For my third essay i'm going to expore Napoleons triangle. First i am going to start with just a normal triangle seen here
Next i will make three equalateral triangles with the legs of my tiangle
it looks a little messy so we clean it up.
The red, blue and green triangles are the triangles formed by making equalateral triangles from our bases. We know need to find the center of the three resulting triangles and connect those to form our Napoleon triangle. We do this by making perpendicular lines from the arcs to the opposite base or leg. If we then put points on the intersections inside our three triangles we get this
We now connect these three intersections and the resulting black triangle is Napoleons triangle
What happens when you move a point on our original triangle arond. you can watch an animation by clicking here
No matter where you move a point in our original triangle Napoleons triangle always remains a equalateral triangle. Pretty cool!