Wheels, Life, and Other Mathematical Amusements
Martin Gardner
Language: English
Pages: 271
ISBN: 0716715899
Format: PDF / Kindle (mobi) / ePub
Gathers mathematical puzzles, problems, games, and anecdotes about mathematical and scientific discoveries.
Penrose Tiles to Trapdoor Ciphers: And the Return of Dr Matrix (Spectrum)
rolling along at high speeds. Who can be sure such creatures have not evolved on other planets?) There may also be submicroscopic swivel devices inside the cells of living bodies on the earth, designed to unwind and rewind double-helix strands of DNA, but their existence is still conjectural. A rolling wheel has many paradoxical properties. It is easy to see that points near its top have a much faster ground speed than points near its bottom. Maximum speed is reached by a point on the rim when it
fold can put a pair of such cells together. The square puzzle with the faces and prison windows is solved from the starting position shown. Fold the top row7 back and down, the left column toward you and right, the bottom row back and up. Fold the right packet of three cells back and tuck it into the pocket. A face is now behind bars on each side of the final packet. The central face of the square cannot be put behind bars because its cell is diagonally adjacent to each of the window cells. Space
bibliography. As a wheel travels a straight line, any point on its circumference generates the familiar cycloid curve. When a wheel rolls on the inside of a circle, points on its circumference generate curves called hypocycloids. When it rolls on the outside of a circle, points on the circumference generate epicycloids. Let Rlr be the ratio of the radii, R for the large circle, r for the small. If Rlr is irrational, a point a on the rolling circle, once in contact with point b on the fixed
interval e > 0, however small, the tortoise travels a distance of l e , Achilles runs a distance of 5 e and the fly goes 10e. Hence in an arbitrarily small time after the meeting the fly leaves the interval between the tortoise and Achilles. Even if we have shown how Achilles can perform the 'supertask' of catching the tortoise, and how the tortoise can perform the 'supertask' of initiating its motion, it appears that the fly now faces the new 'supertask' of continuing to fly back and forth
numbers are, as Leech puts it, "hideous." He suspects that the smallest such brick may be one with edges of 7,800, 18,720, and the irrational square root of 211, 773, 121. Of course the brick's volume is also irrational. A much easier geometric problem, which I took from a puzzle book by L. H. Longley-Cook, is illustrated in Figure 9. A rectangle (the term includes the square) is drawn on graph paper as shown and its border cells are shaded. In this case the shaded cells do not equal the unshaded