Western Kansas world. [volume] (WaKeeney, Kan.) 1885-current, 1890-11-08
MATHEMATICAL PROBLEMS.
Mathematics for the Million.
Translated from the Danish.)

Translated from the Danish.l
Mathematical problems are in meas
IRE akin to puzzles. There is some
thing exciting in the boldness with
which our understanding is challenged
to prove its strength, and it imparts a
feeling of satisfaction to unravel mys-
teries which have for time bafded our
efforts. Such mental exercises have In
all ages been attractive to both young
and old, and for this reason we think
our readers will be amused by some re-
Elections concerning an algebraic
quantity which has cleverly been de-
signated "Whewp It consists of three
9s, the second as the exponent of the
9rst, and the third as the exponent of
the second, which means that shall
first be multiplied 9 times by itself,
viz. Observation-Disclosures, giving the
number 387, 400, 489. The product thus
found indicates how many times 8 a
second time is to be multiplied by itself /;
but what multiplied 387, 420, 489 times
by itself gives as a product is not so
easily figured out as the former null
duplication. It would require 1863, 693, =
100 ciphers, and to count it, working
ten hours daily, would take fifteen years
and go days, not to mention the time
passed in computation. Scientists tell
Us there are infusoria so small that 40, :
00O,000,O00 of such are found in one
cubic inch of water. A ball the size of
the globe would contain 2, 429, 093, 900,
100000, 900, 900, OO0, OOO, OO0 100000, or
two sextillions four hundred and
twenty-nine thousand and ninety-three
quintillions of such animals. But this
number is far from being "whew." A
ball that should be able to hold "whew"
of the infusoria here mentioned, at the
rate of 40, 900. 000,0 900 to the cubic inch
of water, would contain an inconceiv-
able number of globes, for the distance
between the surface of such ball and
its center would require 554, 539, 612
ciphers for its expression in miles.
How great length such a number OF
miles would have can be seen from the
following comparison;
Light travels 1872, 600 miles a second,
thus using eigh inutes and thirteen
seconds to traverse the distance from
Euo Suu " luC car ILL., Dul "
the distance from the surface of the
aforesaid ball to its center light would
need number of years written with
123, 231, O12 figures.
Still another relation may serve to
show @whew's" crushing dimensions.
Light accomplishes in every second
about five hundred billions of oscilla.
tons, number so great that the
loudest note ever measured, which
makes $4,000 vibrations in a second
must sound 40 years to perform Sc
der to traverse the radius of the above
mentioned ball light would require thi:
vast number of years, yet it does not
more than infnitesimally approach the
~whew" vibrations.
The story of the inventor of the game
of chess is well known. The King o.
India babe him name his own reward
upon which he asked to receive the
number of grains of wheat that would
be produced if one grain of wheat were
paid him for the first square of the
-chessboard, two for the second, four fol
the third, eight for the fourth, and so OF
doubled up for ever square of the sixty
four. When these amounts were added
the sum was found to be Is, 446, IA, 073,
T09, 551, 615 of grains, or in other words
such a quantity that Herewith all tn,
continents of the earth could be covered
with q layer one-third of an inch II
thickness, and that if the same GROUND
were sown with wheat IN the prope
manner it would take more than sevent,
wears to produce the above amount o
wheat, which is equal to thirty-four bil
lion bushels.
One stands aghast before this mum
Der, and still it is next to nothing a
compared with ~whew," for il we were
IN the same manner to double up tn,
amount until it reached @whew" numbe
of grains the chess-board, instead o
having Ga squares, must have had !, 22S,
093, 1874 squares, In which case II eacl
square had one square inch OF surfac'
the space covered would be an are
equal to 1913 acres.
We once saw some calculations, les
indeed in proportion than ~whev, We
of a character not less astounding. u
which numbers hardly to be conceive'
of were made In q measure comprehen
sible BY being compared with quanttie
of q more familiar nature.
For instance, If one cent were set on
at compound interest IN the year l q
four per cent, the LIST of January, 1856
it would amount to l quintillion 2O1, -
quadrillions, $50, 600 trillions of dollars
If We were to take this sum as q capita
and would use its yearly interest Cfou
per cent. }, then the income tax VI
should have to pay at the rate OF on
per cent, would be 40 quadriIlion
SIS, 800 triIlions of dollars. If we pal'
the Tax Collector this sum In silver d
would need 3.OO3. 645. 900. 0OOs oOO, 600,