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On the projection of the three vertices of an equilateral triangle

M. Gabriella Kuhn, N. Silvio Riccobon

Abstract

We prove the following Theorem: Given any three distinct points on a straight line r, there exist an equilateral triangle, whose circumcenter lies on r, such that the projections of its vertices on r are exactly the three given points.

On the projection of the three vertices of an equilateral triangle

Abstract

We prove the following Theorem: Given any three distinct points on a straight line r, there exist an equilateral triangle, whose circumcenter lies on r, such that the projections of its vertices on r are exactly the three given points.
Paper Structure (8 sections, 46 equations, 9 figures)

This paper contains 8 sections, 46 equations, 9 figures.

Table of Contents

  1. Introduction
  2. The signed measurement of oriented segments
  3. Theorem of the three aligned points
  4. 1st Step
  5. 2nd Step
  6. 3rd Step
  7. 4th Step
  8. Corollary

Figures (9)

  • Figure : Figure 0: What we have to prove
  • Figure : Figure 0.1 : The Symmetric Solution
  • Figure : Figure 1.1
  • Figure : Figure 1.2
  • Figure : Figure 1.3
  • ...and 4 more figures