Student Investigation 17

Supplementary Investigation 17

Hexagon Pattern

Tool(s) Geometers Sketchpad

Data File(s) si17

Focus In the Koran, the holy book of Islam, there are strong prohibitions against idolatry of any sort. Many of the early leaders of Islam interpreted these statements as an injunction against the representation of humans or animals in art. While this tradition may have frustrated some Islamic artists, others took up the challenge and became the greatest pattern makers of their time. Instead of covering buildings and other surfaces with human figures, they developed complex, decorative patterns with which to adorn palaces and mosques and other public places. Three types of patterns were developed: designs derived from plant life; designs based on calligraphy; and designs based on geometric shapes.

Islamic patterns emphasize five basic design principles.

1. They are made up of a small number of repeated geometric elements that create a complex whole by repeating a few elements.

2. They are two dimensional both in form and intent. No attempt is made to create a three dimensional effect or representation.

3. They radiate symmetrically from a central point. Westerners who attempt to "read" the art from left to right and top to bottom often fail to see the whole work as intended by the artist.

4. They are not designed to fit within a rectangular frame. Unlike Western art which typically begins with a rectangular frame that is as much a factor in the design of the work as any other element, Islamic art begins with a central point and patterns that radiate from that point until they encounter some barrier.

5. They are constructed from patterns of circles.

For instance, using circles as a tool, a hexagon may be constructed without resorting to measurement.

Tasks

1. Measure the sides of the hexagon. Are they all the same? Measure the angles of the hexagon. Are they all the same?

2. Surround the original hexagon with hexagons of the same size. Describe your strategy and list the distances and angles associated with the translations.

3. Do you think that the plane could be tiled with the hexagon? Explain your reasoning.

A division of International Thompson Publishing, Inc.