The nine-point circle owes its discovery to a group of famous mathematicians over the course of about 40 years, though it is most generally -though perhaps not most fairly- attributed to Karl Feuerbach, a German mathematician who "rediscovered" it in the nineteenth century (however it was known even to Euler) (Dorrie, "100 Great Problems"); and its subsequent properties and corrolaries were explored heavily for some 30 years after, and are still being investigated today. The first major discovery that led to the discovery of the nine-point circle was by Benjamin Bevan in 1804 as he made a mathematical proposal that inevitably established the conclusions that “the nine point center bisects the distance between the circumcentre and the orthocenter, and that the radius of the nine-point circle is half the radius of the circumcircle”(Mackay, "History of the Nine Point Circle").
A mathematician by the name of John Butterworth later in 1804 proved this proposal and subsequent conclusions in mathematical journals, and in 1807 formed a key question for the further exploration of Benjamin Bevan’s proposed phenomenon. He asks, “When the base and vertical angle are given, what is the locus of the centre of the circle passing through the three centres of the circles touching one side and the prolongation of the other two sides of a plane triangle?” in 1806. In response a man by the name of John Whitley made the important discovery that the circumcircle of a triangle intersects two of the midpoints of the sides, two of the feet of the altitudes of the triangle, as well as two of the mid points of the segments intercepted between the orthocenter and the vertices. At this point in time only seven of the nine points had been discovered. It is worth noting that by the nature of Whitney’s proof he must have been aware of the other two points, and he could have easily proven them. However, because of the purpose he had when creating the proof he was not required to prove their existence, and therefore they were not even mentioned in his proof" (Mackay, "History of the Nine Point Circle").
The discovery of the full nine-points and the full nine points were fully mentioned for the first time in 1821 by Jean-Victor Poncelet and his partner Bianchon in a mathematical journal. Soon after in 1822 Karl Feurbach proved the existence of the same circle independently and received much of the credit for its discovery. Up until this point in time there was no official name for this circle that had been discovered but in 1842 a man by the name of Olry Terquem coined the term the nine-point circle in an analytical proof investigating some of the subsequent properties of the circle. Today we know of at least 25 important points that actually lie on the so called "Nine point circle" (Mackay, "History of the Nine Point Circle").
Although the nine-point circle is a very interesting and unique mathematical phenomenon, it does not have many practical uses outside the world of academia. People within academia care about the nine point circle because its distinct characteristics can be used in several related mathematical discussions and discoveries. These include Lester's theorem, Feurbach's theorem, and the nine point hyperbola, amongst numerous other mathematical proofs and ideas.
A mathematician by the name of John Butterworth later in 1804 proved this proposal and subsequent conclusions in mathematical journals, and in 1807 formed a key question for the further exploration of Benjamin Bevan’s proposed phenomenon. He asks, “When the base and vertical angle are given, what is the locus of the centre of the circle passing through the three centres of the circles touching one side and the prolongation of the other two sides of a plane triangle?” in 1806. In response a man by the name of John Whitley made the important discovery that the circumcircle of a triangle intersects two of the midpoints of the sides, two of the feet of the altitudes of the triangle, as well as two of the mid points of the segments intercepted between the orthocenter and the vertices. At this point in time only seven of the nine points had been discovered. It is worth noting that by the nature of Whitney’s proof he must have been aware of the other two points, and he could have easily proven them. However, because of the purpose he had when creating the proof he was not required to prove their existence, and therefore they were not even mentioned in his proof" (Mackay, "History of the Nine Point Circle").
The discovery of the full nine-points and the full nine points were fully mentioned for the first time in 1821 by Jean-Victor Poncelet and his partner Bianchon in a mathematical journal. Soon after in 1822 Karl Feurbach proved the existence of the same circle independently and received much of the credit for its discovery. Up until this point in time there was no official name for this circle that had been discovered but in 1842 a man by the name of Olry Terquem coined the term the nine-point circle in an analytical proof investigating some of the subsequent properties of the circle. Today we know of at least 25 important points that actually lie on the so called "Nine point circle" (Mackay, "History of the Nine Point Circle").
Although the nine-point circle is a very interesting and unique mathematical phenomenon, it does not have many practical uses outside the world of academia. People within academia care about the nine point circle because its distinct characteristics can be used in several related mathematical discussions and discoveries. These include Lester's theorem, Feurbach's theorem, and the nine point hyperbola, amongst numerous other mathematical proofs and ideas.