By Martin Gardner
This ebook will be loved through a lay individual. It calls for no distinct prior wisdom. it's only aircraft enjoyable in addition to fascinating and in many ways novel. Gardner is an efficient author and may preserve your curiosity. i've got obvious a couple of books on math puzzles and video games, this one was once the easiest I had visible whilst I first observed it. (since then I learn different Gardner books that surpass this in, no less than, volume.) when you are curious in any respect you'll love it.
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Extra resources for Mathematical circus: more puzzles, games, paradoxes, and other mathematical entertainments from Scientific American with a preface by Donald Knuth, a postscript from the author, and a new bibliography by Mr. Gardner: thoughts from readers, and 105 drawing
A sphere of any dimension, made of sufficiently flexible material, can be turned inside out through the next-highest space. Just as we can twist a thin rubber ring until the outside rim becomes the inside, so a hypercreature could seize one of our tennis balls and turn it inside out through his space. He could do this all at once or he could start at one spot on the ball, turn a tiny portion first, then gradually enlarge it until the entire ball had its inside outside. One of the most elegant of the formulas that generalize easily to spheres of all dimensions is the formula for the radii of the maximum number of mutually touching n-spheres.
Let's extend this to Euclidean spaces of all dimensions and call the general n-sphere the locus of all points in n-space at a given distance from a fixed point in n-space. I n a space of one dimension (a line) the 1sphere consists of two points at a given distance on each side of a center point. The 2-sphere is the circle, the 3-sphere is what is commorily called a sphere. Beyond that are the hyperspheres of 4, 5, 6 . . dimensions. Imagine a rod of unit length with one end attached to a fixed point.
While your back is turned ask someone to tear from a full folder any number of matches from one through 10 and pocket them. wo digits in this number and tear from the folder the number of matches equal to the sum. ) These matches he also puts in his pocket. Finally, he tears out a few more matches-as many as he Matches 21 wishes-and holds them in his closed fist. You turn around and take the folder from him, mentally counting the remaining matches as you put the folder in your pocket. You can now tell him the number of matches in his fist.
Mathematical circus: more puzzles, games, paradoxes, and other mathematical entertainments from Scientific American with a preface by Donald Knuth, a postscript from the author, and a new bibliography by Mr. Gardner: thoughts from readers, and 105 drawing by Martin Gardner