The Minneapolis journal. [volume] (Minneapolis, Minn.) 1888-1939, 1904-11-10
WERE TRlPPED BY
ITS SIMPLICITY
CONTESTANTS WRESTLED WITH
THE CUBE-SQUARE PROBLEM.
Always on the Lookout for Trouble,
Mathematicians Worked Hard and
Long Over Geometrical Proposition
That Was Easy-What It All May
Indicate-The Answer.

There is no doubt that the world
America at least-loves to sharpen it's
wits on problems, whether they be
mathematical calculations or mere puz-
zles. Any kind Of an inquiry in the
newspapers that has in it an element Of
In The Journal of Oct. 81, Ole
Sandberg called for assistance in the So
luton OF a practical problem, stating
that it had caused much discussion.
Those who wished to aid him were
prompt and numerous in their responses,
but they were blinded by the manner
duly hard work Of it. The mathemati-
clans were looking for a catch some
where, and instead of employing the
simplest means, the business shorthand
supplied by higher arithmetic, they
went about the solutions in the hard
complicated and Ingenious applications
Of solid geometry. The problem is one
of solid geometry to be sure, but, hav
ing been demonstrated in that science
from time immemoriai, for practical
purposes the results of these demonstra-
tions may be taken without question
and applied in the easiest way.
The puzzle solver is a suspicious man
and nothing trips him like simplicity.
The solutions offered are instructive ex-
amples Of how one may be mislead by
having an eye constantly open for
trouble. Undreamed Of difficulties
time and paper were wasted in hunting
up imaginary catches Several arrived
at the conclusion that the problem was
incapable of solution and suggested
that it had been proposed merely to af-
ford chance of laughing at the guile
less ones who should bite on it.
A number of replies were received
| that 1nDrOX1m9tn the correct
but they were arrived at by widely di-
vergent methods. 1t is evident from
the replies that higher. mathematical
knowledge is not one Of the things kept
an excellent argument for the educa-
tors who would cut down the teaching
of arithmetic to the simplest processes
on the ground that they are all that are
used or retained by the great majority
of people, and that those who have need
readily obtain the specific knowledge
they need when they come to have use
for it.
The solutions were examined by a
group of ex-collegians most Of whom
were able to recognize the. correct. solu
ton, but not one could give sufficient
grounds in support of his belief. The
demo nstrate off-hand the simplest geo
metrical problem, altho most of them
remember the conclusions and that they
were supported by impeccable logic
From the incident they drew the con
clusion that about all that remains tc
the average collegian of his hare
earned higher mathematics is few
practical formulate which on occasion he
employs with full confidence and ease.
The problem proposed is "What SIZE
cube can be cut from a l2-incl
sphere?" It was assumed, altho not 81
4ol hot II, No +
the eoe 6a
member of the mathematical faculty a
the university is that Of the principal O.
.. the Borup school, in Norman county
The formula used is the edge Of the de
sired cube equals the square root of tn
,, result obtained by dividing the squar
eter is twelve inches; it's square, IA
divided by three is fortv-eight, o
which the square root is 692S2 niche!