 | David Layzer - Science - 1991 - 335 pages
...triangles in a plane. For example, the sum of the angles of any plane triangle is exactly 180°; but the sum of the angles of a spherical triangle is greater than 180° and increases with the area of the triangle. However, the geometry of a patch the size of Kansas... | |
 | Roger Fenn - Mathematics - 2007 - 330 pages
...calculus to be 1 T ..• -. . It follows that the area of the unit sphere is 47c. We have mentioned that the sum of the angles of a spherical triangle is greater than -. It turns out that this "excess" is equal to the area of the triangle. We first find the area of... | |
 | Claude Bruter - Mathematics - 2002 - 364 pages
...machines comes out essentially from the inequality 1 1 1 — H --- h .. > 1, pqr implied by the fact that the sum of the angles of a spherical triangle is greater than TT. A very natural extension of this would be to have "machines for building symmetry" in hyperbolic... | |
 | Charles Coulston Gillispie - Science - 2009 - 615 pages
...trigonometry, in effect treating their data as if the earth were flat and neglecting the inconvenience that the sum of the angles of a spherical triangle is greater than 180°. Less easily satisfied was Legendre, the mathematical member of the French team, whose analysis... | |
 | Great Britain. Parliament. House of Commons - Bills, Legislative - 1853 - 520 pages
...circumstances? What point in Reaumur's and in Centigrade scale correspond to 44° Fahrenheit. (8.) The sum of the angles of a spherical triangle is greater than two right angles, and less than six. Show that the angles at the base of an isosceles triangle are equal. (9.) Express... | |
 | 288 pages
...the third side, and the sum of the three sides is less than the circumference of a great circle. 95. The sum of the angles of a spherical triangle is greater than two right angles, but less than six right angles. 96. The planes of the small circles of equal radii, on a sphere, envelop... | |
 | United States. War Department - 190 pages
...degrees of the central angle subtended at the center of the sphere in the plane of the circle.) (6) The sum of the angles of a spherical triangle is greater than ,0 180° and less than 540°. Any angle of a spherical triangle must be less than 180°. (c) The sum... | |
 | Education - 1903 - 780 pages
...regular polyhedron? (b) How many regular convex polyhedrons are possible? (c) Name them. 3. Prove: The sum of the angles of a spherical triangle is greater than one, and less than three straight angles. 4. The angles of a spherical triangle are 120°, 270°, and... | |
 | Education, Elementary - 1900 - 1022 pages
...greater side, and conversely. 5. The sum of the sides of a spherical triangle is less than 360°. 6. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. 7. I (the first of two spherical triangles is polar to the second, then... | |
| |
The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC... 
