EUCLID CHALLENGE

Successful Response by Milton Mintz

May 10, 2002


Page 1: Background

 

Euclid Challenge: With unmarked straightedge and compass,

  1. Trisect any angle

  2. Square a circle

  3. 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”:

  1. Trisect any angle
  2. Square a circle.

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 :

  1. The millions of people who had geometry classes and were told “It is impossible to 
    successfully
    respond to Euclid Challenge”;

  2. The geometry Teachers and Professors, high school and college, who are now instructing 
    their students: “It is impossible to successfully respond to Euclid Challenge”;

  3. 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.


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