Evening star. [volume] (Washington, D.C.) 1854-1972, 1931-08-12
EDUCATOR DOES ''MPOSSIBLE''
FEAT OF TRISECTING AN ANGLE
Duquesne President Solves
Geometric Problem Thought
InSolvable.
New Theories Will Alter Text
Books-ScholarS BaffIed
for Centuries.
Special Dispatch to The star.

Special Dispatch to The star.
CHIPPEWA FALLS, Wis, August II
(N.A.NA.) WORKING at the problem in
his spare moments, to satisfy his own
curiosity and to prove the supposedly
improbable, a modern scholar has ac-
complished what the ancient thinkers
were unable to do.
He has trisected an angle by plane
geometry.
This, on the face of it, may not sound
impressive. To those who have more
than a passing interest in mathematics
it will be of more than average i'm
portance. To the general public it will
not sound nearly as interesting as
new airplare record or the invention of
some new form of engine.
1t means. however, that one of the
three so-called insolvable problems Of
mathematics has been solved.
1t means, moreover, that schoolboys
will IN the future find their geometry
just bit more complicated.
Introduces New Figure.
It means, also, that the public In
general will, in time, have q new idea
for arrangement. There will be a new
plane figure in addition to the well
known circle, square, rectangle, paral-
telegram, tTapezoid and so on.
The modern scholar responsible for
this is Rev. Father j. J. Callahan, pres
ident of Duquesne University at Pitts
burgh Pa, who is spending week here
to participate in the seventy fifth ami
versary celebration of the Notre Dame
parish which he served as pastor some
10 years ago.
To understand what Father Gala
han has done it is necessary to visual
ize or draw an angle. The letter ''V"
will do as an example. The problem
now Is to divide the letter 'V" into
three equal angular parts. Or, If you
want to draw a hoop connecting the
top points of the "V'' TO divide the sub
tending arc into three equal parts.
Then prove your division correct by
propositions Of plane geometry.
Accepted rs InsOlvable.
To date, plane geometry has been
able to divide an angle into two equal
angular parts, but not into three. Sew
eral thousand years ago, Hippiss OF
ELIAS, an ancient scholar. set himself
to the task of trisecting an angle. He
finally gave up. Others tried and
failed. At last the problem was handed
down to posterity as being insolvable
and was accepted as such. Further
more. modern science found ways and
means Of trisecting an angle by me-
chanical methods. Plane geometry.
which once had an immense practical
value, became more and more purely
academic study.
Today an engineer can, mechanically,
in laying out a field, for example. tri-
sect an angle through the use of in
etruments and proven measurements.
A few hundred years ago 1t would have
been impossible, since plane geometry
was lacking on that point.
The two other allegedly insolyable
mathematical problems are the dupli-
cation of q, cube, or doubling the vol
urne Of a cube, and the squaring Of n
circle, which means getting the exact
area Of given circle into a square.
Has Little Practical Value.
An three problems have been worked
out BY higher mathematics, through the
use Of equations and higher curves, but
Father Callahan is the first to solve
the first one through plane geometry.
His discovery has little II any prac-
ticai value It's chief interest Is In the
formulation of 3 new idea and in prov
ing that the ancient thinkers were
wrong in their conclusions concerning
the trisection of an angle.
How it all came about was explained
ldSL hAkllt pS Idbl4CA S0AA6Ah1AAf WIN 40
So years old, slightly gray about the
temples, with dark eyes that are alert
and humorous, and mind that works
very fast
II was all by accident, he said, that
he happened to solve a problem that
has been puzziing mathematicians for
several Thousand years. In fact. the
story Of how the angle happened TO be
trisected by plane geometry begins
when man who had read somewhere
that the angle could not be so
divided wrote to Father Callahan for
information Father Callahan, who has
gained a reputation for his attacks on
the validity of the Einstein theory,
wrote back that the problem had al
ways been accepted as insolvable.
Decided to Try Problem.
The man who desired information,
however. could not be put on SO easily
He came TO Pittsburgh TO discuss the
matter in person. The problem was
thus presented very definitely to Father
Callahan,
There is no reason why an angle
can't be trisected," he said TO himself
one night Just before retiring.
Then, half awake" Father Callahan
explained today, II thought of method
of proof that would require that certain
dAtAlcS dAtA 4A&Eo RAOHNA NANc@- 1920
a theorem, but there were no PROPOSE
tions in Euclidian geometry that would
prove that the necessary angles and
lines were equal. ! was given faint
idea Of the new plane figure I needed,
and that was all.
II kept thinking about this. In my
spare time worked out geometrical
proof of the figure. When I got this
proof the rest was easy.
Answer Is Simple.
by using this figure can now work
out a geometrical proof Of trisection
of an angle as easily as you would prove
any Of the more familiar propositions Of
plane geometry.
MY new figure has regularity and
a definite law II contains a definite
geometrical proposition. BY proving 1t
you have proof and construction Of the
trisection Of an angle
BY the same procedure, Father Cal
lanan claims, it Is now possible to divide
an angle into six equal angular parts
or any multiples Of three.
The exact nature Of the new figure,
or the geometrical proof Of the figure
and Of the trisection Of an angle Father
Callahan declines to reveal for the time
being. He intends 20 copyright his proof
first and 70 include ii in new text
book on plane geometry, which he Is
now preparing.