matematicas visuales visual math

The three points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle called the Morley Triangle.

This was a surprising discovery made by Frank Morley (1899).

We start with any triangle and trisect each of its angles...

Morley Theorem: We start with any triangle and trisect its angles | matematicasVisuales

Extend the trisections ...

Morley Theorem: extending the trisectors | matematicasVisuales

We consider the three points of intersection of the adjacent trisectors ...

Morley Theorem: We consider the three points of intersection of the adjacent trisectors | matematicasVisuales

And we always get an equilateral triangle.

Morley Theorem: And we always get an equilateral triangle | matematicasVisuales

In the near future I am going to publish an animation with John Conway's proof of Morley's Theorem.

REFERENCES

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer.
Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: John Wiley and sons, 1969.

MORE LINKS

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Steiner deltoid is a hypocycloid related with the nine point circle of a triangle.
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