What Is A Tessellation In Math

Tessellations are patterns formed by tiling shapes together without any gaps. Regular tessellations are created using regular polygons.

For a shape to tessellate, the sum of the interior angles of the shapes meeting at any vertex must be 360 degrees. This means that 360 must be perfectly divisible by the interior angle of the polygon, without any decimal remainder.

An equilateral triangle has interior angles of 60 degrees. Since 360 divided by 60 is 6 (a whole number), equilateral triangles will tessellate.

A regular pentagon has interior angles of 108 degrees. Dividing 360 by 108 results in a decimal, indicating that a regular pentagon will not tessellate.

The video challenges viewers to determine if other regular polygons will tessellate by applying the same rule.