| JOHN WESLEY YOUNG - 1911
...be extended indefinitely. It involves the assumption that a line is finite in length. In Riemann' s **geometry, the sum of the angles of a triangle is always...forming a limiting case, as it were, for both of them.** Resume. — It is not our purpose to study the various geometries in detail. We shall be satisfied... | |
| William Carl Placher - Religion - 1989 - 178 pages
...straight line parallel to the original line could be drawn through a point not on the line. The sum **of the angles of a triangle is always greater than two right angles,** the ratio of the circumference of a circle to its diameter is always less than pi. You can draw more... | |
| Jean Dieudonne - Mathematics - 1998 - 287 pages
...great circles of E, that is to say, the semi-ellipses whose major axis is a diameter of LI, and the sum **of the “angles” of a “triangle” is always greater than two right angles.** Another example is the definition of lengths on what is known as the “flat torus”. A “crude”... | |
| Donald C. Benson - Mathematics - 2003 - 280 pages
...of great circles must intersect. There are no "parallel lines." As seen in Figure 4.9, in elliptic **geometry the sum of the angles of a triangle is always greater than** 180°. 78 Figure 4.14. Spherical model for elliptic geometry. We will verify just one axiom, the incidence... | |
| Edmund Whittaker - Science - 1949 - 212 pages
...All straight lines return into themselves, and are of the same length, and space is finite. The sum **of the angles of a triangle is always greater than two right angles,** the excess being proportional to the area of the triangle, exactly as with triangles formed by great... | |
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