# Featured

## Fractals in Pascal's Triangle (5s, 1s, 2s, 4s in 1, 2, and 3 digits; multiples of 10, 2, 4, and 8)

We created beautiful fractals last week from mere triangles, quadrilaterals and inscribed circles. The children did a wonderful job of mimicking nature’s obsession with fractals. I showed them the following video of 15 plants that form spectacular fractals.

## Fractals: Self-Similarity--Inscribed Triangles, Circles, Quadrilaterals, Right Triangles

**Fractals** are self-similar objects. What does self-similarity mean? If you look carefully at a fern leaf, you will notice that every little leaf - part of the bigger one - has the same shape as the whole fern leaf. You can say that the fern leaf is self-similar.

## Constructing Regular Hexagons, Equilateral Triangles, and Derivative Works

Last week, we explored the three regular polygons that tessellate: the square, the equilateral triangle, and the regular hexagon. Creating a regular hexagon or an equilateral triangle can be done with only a compass and straight edge. This was the only way the ancient Greeks explored geometry.

## Tessellations of Regular Polygons and Irregular Escher-like Shapes

A Tessellation is a repeating pattern of polygons that covers a plane with no gaps or overlaps. Typically, the shapes that make up a tessellation are polygons or similar regular shapes. The only regular polygons that tessellate on their own are equilateral triangles, squares, and regular hexagons. Regular polygons have equal sides and equal angles.