Geometric Exploration: Patterns in the Triangle

Graph paper plots of triangle. Our work here will be developed further on the remainder-coloring day and the fractal day.

Spit the class into 4 groups. Each group will color graph paper in one of two ways. (See Appendix for samples.)

• Turn paper diagonally. Color in one square near the top-center of the page. Now, moving down the page, color in a square only if exactly one of the two adjacent squares above it is shaded.
• Like the first group, but with "1" replacing "color" and "0" replacing "uncolored".
• This group will use a copy of the triangle, white-out the even numbers and black-out the odd numbers.
• Fill in a row and column (17 squares long) along the top and the left edge of the page. Complete the square of size 9 that shares a corner with the edge you've drawn. Continue, by completing half-size squares (rounding up!) for every new corner you create with your shading.

Discussion: Notice that all three rules give nearly identical triangles. Discuss how they are the same and different.

Homework: Modify one of these rule sets and generate a creation of your own. See if there are any similarities to the designs we discovered today