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.
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Famous quotes containing the word discovery:
“He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one.”
—Henry David Thoreau (1817–1862)
“We early arrive at the great discovery that there is one mind common to all individual men: that what is individual is less than what is universal ... that error, vice and disease have their seat in the superficial or individual nature.”
—Ralph Waldo Emerson (1803–1882)
“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)