By Martin Gardner
This can be a selection of informative extracts from Gardners' "Scientific American" column. every one brain-teasing article has been up to date to incorporate new mists, new principles, and new suggestions. Highlights contain new chapters-one on pi and poetry, one on minimum sculpture - and exciting forays into time reversal, types of fractions and magic, and an imaginary "Math Zoo" with its personal book, "ZOO-NOOZ".
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Extra resources for Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine
The second problem was to use Euler's formula, F + C - E = 2 , to show that no sphere can be covered with a "regular map" of hexagons, each vertex the meeting point of three edges. Assume such a map exists. Each hexagon has six edges and six corners. Therefore if the hexagons did not share corners and edges, there would be six times as many edges a s faces. Each corner is shared, however, by three faces; FIGURE 23 The "other" eight-sided deltahedron therefore the number of corners in such a map must be 6Fl3.
Start with 1 at the top and 1 below it. Since 1 plus 1 equals 2, place 2 at the end of the second row. Bring: the 2 back to start the third row. The sum of 2 and the number above it is 3 , and so put 3 to the right of 2. The sum of 3 and the number above it is 5, and so 5 goes to the right of 3. Continue in this manner, observing the following two rules: The last number of each row is the first number of the next row, and all other numbers are obtained by adding the desired number's left neighbor to the number above the neighbor.
W. Becker, in The American Mathematical Monthly, 48, 194 1, pages 701-703. " Gian-Carlo Rota, in The American Mathematical Monthly, 7 1, 1964, pages 498504. " George E. Andrews, in Encyclopedia of Mathematics and Its Applications: Vol. 2, edited by Gian-Carlo Rota, Addison Wesley, 1976. " Aileen Gatten, in Monuments Nipponica, 32, 1977, pages 35-48. The Tale of Genji. Murasaki Shikubu. Knopf, 1978. " John Riordan, in Annals of the New York Academy of Sciences, 3 19, 1979, pages 445-465. " D. P.
Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine by Martin Gardner