EUCLID CHALLENGE

Successful Response by Milton Mintz

May 10, 2002

Page 3: Trisection of Any Angle by Straightedge and Compass

Introduction

 This method received the following review by Professor Clifford J. Earle:

1. Construction of an angle trisector is successful
2. Points are moved at a uniform rate
3. The method goes beyond traditional Euclidian methods

1. Angle trisector: Accomplished by using straightedge and compass only. No scratches on the straightedge that were used by Archimedes.
    
2. “Uniform Rate”: This Method includes PROOF of the accuracy of its use of the SAME Uniform Rate by BOTH hands.
   (Hippias used a “Uniform Rate” in his “Non-Euclidian device” over two thousand years ago. His use of a “Uniform Rate” has been accepted over the years, but he used tools other than “straightedge and compass only”).
    
3. Traditional Euclidian Methods:
   1. Pierre Wantzel proved during the 19^th century that it was impossible to trisect all angles by straightedge and compass, when following the “Traditional Euclidian Methods”.
   2. That is why to “successfully construct a Trisector”,  using only a “straightedge and compass only”, it was necessary for the attached Method to go “Beyond the Traditional Euclidian Methods”.

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