Tilings (Tessellations) and Angles

Tilings cover a plane with identicle shaped pieces that do not overlap or leave any blank spaces. Tiling can be done with one, two, or any infinate number of shapes.

Example

 

There are two types of Tiling.

1. Regular: a pattern created by repeating a regular polygon. There are only three regular tessellations. They are triangles, squares, and hexagons. Only the initial shape is used and adds up to 360 degrees at the vertex. Basically the shapes fit tother with one another all the way around each other perfectly. (Shape ONLY)

 

2. Semi-Regular: made of two or more regular polygons and the pattern at every vertex has to be the same. This requires more than one shape to make the pattern because not all shapes can perfectly surround their own shapes without any gaps. A semi-regular tiling uses more than one regular polygon in order to add up to 360 degrees at the vertex. There are only eight semi-regular tessellations. (Shape+ different shape, etc.)

Angles

It is often easiest to understand an angle first before trying to understand them when it comes to shapes like a right triangular prism or right rectangular prism.

There are three kinds of angles: acute, obtuse, and reflex. An (A)acute angle is an angle in which its measure is less than 90 degrees. A (B)obtuse angle has a measure of more than 90 degrees but less than 180 degrees. A (C)reflex angle has a measure of more than 180 degrees but is less than 360 degrees. (note: the initial side of an angle doesn't move but the terminal side does)

(A)

(B)

(C)












Example(s) of if you know one angle, how to find the other.