Shapes and Spaces

Pieces of shapes can be combined to form different 3-dimensional objects in spaces.

Get some equilateral triangles.

Try taping the edges of 3 equilateral triangles around a point.
You get a convex tent (tetrahedron).

How about taping 4 or 5 triangles together?
You still get convex tents, but with different shapes (square pyramid, pentagonal pyramid).

Try using 6 triangles.
You get a flat surface!

How about 7or 8 triangles?
The surface ripples up and down.

Triangles can also form other shapes... such as a dome.

The Secret ...

What makes taped triangles to create a flat surface?

The trick is: if the sum of the angles around a point = 360o, then the surface will be flat.

In our case, each angle of a equilateral triangle is 60o, so we need 6 triangles to form a flat surface (6 * 60o = 360o). Otherwise, the shape will be floppy!