Math Question by HM

Henry

Hiffin — 2014-10-31 14:21:49 UTC

The theme I will be sharing with you today is: Which Polygons can be used to tile a surface without any overlaps or gaps?

Tiling

Hiffin — 2014-10-31 14:23:34 UTC

In order to tile properly, you have

to have the exterior angles of whichever shapes

are touching the vertex, sum up to 360.

Tool

Hiffin — 2014-10-31 14:27:21 UTC

Here is a tool to help you visualize what you will be tiling.

Squares

Hiffin — 2014-10-31 14:41:06 UTC

Squares are one of the easiest polygons to tile beacuse they have four exterior angles of 90 degrees.

Triangles

Hiffin — 2014-10-31 14:42:54 UTC

Triangles are also a very easy polygon to tile, because each exterior angle is equal to 60 degrees, meaning that three triangles is equal to 180 degrees. This will help when you tile because you can make a easy flat surface without using squares.

Henry

Hiffin — 2014-10-31 14:47:06 UTC

Please try to make a tile with all the polygons I give you, using the tool on the right.

Hexagons

Hiffin — 2014-11-02 23:21:03 UTC

Hexagons can be used to tile with a number of shapes. They can tile with other hexagons to form a honeycomb like pattern, and can also tile with equalateral triangles.

Octagons

Hiffin — 2014-11-02 23:25:57 UTC

Octagons can be tiled with squares to form a grid like pattern.

Dodecagon

Hiffin — 2014-11-02 23:37:44 UTC

Dodecagons can be tiled by putting 4 triangles and a square in the center of 4 dodecagons in a star pattern. Also, dodecagons can tile by having three together and an equilateral in the center of the three.

Henry

Hiffin — 2014-11-02 23:44:08 UTC

There are other ways to tile and other polygons that can tile, but using these shapes there are an infinite amount of tessellations you can create.