¶ Spherical Triangle Sequence
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Index Entry
Spherical Triangle Sequence:
"traveled a triangular course with three right angles, which means that this particular spherical triangle’s angles do not add up to 180°. In fact, they add up to 270°.
"This is a typical spherical triangle. The spherical triangle’s angles add up to a variety of sums other than 180°. The amount that the spherical triangle’s angles add up to more than 180° is called the spherical excess. The excess may vary all the way from 720° to 1°.
“Now if we make the triangle bigger (Figure 2), we can go, for instance, to the regular spherical tetrahedron each of whose four spherical surface triangles has three corners consisting of 120° each. Its spherical excess is then 360° minus 180°, which is an excess of 180°. If we draw one spherical triangle on the Earth’s surface with each of its corners having 120° angles, it will divide the total spherical surface of the Earth into two areas each of which is bound by a closed line of three angles and three edges.”
¶ Citations
- BEIRUT Address, p.24, 4-6 May’67
