Note: This is a first foray for the #mathartchallenge into Islamic Geometry. I would be a fool to not take this opportunity to teach you about Samira Mian. Her online courses are fantastic, and her tutorials are great. So are is her instagram!
The Challenge: Construct an 8-pointed star, and possibly tile it?
Materials needed: Straight edge, writing utensils, paper, compass? (There are tutorials for both compass and no compasses below.)
Math concepts you could explore with this challenge: angles, circles, geometric construction, Islamic geometry, symmetry, tessellations, vertices/intersections
Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!
6.) Attend to precision. By attending to precision and making certain the intersections that are intended to meet, do actually meet, your final image will be cleaner. What strategies can you use to make sure you are being precise?
7.) Look for and make use of structure. Part of this construction requires you to make use a 2 squares, one with edges parallel to the horizon, and one with edges meeting the horizon at 45 degree angles. Can you see where those squares are? How might that help you be more precise with your construction?
8.) Look for and express regularity in repeated reasoning. When tiling, pay attention to the structure that is actually getting tiled. It is not the 8 pointed star itself that’s repeated. What is repeated?