The Indianapolis times. [volume] (Indianapolis [Ind.]) 1922-1965, 1933-08-08
-Oietz on Science
TWO LETTERS
SPELL FIGURE
WITHOUT END
Pr Would Go On Even If
Carried TO 1000 Deci-
NAL Places.
BY DAVID DIETZ
Soripps Howard Science Editor

II time hangs heavy on your
hands and you want to keep busy
for the next ten or twenty years,
you might try calculating the value
Of "pi" to 1000 decimal places. DR..
Edward Kasner. professor Of mathe-
MATES at Columbia university, es-
Inmates that 1t would take a decade
or two to do the Job. depending or
how good a calculator you are
incidentally. IL will make you
more or less famous. insurlng ; Oh at
least one mention on the front pages
OF the worlds newspapers and
thereafter at least foOtnote in all
histories of mathematics. For no
one has yet done II.
"Pi." as you Will recall IS the
technical name for the ratio Of the
circumference Of a circle 20 It's
diameter The figure usually used
for it is 314l6
Kasner says that the number
NAV be considered the most impor-
tant in the entire history of mathe-
mates.
II was known in biblical times to
be approximately 3. The Egyptians
did a little better later and made
1t 3l6. BY the time of Ptolemy, the
famous astronomer who lived about
$50 A. D. our commonly used value
of 3l4l6 was known.
Centuries licked off their days
before that figure was much I'M
proved on. although some progress
was made in the Middle Ages.
Number on Tombstone
In 1896 Dutch mathematician by
the name of LudoIph van Ceulen
calculated the value of "pi" to
thirty-flve decimal places When he
died the number was carved on his
tombstone in the churchyard in
Layden. where he was buried
In Germany "pi" is still called the
Ludolphian number. although that
name is not familiar in other coun-
tries.
Ludolphs work was improved in
1899 when an Englishman by the
name of Sharpe carried the calcu-
lation to Seventy-one decimal /
places. This record stood for more /
than a century. but in 1924 light
ming calculate" named LJase. a
German in the employ of the
famous mathematician. Gauss. cal I
culated the number to 200 decimal
places.
in 1854 Richter set a new record .
by carrying it to 500 places and in
1873 an Englishman named Shanks /
calculated 707 places.
Ten Places Suffice
While these calculations are in
teresting. they are not particularly
useful Savants rarely have any
use for more than ten decimal
places in the value of 'pi.'
The late Professor Simeon New
comb. famous American mathema-
tician and astronomer. cnce said. /
Ten decimal places are sufficient .
to give the circumference of the /
whole visible universe to 4 quantity /
imperceptible with the most power
full microscope.
Kasner. however. thinks that the I
ten or twenty years it would take I
to calculate 1000 decimal places /
would not seem like a waste of /
time in comparison with the billions !
of hours spent by millions Of people /
on crossword puzzles and contract /
bridge
Mathematician know from their I
calculations that "pi' will never /
come out a whole number. II could
be carried on 10 10000 decimal /
places or 100000 decimal places and /
still there would be a remainder. In !
the parlance of the mathematician. /
the number is Irrational and
transcendental."
Another number which never ends .
is the decimal expression of the I
square root OF two This number
has never been carried out TO more
than 200 decimal places but it is
known that it never ends and never
repeats and that no known simple
law will give the success Of digitS.
Squaring Circle Impossible
The fact that "pi" is a tranScen-
dental number prevents the solution
OF the problem known as "squaring
the circle" that is constructing a
square equal in area TO a given circle
with use of only a compass and
ruler
But while the square root of two
is a never-ending decimal, 1t Is
easily obtained by geometrical con-
StructiOn. All that is necessary Is
TO draw a square whose sides are
equal to unity. The diagonal Of the
square is then the square root OF
two. No doubt YOU will recall that
the hypotheneuSe OF a right-angle
triangle is equal 10 the square root
OF the sum OF the squares of the
two sides.
Kasner tells us that it is recorded
that when the Greeks discovered
that the square root Of two was not
equal TO any rational number. they
celebrated the discovery by sacrific-
ing 100 oxen.
Perhaps one Of the things wrong
with our age IS that mathematics
no longer receive such enthusiastic
popular acclaim.
.t@&I-R0s RaNf