Nnapoleon's theorem pdf files

Napoleon s theorem, on each side of a given arbitrary triangle describe an equilateral triangle exterior to the given one, and join the centers of the three thus obtained equilateral triangles. Napoleon s chair can be seen in the lefthand side of the painting, napoleon s death on the island of st. Pdf development of napoleons theorem on the rectangles in. A generalization of the napoleons theorem awesomemath. There is a historical anecdote about napoleon who was emperor of the french. Pdf napoleons theorem in regular polygons researchgate. Napoleons theorem and generalizations through linear. Geombinatorics 102001, 116 121 116 a relative of napoleon s theorem branko grunbaum department of mathematics, box 354350 university of washingtonseattle, wa 981954350 email. The classical napoleon s theorem states that the centers of the equilateral triangles which were built to the sides of any triangle are the vertices of an equilateral triangle. Pdf in this article we discuss napoleons theorem on the rectangles having two pairs of parallel sides for the case. The proof of napoleons theorem is carried out using a congruence approach. Anecdote about napoleon bonaparte 17691821 napoleon was known as an amateur mathematician. In geometry, napoleons theorem states that if equilateral triangles are constructed on the sides.

Geombinatorics 102001, 116 121 a relative of napoleon. A generalization of the napoleons theorem khakimboy egamberganov abstract in this article we present a generalization of the napoleons theorem. To give another proof napoleon s theorem, and in the process discover how to express the sides of the napoleon s triangle in terms of the sides of the given triangle, consider the general case of a triangle with edge lengths a,b,c placed on a cartesian coordinate system with the side c on the x axis as shown below. It is known that napoleon bonaparte was a bit of a mathematician with a great interest in geometry. In this article we discuss napoleon s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. Napoleons theorem states that if equilateral triangles abc, bca, and cab are erected outwardly on the sides of any triangle abc, then the centroids c. A remarkable theorem of elementary geometry is often called napoleon s theorem. The aim of this work is to use napoleon s theorem in different regular polygons, and decide whether we can prove napoleon s theorem is only limited with triangles or it could be done in other. With the three sides of the triangle as bases, construct three equilateral triangles, each one outside. Napoleons theorem states the fact that if equilateral triangles are drawn. The proof of napoleon s theorem is carried out using a. Napoleons theorem does not specify whether the equilateral triangles constructed need to be outward.