History
Geometrical problems involving tangent circles have been pondered for millennia. In ancient Greece of the third century BC, Apollonius of Perga devoted an entire book to the topic. Unfortunately the book, which was called On Tangencies, is not among his surviving works.
René Descartes discussed the problem briefly in 1643, in a letter to Princess Elizabeth of Bohemia. He came up with essentially the same solution as given in equation (1) below, and thus attached his name to the theorem.
Frederick Soddy rediscovered the equation in 1936. The kissing circles in this problem are sometimes known as Soddy circles, perhaps because Soddy chose to publish his version of the theorem in the form of a poem titled The Kiss Precise, which was printed in Nature (June 20, 1936). Soddy also extended the theorem to spheres; Thorold Gosset extended the theorem to arbitrary dimensions.
Read more about this topic: Descartes' Theorem
Famous quotes containing the word history:
“I believe that in the history of art and of thought there has always been at every living moment of culture a “will to renewal.” This is not the prerogative of the last decade only. All history is nothing but a succession of “crises”Mof rupture, repudiation and resistance.... When there is no “crisis,” there is stagnation, petrification and death. All thought, all art is aggressive.”
—Eugène Ionesco (b. 1912)
“While the Republic has already acquired a history world-wide, America is still unsettled and unexplored. Like the English in New Holland, we live only on the shores of a continent even yet, and hardly know where the rivers come from which float our navy.”
—Henry David Thoreau (1817–1862)
“In history an additional result is commonly produced by human actions beyond that which they aim at and obtain—that which they immediately recognize and desire. They gratify their own interest; but something further is thereby accomplished, latent in the actions in question, though not present to their consciousness, and not included in their design.”
—Georg Wilhelm Friedrich Hegel (1770–1831)