 304723.169
objectType: label: Object Name
content: Geometric Model
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