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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. Consider an arbitrary triangle ABC with a point P 1 on its edge BC.
He is really interested in problems 3 and 4, but the answers to the easier problems 1 and 2 are needed for proving the answers to problems 3 and 4. 1st problem [ edit ]
Midpoint theorem (triangle) Mollweide's formula; Morley's trisector theorem; N. ... Thomsen's theorem This page was last edited on 2 June 2024, at 17:31 (UTC). Text ...
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]
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.
[1] An easy formula for these properties is that in any three points in any shape, there is a triangle formed. Triangle ABC (example) has 3 points, and therefore, three angles; angle A, angle B, and angle C. Angle A, B, and C will always, when put together, will form 360 degrees. So, ∠A + ∠B + ∠C = 360°
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 ]
Louis Melville Milne-Thomson CBE FRSE RAS (1 May 1891 – 21 August 1974) was an English applied mathematician who wrote several classic textbooks on applied mathematics, including The Calculus of Finite Differences, Theoretical Hydrodynamics, and Theoretical Aerodynamics.