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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.
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.
Multiple proofs of this impossibility are known, and form part of the proof of Kuratowski's theorem characterizing planar graphs by two forbidden subgraphs, one of which is ,. The question of minimizing the number of crossings in drawings of complete bipartite graphs is known as Turán's brick factory problem , and for K 3 , 3 {\displaystyle K ...
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 ]
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In fluid dynamics the Milne-Thomson circle theorem or the circle theorem is a statement giving a new stream function for a fluid flow when a cylinder is placed into that flow. [ 1 ] [ 2 ] It was named after the English mathematician L. M. Milne-Thomson .
In graph-theoretic terms, the theorem states that for loopless planar graph, its chromatic number is ().. The intuitive statement of the four color theorem – "given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color" – needs to be interpreted appropriately to be correct.
In mathematics, the Laurent series of a complex function is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be applied.