Martin Gardner's Sixth Book of Mathematical Diversions from "Scientific American"
Martin Gardner
Language: English
Pages: 262
ISBN: 0226282503
Format: PDF / Kindle (mobi) / ePub
The New York Times (02 October 2015)
Penrose Tiles to Trapdoor Ciphers: And the Return of Dr Matrix (Spectrum)
This ans\ver was reduced to 25 rods [see Figure 431 hy 57 Sciertti.fic Antericcl~rreaders. As I was recoveriilg from the shock of this elegant irnprovernent seven readers C;. C . Baker, Joseph H. Engel, Kenneth J. Fawcett, Kichard Jenney, Frederick R. Kling, Bernard hl. Schwartz, and Glenwood 43. 25-rod solution for square-bracing 44. 23-rod solution \J7einert- staggered me with the 23-rod solution shown in Figure 44. Later, about a dozen more readers sent the same solution. The rigidity of
\Ye know provided by Euclid's proof, which may go back to the Pythagoreans, that the square at once that one eye must have been kissed at least one more time than the other. root of 2canllot be expressed as a common Mathematical Games fraction (a fraction with an integer above and an integer below the line). Since the diagonal of a unit square has a length equal to the square root of 2, this nleans that no ruler, however finely graduated, that accurately nleaslires the sicle of the square will
those exasperating, unruly integers that refuse to be divided evenly by any integers except themselves and 1. Some problems concerning primes are so sinlple that a child can understancl them and yet so deep and far from solved that Inany mathematicians now suspect they hace no solution. Perhaps they are "undecidable." Perhaps number theory, like quantum mechanics, has its ouTn uncertainty principle that inakes it necessary, in certain areas, to abandorl exactne!;~ for probabilistic formulation.
the position of the chosen card. Tlle secret lies in observing, at each pickup, whether the pile with the selected card goes on the top, the botto~n,or ill the niiddle of the assembled facetfo~vnpacket. are s designated 0 for the top, These p o s i t i o ~ ~ 1 for the middle, 2 for tlle bottom. The ternary numl~cr expressed by the three pickups, written fro111 r i g h t to left, is the nuniber of cards above the chosen card after the final pickup. For example, suppose tlie first pickup puts tlle
equivalent to the surface of a doughnut or a cube with a hole bored through it. Figure 7 shows how a flat, square-shaped model of a torus is easily made by folding the square twice, taping the edges as shown by the solid gray line in the second drawing and the arrows in the last. The torus is two-sided, closed (no-edged) and has a chromatic number of 7 and a Betti number of 2. One way to make the two cuts is first to make a loop cut where you joined the last pair of edges (this reduces the torus