Geometric Model by A. Harry Wheeler, Spherical Polar Triangles

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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 A2, B2, and C2, with sides a 2, b2, and c2. A is the pole nearest A2 of the great circle of the sphere that includes the arc B2 C2. B is the pole nearest B2 of the great circle that includes the arc A2C2. C is the pole nearest C2 of the great circle that includes arc A2B2. Also, spherical triangle A2B2C2 is the polar triangle of spherical triangle ABC (A2 is the pole nearest A of a great circle through BC and so forth).
In this model, the point C moves along the arc AC and the point B2 along the arc B2C2.
The model is among those Wheeler dubbed collapsible.
G. van Brummelen, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton: Princeton University Press, 2013.
Currently not on view
Wheeler, Albert Harry
Wheeler, Albert Harry
place made
United States: Massachusetts, Worcester
associated place
United States: Massachusetts, Worcester
Physical Description
paper (overall material)
tan (overall color)
cut and folded (overall production method/technique)
average spatial: 7 cm x 9 cm x 5 cm; 2 3/4 in x 3 17/32 in x 1 31/32 in
ID Number
accession number
catalog number
Credit Line
Gift of Helen M. Wheeler
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Spherical Trigonometry
Data Source
National Museum of American History


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