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Thomsen's theorem, = 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.
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.
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]
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 ...
Haboush's theorem (algebraic groups, representation theory, invariant theory) Harnack's curve theorem (real algebraic geometry) Hasse's theorem on elliptic curves (number theory) Hilbert's Nullstellensatz (theorem of zeroes) (commutative algebra, algebraic geometry) Hironaka theorem (algebraic geometry) Hodge index theorem (algebraic surfaces)
Due to the Pythagorean theorem the number () has the simple geometric meanings shown in the diagram: For a point outside the circle () is the squared tangential distance | | of point to the circle . Points with equal power, isolines of Π ( P ) {\displaystyle \Pi (P)} , are circles concentric to circle c {\displaystyle c} .
The use of the Pythagorean theorem and the tangent secant theorem can be replaced by a single application of the power of a point theorem. Case of acute angle γ, where a < 2b cos γ. Drop the perpendicular from A onto a = BC, creating a line segment of length b cos γ. Duplicate the right triangle to form the isosceles triangle ACP.
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 ]