matematicas visuales visual math

We can start with a triangle and its circunscribed circle. If P is any point belonging to this circuncircle:

Simson Line, Simson-Wallace Line: triangle and circuncircle | matematicasVisuales

Then we can consider the feet of the perpendiculars from P to the three sides of the triangle (these are ortogonal projections of a point onto the sides or their prolongations):

Simson Line, Simson-Wallace Line: feet of perpendiculars to the three sides of a triangle | matematicasVisuales

These three feet of the perpendiculars lie on a line:

Simson Line, Simson-Wallace Line: three points that are collinear | matematicasVisuales

This line is called the Simson Line of P respect to the triangle or Wallace-Simson Line. The first to mention this line was Wallace (1768-1843), in 1799, thirty years after Simson's death (1687-1768).

REFERENCES

Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: John Wiley and sons, 1969.
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer.
Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, 1965.

MORE LINKS

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Interactive 'Mostation' of the property of central and inscribed angles in a circle. Case II: When one chord that forms the inscribed angle is a diameter.
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Interactive 'Mostation' of the property of central and inscribed angles in a circle. The general case is proved.
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Morley Theorem
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John Conway's proof of Morley's Theorem
Interactive animation about John Conway's beautiful proof of Morley's Theorem