# Asymmetric Propeller

What Is It?

A Mathematical Droodle

What if applet does not run? |

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Copyright © 1996-2018 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

- Asymmetric Propeller (An Interactive Gizmo)
- Asymmetric Propeller: a Generalization
- A Case of Similarity
- Napoleon's Propeller
- Asymmetric Propeller and Napoleon's Theorem
- Asymmetric Propeller by Plane Tiling
- The Final Chapter of the Asymmetric Propeller Story
- Asymmetric Propeller, the XXI Century

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

Copyright © 1996-2018 Alexander Bogomolny

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