Mathematical_Recreations-Kraitchik-2e

Geometric Recreations ~09
the 20, and 4 of the 30 - in all, 12 of the 62. This dissection
of the spherical surface was considered by Felix Klein.
Mr. Royal V. Heath has placed the numbers from 1 to 62
on the 62 points in such a way that the sum of the 12 numbers
on each of the 15 great circles, as well as the sum of the
numbers at each of the 12 points where 10 triangles meet
(i.e. the vertices of the icosahedron), add up to 378 (Figure
97).
FIGURE 97.
Spherical Mosaic with Magic Features.
4. TOPOLOGY
There are certain geometric questions in which the specific
size and shape of the objects under consideration are of
no importance - only their relative position matters. One
may bend, stretch or tear the figure (provided the edges are
sewn up again as they were) without altering the essential
nature of the problem. Such questions are called topological.
1. The problem of the Konigsberg bridges provided the
occasion for the first researches in topology. The problem
was proposed and solved by Euler. It consists in determining
whether one can pass just once over all the bridges over
the river Preger at Konigsberg. The arrangement of the