Totally Tessellated: Division Technique, page 2/4

Division Technique (2/4)

1. Introduction
2. Centroids
3. Diagonals
4. Midpoints
5. Other
6. Hands-On
Activities

Diagonals
In a polygon, any line segment that joins two non-adjacent vertices is called a diagonal. A division technique that uses diagonals is as follows: given a polygon, draw all of its diagonals. The new polygons that are produced replace the original polygon.

Drawing diagonals produces interesting three-dimensional effects. Try some variations of your own and experiment with these three-dimensional effects.

Example (animated)

An easy way to draw the diagonals of a polygon is to go in order: draw all the diagonals from each vertex in order.

Now let us see what happens when this diagonal technique is applied to entire tessellations:

Example (1)

The 4.6.12.6 semiregular tessellation Example (2)

The diagonals of each polygon are drawn

Example (3)

The new shapes that are created are now colored

Here is very different example of the diagonal technique:

Example (1)

A tessellation of quadrilaterals Example (2)

The diagonals of each quadrilateral are drawn in white.

Example (3)

The new shapes that are created are now colored

There are other ways to use diagonals to divide polygons because not all diagonals have to be drawn. For example, we could draw only every other diagonal (counting them in order). Experiment! There are no rules.

Real examples of the division technique:

You may proceed to the templates page to access many ready-made tessellations on which you can practice the division techniques.

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