## Special Cases of Napoleon Triangles

##### Abstract

The first chapter of this thesis provides a brief history of Napoleon’s theorem. Napoleon
is attributed with proposing a theorem that bears his name is geometry. Since his
authorship is often questioned, we examine: Could Napoleon have proposed the theorem
that bears his name? Did he prove the theorem?
In the second chapter, special cases of Napoleon triangles are studied. The following
questions are addressed: If an isosceles (right angle) mother triangle is given, what
properties must the external and internal Napoleon triangles have? What properties must
the external and internal Napoleon triangles of a mother triangle have to ensure that the
mother triangle is an isosceles (right angle) triangle?
In the third chapter special cases of relative Napoleon triangles are studied. The same
questions explored in Chapter 2 are asked here as well. If a triangle is an isosceles (right
angle) mother triangle, what properties must the relative external and relative internal .
Napoleon triangles have? What properties must the relative external and relative internal .
Napoleon triangles of a mother triangle have to ensure that the mother triangle is an
isosceles (right angle) triangle?