This is the name for a family of triangles which all their sides are equal.
For instance: The basic 1-floor perfect triangle
This is a the simplest triangle to count.
The whole shape is a triangle so we have only 1 triangle in it.
Let’s sort & count the triangles.
We can easily see there are 4 basic triangles in it. One is in the top floor and three are in the base floor. We can’t find any triangle which consist of 2 or 3 basic ones but…
The whole shape (which is made of 4 triangles) is also a triangle so we have 4+1 = 5 triangles in it.
And what about the 3-floors perfect triangle?
You can count by the floors from top downwards 1+3+5=9 basic triangles.
That means the floors number is doubled by itself.
If we examine the shape it is clear that there are no triangles that are made of 2 or 3 basic ones.
But when you look at the diagram you can see there are exactly 3 triangles that contain 4 basic ones.
There are no triangles which are made of 5 or 6 or 7 or 8 basic ones.
But of course there is one big triangle composed of 9 basic ones which is the whole shape.
Let’s sum it all up: we have a total of 9+3+1=13 triangles in this 3-floors regular triangle.
the 4-floors perfect triangle?
And how many are in
the 5-floors perfect triangle?
…and in the 6-floors perfect triangle?
Can you find connections between the number of floors in such a triangle and the number of triangles you can find in it?
All these questions are answered in the e-book:
It will be available soon in Amazon.com!