odd numbers creates Sierpinski's fractal triangle!
This triangle of numbers has many patterns and uses explained by the French mathematician Blaise Pascal. In other cultures, it was previously drawn and investigated as "Staircase of Mount Meru," "Khayyam triangle," "Yang Hui's triangle," and "Tartaglia's triangle," as mentioned in the Wikipedia entry on Pascal's triangle. Learning to see patterns and think about how they would extend is one of the most important skills in science and mathematics. This design shows rows 0 to 7 of Pascal's triangle, and an interesting challenge is to figure out what would go in row 8. The pattern also shows Sierpinski's triangle, which is a fractal that could continue into infinite complexity. How? You could subdivide each pink triangle and color its new middle triangle purple. And you could do that again with all the new, smaller pink triangles.