Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine
Martin Gardner
Language: English
Pages: 328
ISBN: 0716721899
Format: PDF / Kindle (mobi) / ePub
This is a collection of informative extracts from Gardners' "Scientific American" column. Each brain-teasing article has been updated to include new mists, new ideas, and new solutions. Highlights include two new chapters-one on pi and poetry, one on minimal sculpture - and intriguing forays into time reversal, forms of fractions and magic, and an imaginary "Math Zoo" with its own publication, "ZOO-NOOZ".
God on the Streets of Gotham: What the Big Screen Batman Can Teach Us about God and Ourselves
The Comic Toolbox: How to Be Funny Even If You're Not
cm/sec." Thomas H. Hay told me about a species of wood lice (also called slaters, sow-bugs, and pill-bugs) that, when alarmed, curl into a ball and roll away. Hay said his children call them roly-polys. While working underneath his car, with a trouble light beside him, he often finds the roly-polys "advancing in inexorable attack. I fantasize that they are Martian armored vehicles, released from a tiny spacecraft. Fortunately, they move so slowly that my work is finished before they constitute a
mathematics hugely a s a form of intellectual play. As a child he had had an intense interest in chess problems, puzzles, mathematical card tricks and secret codes. This sense of amusement runs through all his mature writings. He even coined the word "musement" for a mental state of free, unrestrained speculation, not quite as dreamy as reverie, in which the mind engages in "pure play" with ideas. Such a state of mind, he maintained, is the first stage in inventing a good scientific hypothesis.
specified. The radius of each circle is obtained by multiplying the radius of the next-smallest circle by the sum of the golden ratio and its square root, a number that is slightly more than 2.89. The contact points of the circles lie on an equiangular spiral shown by the broken curve. FIGURE 72 H. S. M. Coxeter's golden sequence of tangent circles The solution to "The Packer's Secret" is shown in Figure 73. In doing the actual puzzle, it is expedient to start with one penny in the center;
same size? The solution to this problem was discussed in an article by graph theorist William T. Tutte that is reprinted in my 2nd Scientific American Book of Mathematical Puzzles & Diversions. At the time Tutte wrote, the best solution known ("best" meaning with a minimum number of different squares) required 24 squares. In 1978 this figure was lowered to 21 squares by A. J. W. Duijvestijn, a Dutch mathematician, a s was reported in Scientific American (June, 1978, pages 86-88, see Figure 77).
generalized to three dimensions by Kim. There is an elegant proof that a cube cannot be cut into smaller cubes no two of which are alike. (See my 2nd Scientific American Book of Mathematical Puzzles & Diversions, page 208.) Can a cube be "boxed" by cutting it into smaller boxes (rectangular parallelepipeds) so that no two boxes share a common edge length? The answer is yes, and Kim was able to show that the minimum number of interior boxes is 23. Later William H. Cutler FIGURE 79 The smallest