Napoleon's Theorem NAPOLEON S theorem. If equilateral triangles are erected externally on the sides of any triangle then their centers form an equilateral http://axp.mat.uniroma2.it/~tauraso/Java/Napoleon/napo.html
Napoleon's Theorem Napoleon s theorem. Amer., pp. 6065, 1967. Pappas, T. ``Napoleon s theorem. The Joy of Mathematics. San Carlos, CA Wide World Publ./Tetra, p. 57, 1989. http://icl.pku.edu.cn/yujs/MathWorld/math/n/n020.htm
Extractions: If Equilateral Triangles are erected externally on the sides of any Triangle , then the centers form an Equilateral Triangle (the outer Napoleon Triangle ). Furthermore, the inner Napoleon Triangle is also Equilateral and the difference between the areas of the outer and inner Napoleon triangles equals the Area of the original Triangle See also Napoleon Points Napoleon Triangles References Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 60-65, 1967. Pappas, T. ``Napoleon's Theorem.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 57, 1989. Didaktik der Mathematik Wentzel, J. E. ``Converses of Napoleon's Theorem.'' Amer. Math. Monthly
Napthm Napoleon s theorem is the name popularly given to a theorem which states that if equilateral triangles are constructed on the three legs of any triangle, the http://www.pballew.net/napthm.html
Extractions: and the Napoleon Points Napoleon's Theorem is the name popularly given to a theorem which states that if equilateral triangles are constructed on the three legs of any triangle, the centers of the three new triangles will also form an equilateral triangle. In the figure the original triangle is labeled A, B, C, and the centers of the three equilateral triangles are A', B', C'. If the segments from A to A', B to B', and C to C' are drawn they always intersect in a single point, called the First Napoleon Point. If the three equilateral triangles are drawn interior to the original triangle, the centers will still form an equilateral triangle, but the segments connecting the centers with the opposite vertices of the original triangle meet in a (usually) different point, called the 2nd Napoleon Point.
Index A Generalization of Napoleon s theorem. Napoleon s theorem Explorations. Napoleon s theorem (Jessica D. Dwy). Interactive Geometry Problem. http://poncelet.math.nthu.edu.tw/chuan/99s/
Napoleon Theorem Napoleon s theorem. (?). 2, 114, Generalize Napoleon s theorem. (). http://poncelet.math.nthu.edu.tw/usr3/summer99/18/work14.html
Extractions: Napoleon's Theorem Illustrate Napoleon's Theorem : the centers L, M, N of the three equilateral triangles DBXC, DCYA, DAZB built outwards on the sides BC, CA, AB of an arbitrary triangle DABC are the vertices of an equilateral triangle. The same is true of the centers of the three inward equilateral triangles. Generalize Napoleon's Theorem.
Extractions: Home ClassPad News Overview Buy a ClassPad Now ... Saltire Family of Websites Napoleons Theorem with the Casio ClassPad Napoleons theorem offers a tour de force for constraint geometry. The theorem states that for any arbitrary triangle, if you construct an equilateral triangle on each edge, and join the centers of the incircles of these triangles, then the resulting triangle is equilateral. The theorem is named for, and supposedly discovered by, Napoleon Bonaparte, himself no stranger to tours de force. Now lets join the centers of these circles. Shading the resulting triangle makes it stand out from the cats cradle of lines and circles. If youre not convinced that it is indeed equilateral - and why should you be, Napoleon was more famous for geopolitics than geometry - inspect its side lengths
Originator Of Napoleon's Theorem? forum.swarthmore.edu/ces95/napoleon.html @fph s ps, pdf, A proof of Napoleon s theorem (given a triangle, erect equilateral triangles on its sides then their centroids form another equilateral triangle) which http://forum.swarthmore.edu/epigone/geometry-college/ninmaxsmel
ICTCM-8 Abstract In elementary Euclidean geometry this result is known as Napoleon s theorem. Consider the following generalization of this construction. http://archives.math.utk.edu/ICTCM/abs/8-C96.html
Extractions: E-mail: firstname.lastname@example.org If equilateral triangles are constructed outwards or inwards on the sides of any given triangle, the centroids of these triangles are the vertices of an equilateral triangle. In elementary Euclidean geometry this result is known as Napoleon's Theorem. In this paper we adapt the foregoing construction to certain classes of spherical triangles and use a CAS to determine various values of s,t with the properties given above.
Math Resources From Grau-Hall Scientific Mutually prime integers, My logo, 9Point Circle, Nine point cirle, Nagel point, Napier Bones, Napoleon s theorem, Napoleon s theorem, a generalization http://www.grauhall.com/math.htm
Napoleon.html Here is a very short code that proves Napoleon s theorem that says that if you erect equilateral triangles on the three sides of an arbitrary triangle, then http://www.math.temple.edu/~zeilberg/mamarim/mamarimhtml/Napoleon.html
Extractions: BY SHALOSH B. EKHAD (Exclusive to the Personal Journal of Shalosh B.Ekahd and Doron Zeilberger.) Written: Jan. 4, 1998 Thanks to Rene Descartes all plane geometry is routine in principle, and thanks to computer algebra, it is also routine in practice. However, it is still a challenge to write Maple code that takes as few characters as possible. Here is a very short code that proves Napoleon's Theorem that says that if you erect equilateral triangles on the three sides of an arbitrary triangle, then their cirmcumcenters forms yet another equilateral triangle. Maple Source Code (Plain Text File) The Personal Journal of Shalosh B. Ekhad and Doron Zeilberger Doron Zeilberger's Home Page Shalosh B. Ekhad's Home Page
Gleichseitiges Dreieck theorem (A proof by tesselation, A proof with complex numbers, A second proof with complex numbers, Two proofs http://www.mathematische-basteleien.de/dreieck.htm