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:
“As the mother of a son, I do not accept that alienation from me is necessary for his discovery of himself. As a woman, I will not cooperate in demeaning womanly things so that he can be proud to be a man. I like to think the women in my son’s future are counting on me.”
—Letty Cottin Pogrebin (20th century)
“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)
“That the discovery of this great truth, which lies so near and obvious to the mind, should be attained to by the reason of so very few, is a sad instance of the stupidity and inattention of men, who, though they are surrounded with such clear manifestations of the Deity, are yet so little affected by them, that they seem as it were blinded with excess of light.”
—George Berkeley (1685–1753)