Can you fit an infinite amount of triangles in a nonagon?

Question

A nonagon has 9 sides.

A triangle has 3 sides.

9 can be divided by 3.

My theory is if you took a regular nonagon, could you fit an infinite amount of triangles inside of it, disregarding the triangles having a static size?

Let the triangles be able to shrink each time a new one is added. Would you be able to fit an infinite amount without ever leaving an empty gap inside of a nonagon?

DWRead · Answer

A regular nonagon can be divided radially into 9 congruent, isosceles triangles.
Each triangle can be divided radially into three triangles (although they will not be congruent).

Morningfox · Answer

Any plane shape with straight sides can fit an infinite number of triangles inside it, if the triangles are infinitely small.

D g · Answer

Guess what you just stumbled on the basis of calculus.

The thought is that if you can count or add up the infinitesimally small areas or volumes you can find something about the object such as volume or area ....  Since the tiny parts are infinitely small you can get an infinite number in them

Can you fit an infinite amount of triangles in a nonagon?

3 Answers