Make a Sierpinski Triangle
The Sierpinski triangle was named after its inventor, the Polish mathematician Wacław Sierpiński. This intriguing design consists entirely of simple equilateral triangles.
Steps
- Print out triangular Transfer Images Using a Grid and a Computer paper. You can make your own in a graphics program, print out the image next to this step (click to enlarge), or print it out from here.
- Draw an equilateral triangle. The sides should each have a number of triangles that is a multiple of four. This example will start with a large triangle that is 16 triangles to a side.
- Don't colour the triangles yet. Just trace the outsides of the ones you will colour.
- Divide this triangle into four smaller triangles. Leave the one in the middle blank.
- Divide all the coloured triangles into four smaller triangles just as you did the first one. Again, leave the middle triangle of each set blank.
- Divide the next smaller coloured triangles into fours, leaving the center of each blank.
- Divide the next smaller triangles. Colour them as mentioned in the previous steps.
- Keep dividing triangles as many times as you wish.
- Finished.
Tips
- Sierpinski Triangles can also be called fractals, but fractal is a broad term for, in short, any regular polygon that repeats itself over and over again, getting smaller and smaller. A Sierpinski Triangle is a very specific type of fractal.
- Instead of different colours, try using different shades of the same colour.
- You may also choose to colour the center triangles a contrasting colour instead of leaving them blank, to obtain a triangle like this one.
- If you want to form a three dimensional shape, glue the designs to a piece of cardstock to make them sturdier.
- Draw more shapes and stick them together to form a pyramid. Cut an extra line around the shape to use for gluing.
- Sierpinski Triangles also relate to Euclidean geometry.
Things You'll Need
- triangular grid paper
- (felt) pens, markers or pencils.
- ruler
- Optional:
- scissors
- cardstock
- glue
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