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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.
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 ...
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 ...
Geometric solutions of the Thomson problem for N = 4, 6, and 12 electrons are Platonic solids whose faces are all congruent equilateral triangles. Numerical solutions for N = 8 and 20 are not the regular convex polyhedral configurations of the remaining two Platonic solids, the cube and dodecahedron respectively.
WASHINGTON — With Donald Trump heading back to the White House, a growing band of younger, more energetic House Democrats is challenging seasoned veterans for powerful congressional posts ...
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Fatal flaw #4: Multiple material misstatements . Finally, the April proxy statement that asked shareholders to ratify Musk’s pay after the court rescinded it was “materially misleading ...