FRACTALS: AN APPLICATION OF NAPOLEON'S THEOREM

Abstract

Fractal geometry allows for interdisciplinary with various topics in mathematics and other fields, from the natural sciences to economics and technology. The present work approaches the construction of a fractal as an application of a very important theorem of plane geometry, known as Napoleon's Theorem. We apply Napoleon's theorem in an equilateral triangle obtaining the famous Star of David, the star's ends form new equilateral triangles and the theorem is used again, this process is applied successively and the result obtained is a fractal that resembles the curve of Koch. The objective of this work is to find the perimeter and the fractal area, for this, concepts of plane geometry, similarity and congruence of triangles and also some discrete math topics, sequences and numerical series will be necessary to achieve this goal.