Taylor Circle Theorem: Triangle, Altitudes, Perpendiculars. Level: High School, SAT Prep, College

From the feet of each altitude of a triangle ABC, draw lines perpendicular to the adjacent sides. Then the feet of these six perpendiculars lie on a circle called the Taylor Circle.

Click the red button below to start the animation. Drag A, C, AC. Activate Step-by-Step bar and use the next step button


The circle is named after H.M.Taylor (1842-1927) who discussed it in 1883.

Reference: The Relations of the Intersections of a Circles with a Triangle, HM Taylor - Proceedings of the London Mathematical Society, 1883.

Dynamic Geometry: You can alter the figure above dynamically in order to test and prove (or disproved) conjectures and gain mathematical insight that is less readily available with static drawings by hand.

This page uses the TracenPoche dynamic geometry software and requires Adobe Flash player 7 or higher. TracenPoche is a project of Sesamath, an association of French teachers of mathematics.

Instruction to explore the illustration above:

  • Animation. Click the red button to start/stop animation

  • Manipulate. Drag points A and C to change the figure.

  • Step by Step construction. Press P and click the left mouse button on any free area to show the step-by-step bar and start the construction:
    Hide the step-by-step bar by using again the combination P + click left mouse button.

Henry Martyn Taylor and the blind student of mathematics

"One Braille notation was devised by the eminent Cambridge mathematician, Henry Martyn Taylor, who was overtaken by blindness in 1894, when engaged in the preparation of an edition of Euclid for the Cambridge University Press. By means of his ingenious and well thought out Braille notation he was enabled to transcribe many advanced scientific and mathematical works, and in 1917, with the assistance of Mr. Emblen, a blind member of the staff of the National Institute for the Blind, he perfected it. It was recognised as so comprehensive that it was soon adopted as the standard mathematical and chemical notation, and is universally used by English-speaking people." Taken from: NEW BEACON, Vol. XVIII, No. 210, June 15, 1934, pp. 146-148




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