## Page View

Niles, Donald E. (ed.) / The Wisconsin engineer

Volume 48, Number 7 (March 1944)

Tanghe, John

Campus notes, p. 11

Page 11

Mathematical Morsels by Walt Graham, me'44 ERE and there there's pure amusement in mathe- matics. Usually it's there but here it's here. Nothing appeals to us like pie, or let's drop the "e" since it is the "natural" thing to do; let's say we've a rea- sonable interest in pi. That the circumference of a circle bore a direct relationship to the diameter was known be- fore we were freshmen. In the Book of Kings and in the Chronicles its value is given as 3. Later the Egyptians had it as 3.16. Archimedes (about 250 B.C.) narrowed pi between 3 1/7 and 3 10/71. In the time of Claudius Ptomely (150 A.D.) the constant, for all practical pur- poses, had its present value. Archimedes' method was very interesting. Drawing a circle, he inscribed and cir- cumscribed it with squares. Letting the diameter be unity, pi was then a value between the perimeters of the two squares. He then "bent" the sides of the inner squares in the middle to form an inscribed octagon and cut off the corners of the circumscribed square to form another octagon. Pi was then between the closer limits of the new perimeters. Archimedes continued this process until he had polygons of 96 sides with which to obtain his value. With the innovation of calculus, however, the sugar was added to the pi and its calculation made much simpler. In 1699 pi was evaluated to 71 places, in 1824 to 200 places, in 1854 to 500 places, and in 1873 to 707 places, which is its present status. It is estimated that even with the most rapidly converging series of today it would take about ten years to find pi to 1,000 places. Let's look at something else! It is interesting that probe and probability have the same Latin "root," so why not probe into probability? GrapicalL' Solve= d Graphically Solved? When you paddled down through the province of Oudh on the river Ganges and into Benares, the sacred city of the Buddhists and Hindus, you no doubt noted the wondrous mosque on the hill. Within this shrine is a brass plaque in which three diamond pins are imbed- ded, upon one of which at the time of the creation Bud- dha placed sixty-four gold disks, each smaller than the one beneath it. The priests of the temple were charged to move these disks eternally from one pin to another, moving only one at a time and placing no disk so that a smaller lies beneath it, until all the disks had been trans- ferred to another of the pins. When this is completed the temple is to crumble and the earth to vanish. If the priests moved the disks at the rate of 20,000 a day, and have been doing so for a million years, an interesting solution awaits you. For Gamblers Only Probably you are more interested in gambling than discovering when the world will end-even if it is tomor- row. However, you are warned that the results are dis- heartening. My slide rule, please! If you stake some given fraction of your fortune, not a big percentage if you like, on each play of a game in which the chances of winning and losing are equal and continue to bet the same fraction of your new fortune on each successive play, you will always lose in the long run. If you are riding the horses when the dominos gal- lop, look out! The odds are 251 to 244 against you (neglecting the pair in your pocket). If you are skeptical, witness the case of our good French friend (and gambler), Monsieur Chevalier De Mere. Mere would bet even money that he could roll a six in one out of every four throws with a die. (Investigation (continued on page 20) THE WISCONSIN ENGINEER 12

This material may be protected by copyright law (e.g., Title 17, US Code).| For information on re-use, see http://digital.library.wisc.edu/1711.dl/Copyright