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Thomsen's theorem, named after Gerhard Thomsen, is a theorem in elementary geometry. It shows that a certain path constructed by line segments being parallel to the edges of a triangle always ends up at its starting point.
Thomsen's theorem This page was last edited on 2 June 2024, at 17:31 (UTC). Text is available under the Creative Commons Attribution-ShareAlike 4.0 License ...
Thomsen wrote 22 papers on various topics in geometry and furthermore a few papers on theoretical physics as well. The latter were mostly written in Italian rather than in German. Thomsen also wrote a book on the foundations of elementary geometry. [1] In elementary geometry Thomsen's theorem is named after him. [5]
Also in 2016, Quizlet launched "Quizlet Live", a real-time online matching game where teams compete to answer all 12 questions correctly without an incorrect answer along the way. [ 15 ] In 2017, Quizlet created a premium offering called "Quizlet Go" (later renamed "Quizlet Plus"), with additional features available for paid subscribers.
If in the affine version of the dual "little theorem" point is a point at infinity too, one gets Thomsen's theorem, a statement on 6 points on the sides of a triangle (see diagram). The Thomsen figure plays an essential role coordinatising an axiomatic defined projective plane. [ 6 ]
For non-integrable Riesz kernels, the Poppy-seed bagel theorem holds, see the 2004 work of Hardin and Saff. [9] Notable cases include: [10] α = ∞, the Tammes problem (packing); α = 1, the Thomson problem; α = 0, to maximize the product of distances, latterly known as Whyte's problem; α = −1 : maximum average distance problem.
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin( α + β ) = sin α cos β + cos α sin ...
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