Discovery
Although he is credited for its discovery, Karl Wilhelm Feuerbach did not entirely discover the nine-point circle, but rather the six point circle, recognizing the significance of the midpoints of the three sides of the triangle and the feet of the altitudes of that triangle. (See Fig. 1, points D, E, F, G, H, and I.) (At a slightly earlier date, Charles Brianchon and Jean-Victor Poncelet had stated and proven the same theorem.) But soon after Feuerbach, mathematician Olry Terquem himself proved the existence of the circle. He was the first to recognize the added significance of the three midpoints between the triangle's vertices and the orthocenter. (See Fig. 1, points J, K, and L.) Thus, Terquem was the first to use the name nine-point circle.
Read more about this topic: Nine-point Circle
Famous quotes containing the word discovery:
“We are all humiliated by the sudden discovery of a fact which has existed very comfortably and perhaps been staring at us in private while we have been making up our world entirely without it.”
—George Eliot [Mary Ann (or Marian)
“It was one of those evenings when men feel that truth, goodness and beauty are one. In the morning, when they commit their discovery to paper, when others read it written there, it looks wholly ridiculous.”
—Aldous Huxley (1894–1963)
“I have known no experience more distressing than the discovery that Negroes didn’t love me. Unutterable loneliness claimed me. I felt without roots, like a man without a country ...”
—Sarah Patton Boyle, U.S. civil rights activist and author. The Desegregated Heart, part 1, ch. 10 (1962)