A Rigorous Geometrical Proof on Constructability of Magnitudes (A Classical Geometric Solution for the Factors: √2 and √(3&2))

Authors

  • Munyambu .C. June Meru University of Science and Technology, Kenya
  • Kimuya Alex Meru University of Science and Technology

Keywords:

Delian Constant, Pythagorean Factor, Constructible Magnitudes, Constructible Points, Rational Numbers, Irrational Numbers, Euclidean Geometry, Doubling A Square, Constructability

Abstract

In the absence of a comprehensive geometrical perceptive on the nature of rational (commensurate) and irrational (incommensurate) geometric magnitudes, a solution to the ages-old problem on the constructability of magnitudes of the forms  and  (the square root of two and the cube root of two as used in modern mathematics and sciences) would remain a mystery. The primary goal of this paper is to reveal a pure geometrical proof for solving the construction of rational and irrational geometric magnitudes (those based on straight lines) and refute the established notion that magnitudes of form  are not geometrically constructible. The work also establishes a rigorous relationship between geometrical methods of proof as applied in Euclidean geometry, and the non-Euclidean methods of proof, to correct a misconception governing the geometrical understanding of irrational magnitudes (expressions). The established proof is based on a philosophical certainty that "the algebraic notion of irrationality" is not a geometrical concept but rather, a misrepresentative language used as a means of proof that a certain problem is geometrically impossible.

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Author Biographies

Munyambu .C. June, Meru University of Science and Technology, Kenya

Department of Education Science (Physics/Mathematics)

Kimuya Alex, Meru University of Science and Technology

Department of Physical Sciences (Physics)

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Published

2020-04-30

How to Cite

Munyambu .C. June, & Kimuya Alex. (2020). A Rigorous Geometrical Proof on Constructability of Magnitudes (A Classical Geometric Solution for the Factors: √2 and √(3&2)). MathLAB Journal, 5, 117-142. Retrieved from https://purkh.com/index.php/mathlab/article/view/730

Issue

Section

Research Articles