Successful Response by Milton Mintz
May 10, 2002
Page 1: Background
Euclid Challenge: With unmarked straightedge and compass,
Trisect any angle
Square a circle
Double a cube
For over two thousand years, geometry teachers have told their students: “Euclid
Challenge
-- It is impossible to have a
Successful Response”.
After creating many failed methods since
1963, I am thrilled to state that in 2000/2001, I was able
to create a
successful response with an “Unmarked straightedge and compass”:
In my introduction of "Trisect any angle" is a review by Professor Clifford J. Earle, Cornell University, an eminent Professor of Mathematics.
The two most
famous Failed attempts to “Trisect any angle” using Euclid’s Tools:
Unmarked straightedge and compass only:
Archimedes: He used a Marked straightedge (two scratches on the straightedge);
Hippias: He used the Uniform Rate with a Non-Euclidian Device, instead of
Euclid’s Tools:
Unmarked straightedge and compass.
My successful
response, using Euclid’s Tools, should be of great interest to :
The millions of people who had geometry
classes and were told “It is impossible to
successfully respond
to Euclid Challenge”;
The geometry Teachers and Professors, high
school and college, who are now instructing
their students: “It is
impossible to successfully respond to Euclid Challenge”;
All Mathematical Societies, including: American Mathematical Society,
American Mathematical
Association of Two-Year Colleges, Association for Women in
Mathematics, Mathematical
Association of America, Society for Industrial and
Applied Mathematics.
One Professor
in an article stated: “What is the most difficult math problem to solve?
The
ancient Greeks began stewing over the following problem: using only a compass
and unmarked
straightedge, divide a 60° angle into three equal parts. In other
words, construct a 20° angle.
No protractors allowed.”
Since 60° is frequently used as a test
angle is the reason I used 30° as my example, so that the
answer could be
doubled.
Home Page | Top of Page | Next Page