The Topeka state journal. [volume] (Topeka, Kansas) 1892-1980, 1914-01-10
THE DOUbllne Of The CUBE



One o. prohaenns Of Ancaents and
Modern 1lathennnttcaans-
There are several problems which
matictans and which have continued to
puxxle modern ones. One of these Was
the squaEin9 Of the circle. another was
the tr1aection OF an angle-Aand
third was the doubling OF the cube.
This was called by the ancients the
.'Delian problem,'' because 1t had to do
with the Delians, or Inhabitants OF the
island OF Delos. In the Mediterranean.
This island was sacred to Apollo and
the year 40 b. c., and there was q
terrible pegtilence in Athens. The
Athenians sent committee Of leading
citizens to Delos to consult the 1am-
ous oracle Of Apollo. to see what could
be done to stay this plague.
Now these oracles Of old were ex-
ceedingly foxy: they never answered q
ways employed ambiguous terms which
could be construed two or more ways;
or they answered In riddles so that
no matter which way the events turn
ed out they could claim to have fore
told them. This il q method which il
stin practiced by slillful politicians.
fortune-tellers ana others.
The altar of Apollo was a marble
block made In the form of an exact
cube. When the Athenians applied for
advice as to how to stamp out the
plague, the priests OF Apollo told them
that first they must double the size Of
Apollo's altar. This looked easy and
the committee went back to Athens
highly pleased with the result of their
mission.
An order was at once given to the
chief marble cutter Of Athens for an
altar Just twice as big as the present
one. This man went quickly to work
and triumphantly produced such an
a1tar-as he thought. It measured Just
twice as big as Apollo's altar in each
direction.
When they took this big cube to
Delos however, the oracle Indignantly
spurned 1t. It was PORTED out that the
new cube. being twice as big on each
SIDE as the original. was therefore
eight times as big altogether, instead of
twice. :
Then the committee set to work
again and 1t was decided to double
the size OF the altar by making two
exact duplicates of the original: that
Is. the new altar was to be the same
SIZE IN two directions and twice as
}--os ~ oAA 0Ae0A WIS IU8QG on that
plan and taken to Delos. The oracle
this time was deeply angered. Any
TOOL could make an altar twice as big
oy simply making a duplicate to 20
alongside It. it said; but the task inn
posed was to produce an altar similar
to the old one and having mathemati-
ca!iy double its volume. To punish the
Atnenians Tor being 30 dull Apollo
| tnen made the pestilence even worse
| than before
According to the tradition the Athe-
mans then consulted the philosonher
fiato on the subject. He told them mas
tney nad 1mpiOusly neglected the stuav
| OF geometry, which was the most nrac.
t1cal OF the sciences, and that thew ",
pelng Justly punished for this ne-,e #
are aIso being punished in this
country ana age for not making orr
education more practical. for in an
way we are as blind to the need. a.
the Athenians were. as
Flato then gave them ApolIons,,.,
conci' ons about incommen.nrah1I.
quantities.. Apollonius was cra ..,
seometer who had lived about two
centuries before and who had eone
oeepiy into comic sections and sfrn,le,.
matters and written a book -, -
subject. oA On the
The story ends here, for the Ath.-
mans, even by the help Of Anollo,s,,.,
treatise. were unable to And the as,
swer to their problem This nrohie,,,
was 70 md what would be the erec
length Of the side of an exact r,,ss.
which should have exactly twice ~
contents OF the original cube. StataS
I alphabetically. the problem was -
1 md in an equation where x-cnhe
equals a-cube. taking for side
OF the unknown and a for q. side If
the known cube for values IN ~
/ equation. lug
The tradition cannot be hfstorfcaIlv
quite true, for Plato was only . hahs,
a year old at the time of the zren+
1 plague In Athens He was \ w.
smart youngster. no doubt, but he va
hardly smart enough at one year Of
age to know anything about ApolIo-
mus equations. However, It doesn't
hurt good story il it isn't literallv
quite true. 80 >---S
We know that Hippocrates worked
many years on this problem Varfous
people got up mechanical instruments
to draw figures to produce the desired
result; this was possible but it was
merely a mechanical working out o1
the problem and not a mathematical
solution of it. Achytas Menaechmus
Diocles and Sporus are some Of the
other mathematician of ancient
times who wrestled with Apollo,s De