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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


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