Evening times-Republican. [volume] (Marshalltown, Iowa) 1890-1923, 1910-01-18
MARVEL IN MATHEMATICS.

Ten.year-old Student Said He Expects
His Theorems to Revolutionize Study
Of Geometry After His Lecture
Harvard Teachers Crowded Round
Him For Further Elucidation.
Psychologists today are astonished
by William James Sidis, the ten-year-
old student of Harvard. who startled
gray haired mathematical professors
by propounding some new theories of
the fourth dimension in lecture which
he recently delivered at Cambridge,
Mass, before the Harvard Mathemat-
ical club.
Distinguished mathematical profess
ors from all over New England were
present and gazed in wonder as the
rosy checked boy in short trousers
placed on the blackboard row after
row of figures to prove his difficult
and profound theories Many of them
frankly protested their ignorance of
the subject Of which the, boy talked so
glibly and again and again called on
him to explain anew some mathemat-
ical theorem
Young Sidis, who was accompanied
by his father, DR. Boris Sidis, the we'll
known psychologist, stepped to the
front and, with childish laugh, be-
gan his lecture. He wore red hand
kerchief such as is commonly worn by
boys in the primary schools, and his
handwriting was that Of child. But
his mind was far from childish. and
some of his ideas were beyond the
comprehension of many of his auditors.
Took Advanced Course.
The fourth dimension, the subject of
the boys lecture. belongs to the high
est branch of mathematics and is COM
monty looked upon as study for only
the oldest and most experienced pro-
fessors. 1t exists only as a mathemat-
icai theory. The three obvious dimen-
sions of space may be illustrated by
straight line, by plane like the top
Of table and by cube. In the fourth
dimension the figures of the third di-
mension-for instance. the cube-are
used as sides. and figure is con-
structed. This figure can be explained
and illustrated only in terms of geom-
etry
Young Sidis has acquired his knowl-
edge of the subject by taking the most
advanced courses in mathematics
given at Harvard. He has worked out
a number Of original theories which
are said to have been accepted by
the mathematicians. The boy started
his lecture by an explanation of the
meaning of the fourth dimension and
then proceeded to show how these
fourth dimensional figures are con-
structed.
Fourth Dimensions Great Value.
people are apt to look on the fourth
dimension space as something of the
oretical value only" said young Sidis.
This is wrong. 1t has great value in
solving some of the most difficult of
geometrical problems. and a good I'M
Outstanding of the subject is apt to
geometry.
The fourth dimensional space is a
Euclidian space with one more dimen-
sion added to it, 1t is formed by a
direct perpendicular to the third di-
mensional space. In reasoning in this
space we take the axioms of plane
and solid geometry as evidence. The
fourth dimensional solid is called a
confguration. Any sort of third d.
mensional space may be the bounda-
ries of the fourth dimensionai space
In the fourth dimensiona space we
use the cube and polygons OF the
third dimensional space as faces and
with these construct the figure Of the
fourth dimension.
These figures cannot be grasped by
our mind, but can be reduced to a
geometric formula and can he con-
structed by the aid Of geometry and
algebra. 1t is possible to construct by
this means figures of the fourth dimen-
sion with 100 sides or faces, called
Observation-Disclosures or figures with
600 sides. called sexicocehedrigons.
Often there are gaps left in the fourth
dimensional spaces. and fill these up
by slipping in polyhedrigons OF the APP
propriate shape.
II attach great value in the working
OUT OIL my theories 10 the uelp gwen
by the polyhedral angles of the dodeca-
hebron which enter into many of the
problems. Some Of the things that
have found out about the fourth d.
mension will aid in the solution of
many Of the problems of elliptical
geometry"
Young Sidis, with the aid Of cray
on, explained the construction of
some fourth dimensiopal figures hith.
erto unknown to the professors. He
said that the new theories advanced
by him at the lecture would revolu-
: tionize the study Of geometry.
After the lecture the members of
the Harvard faculty and many others
who heard young Sidis crowded around
the youthful prodigy to ask him ques-
tons and to have him explain again
some of the more difficult of his the.
cries. which Sidis readily did.
AN fiHPOS1OK5S THICK.
The Cheerful Liar That Made a Fool