Asymmetric Propeller
What Is It?
A Mathematical Droodle


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Explanation

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Copyright © 1996-2017 Alexander Bogomolny

This is a generalization of a theorem about three equilateral triangles, but it also admits a further generalization.

In the current form, it states that a configuration of three similar (and similarly oriented) triangles that share a vertex at which all three non corresponding angles meet has an interesting property. Namely, the midpoints of segments that join not paired "free" vertices of the three triangles form a fourth triangle similar to the given three.

In this form, the theorem is equivalent to the Fundamental Theorem of 3-Bar Motion.

Asymmetric Propeller

  1. Asymmetric Propeller (An Interactive Gizmo)
  2. Asymmetric Propeller: a Generalization
  3. A Case of Similarity
  4. Napoleon's Propeller
  5. Asymmetric Propeller and Napoleon's Theorem
  6. Asymmetric Propeller by Plane Tiling
  7. A Final Chapter of the Asymmetric Propeller Story

|Activities| |Contact| |Front page| |Contents| |Geometry| |Store|

Copyright © 1996-2017 Alexander Bogomolny

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