Download Slicing Pizzas, Racing Turtles, and Further Adventures in by Robert B. Banks PDF
By Robert B. Banks
Have you daydreamed approximately digging a gap to the opposite part of the realm? Robert Banks not just entertains such principles yet, larger but, he offers the mathematical knowledge to show fantasies into problem-solving adventures. during this sequel to the preferred Towing Icebergs, Falling Dominoes (Princeton, 1998), Banks offers one other selection of puzzles for readers drawn to sprucing their pondering and mathematical talents. the issues variety from the wondrous to the eminently useful. in a single bankruptcy, the writer is helping us make sure the complete variety of those that have lived on the earth; in one other, he indicates how an knowing of mathematical curves will help a thrifty lover, armed with building paper and scissors, hold bills down on Valentine's Day.
In twenty-six chapters, Banks chooses themes which are rather effortless to investigate utilizing fairly uncomplicated arithmetic. The phenomena he describes are ones that we come across in our day-by-day lives or can visualize with out a lot difficulty. for instance, how do you get the main pizza slices with the least variety of cuts? to move from aspect A to indicate B in a downpour of rain, for those who stroll slowly, jog reasonably, or run as speedy as attainable to get least rainy? what's the size of the seam on a baseball? If all of the ice on the earth melted, what might occur to Florida, the Mississippi River, and Niagara Falls? Why do snowflakes have six sides?
Covering a huge diversity of fields, from geography and environmental reports to map- and flag-making, Banks makes use of uncomplicated algebra and geometry to resolve difficulties. If recognized scientists have additionally meditated those questions, the writer stocks the ancient info with the reader. Designed to entertain and to stimulate considering, this booklet will be learn for sheer own amusement.
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Additional info for Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics
Example text
7) cannot be traversed without disconnecting a hinge, refolding the flexagon, and reconnecting the hinge. It is included because of its relationship to the trihexaflexagon. 14. It is a ring even edge flexagon (previous section). 1a). 7) by using the threefold pinch flex, in which threefold rotational symmetry is maintained during flexing.
23 point hinges are indicated by dots, and some squares are slightly separated for clarity. 23c. 1b). 23d, which has twofold rotational symmetry. In general, vertex rings can be rotated continuously, although rotation is sometimes restricted by interference between polygons. 23 Even vertex rings of four squares. (a) Box. (b) Flat, hinges diagonally opposite. 23a and b appear alternately. In this sense vertex rings are analogous to rotating rings consisting of polyhedra hinged at common edges, sometimes called kaleidocycles, as described by Conrad and Hartline (1962); Cundy and Rollett (1981); Engel (1969); Hilton and Pedersen (1994); Schattschneider and Walker (1983).
There is one possible flat compound edge ring of squares and one of regular pentagons. There are four possible flat compound edge rings of regular hexagons, two of these are included in the table. 5 Flat compound edge rings of regular polygons Polygon type Number in ring Ring symbol Square Pentagon Hexagon Hexagon Octagon Octagon Enneagon Decagon Decagon Decagon Decagon Dodecagon Dodecagon Dodecagon Dodecagon Dodecagon Dodecagon Overlapping ring. 2 Edge Rings of Regular Polygons 25 polygons. The maximum possible number of polygons in a flat compound edge ring appears to be twice the number of edges on constituent regular polygon.