Kasner Reports 'New Geometry';
Sum of Parts Exceeds the Whole
Columbia Mathematician Tells at the Harvard Tercentenary of
By-Product of Studying Horn Angle, With Its Curved Lines
—Fisher of London Offers a Brain-Teasing Problem.
By William L. Lawrence
Cambridge, Mass., Aug.
Discovery of a new type of geometry
in which the sum of the measure
of the parts is greater than the
measure of the whole was
nounced here today by Professor
Edward Kasner, Research Professor of Mathematics at Columbia
University, before the Mathematical
Association of America, meeting as
part of the program of the Harvard
Tercentenary Conference of Arts
and Sciences.
Professor Kasner's report was
made in the opening lecture on the
two-week program, in which invited
leaders in the sciences and the humanities will take stock of the advance of human knowledge during
the 300 years of Harvard's existence.
From this inventory of learning,
the first of its kind attempted at
any such gathering, it is hoped that
humanity may be helped in charting its course in the present chaos
of conflicting national, social and
economic interests.
At a lecture in the afternoon on
"Uncertain Inferences," Dr. Ron
ald Aylmer Fisher, Professor of Eugenics at the University of London,
presented before the gathering 01
several hundred noted mathematicians a new problem, the answer to
which, he said, is at present unknown, and which he offered "as a
challenge to our mathematical in-
The problem is as follows:
"The agricultural land of a pre-
dynastic Egyptian village is of unequal fertility. Given the height to
which the Nile will rise', the fertility of every portion of it is known
with exactitude,, but the height of
the flood affects different parts of
the teritory unequally. It is required to divide the area between
the several households of the village, so that the yield of the lots
assigned to each shall be in predetermined proportioas, whatever may
e the height to which the river
Professor Fisher added:
"If this problem is capable of a
general solution, one of the pri-