#MathArtChallenge Day 36: Islamic Geometry 10 Point Star

The Challenge: To create this star.

Materials Needed: In an ideal world, you have a compass and ruler, but sans compass, you just need to do your best to divide a circle into 10 equal pieces.
Math concepts you could explore with this challenge: angles, geometric construction, geometry, islamic geometry, lines, vertices/intersections

One fabulous participant did this:

I used a right triangle with leg lengths of 8 and 11 cm to produce a 36 degree angle without a protractor. 11tan36 = 7.99. (Close enough) Ss could do the same at home without access to a special tool.

— Jessica McConnell (@MmeMcConnell) April 21, 2020

For Instructions, I think you’re probably best off with Samira Mian here:

Although I did attempt to do this thread on twitter wherein I forgot that pentagons and hexagons are different things (I hadn’t had my coffee, it’s not my fault!)

Instructions for the connections here! #mathartchallenge pic.twitter.com/ZYPgcQyl5G

— Annie Perkins (@anniek_p) April 21, 2020

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!

1.) Make sense of problems and persevere in solving them. How can you split a circle equally into 10 pieces? What tools might you need for that or what geometric construction?

7.) Look for and make use of structure. Which intersections are necessary? What lines can you only make partial pieces of?