#MathArtChallenge 94: Twelvefold Islamic Geometric Rosette from Samira Mian

12fold rosette full

The Challenge: Make yourself a 12-fold Islamic Geometric Rosette.

Materials needed: Compass, straight edge, paper, pencil, colors
Math Concept: geometry, intersections, tessellating, polygons, proportions

All of the instructions I followed here can be found at Samira Mian’s website. If you aren’t already familiar with how much I respect and admire this woman, you probably haven’t been following me particularly closely. I couldn’t do the last 10 without nodding to Samira. Her work is an absolute gift to the mathematics community. You should probably definitely go take her first and second online classes.

12fold rosette detail

Here’s the time lapse of me making it:

Things to ponder:

  • Check out how different the rosette looks when it’s in a 4 fold or a 6 fold tiling (you can see both at Samira’s page). What shapes change? How are the tilings similar or different?
  • What other ways could you highlight shapes? Is there a way to have a laced pattern with alternating shapes colored or empty? (Positive and negative space)

(p.s. I know this is a day late. I was at the EduColor summit yesterday and it was just necessary for me to spend my time there. I’ll still try to post another later today.) 

Depending on how you use this activity, you may engage with different standards. 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 does this rosette change when it is tessellated in 4fold vs 6fold symmetry?

6.) Attend to precision. What do you notice about this construction compared with other Islamic constructions?

#MathArtChallenge Day 13: Overlapping Circles

The #MathArtChallenge is just a fun, simple way to engage our brains during this time of unease. All tasks are low tech: paper, pencil, maybe string. Nothing fancy. I would LOVE to see what you come up with. Post on social media with the hashtag #MathArtChallenge!

THE CHALLENGE: Can you figure out all of the ways that 3 circles overlap?

2020-03-28 08.02.03

MATERIALS NEEDED: Curiosity and patience. Whatever medium you like! Please watch ONLY the first 1 minute and 20 seconds of this video. If you watch more, the answer will be given away! Don’t ruin it for yourself! It’ll be so satisfying if you do it yourself!

#MathArtChallenge Day 8: Apollonian Gaskets

THE CHALLENGE: Draw a large shape. Then place a large circle inside that shape, touching the edges of the original shape. Then draw the next largest circle you can, and repeat drawing the next largest circle you can. (See video below for examples.)

Materials Needed: Writing utensil, paper.
Math Concepts: Ratios, radius, tangency (tangent circles), proportions, area, perimeter

If you’re interested in some of the math behind this, this is a great article, featuring the work of mathematician Hee Oh.

Vi Hart also has a great video along these lines, demonstrating some serious doodle skills.

Depending on how you use this activity, you may engage with different standards. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

5.) Use appropriate tools strategically. What tools make this easier or more difficult? Is it necessary or better to use a compass and be completely precise, or is it better to “eye-ball” it?

7.) Look for and make use of structure. How does the radius of the largest inner circle affect the radii of the other circles?

8.) Look for and express regularity in repeated reasoning Compare multiple drawings. How does the choice of largest inner circle affect the final outcome? The amount of positive to negative area?

#MathArtChallenge Day 7: Cardioids!

Day7 MAC Cardiod

THE CHALLENGE:

Materials Needed: Paper, circle to trace (yogurt or oatmeal lid?), writing utensil, straight edge (doesn’t have to be a ruler, could just be a piece of cardboard cut straight or any other number of things.
Math Concepts: Sequences, Modular arithemetic, angles, geometric construction, ratios

Depending on how you use this activity, you may engage with different standards. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

2.) Reason abstractly and quantitatively. What shapes/patterns appear in each cardioid? How can you predict what the results will be before you create one based on the ratio between the “skips”?

3.) Construct viable arguments and critique the reasoning of others. Create an hypothesis to predict how any new cardioid will appear.

6.) Attend to precision. What happens if you make a mistake? How likely is it to “ruin” the final outcome? How can you avoid mistakes?

#MathArtChallenge Day 6: Circle Toruses!

THE CHALLENGE: Find a smaller circle you can trace. Then trace large circle to use as a guide. Finally, trace a bunch of smaller circles in a ring to create a torus (more commonly known as a donut).

Materials Needed: Paper, writing utensil(s), circles/compass. The circles can be whatever, but rigid is helpful and even better if they’re empty (masking tape is great!)

use tape

Here are mine!

Depending on how you use this activity, you may engage with different standards. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

3.) Construct viable arguments and critique the reasoning of others. What kinds of interactions between two tori can be made? What can you deduce about the relative radii of tori that “intersect”?

5.) Use appropriate tools strategically. What tools work best for creating these tori? How might you make an image like this best without a compass? Is there a tool that is actually better than a compass? Why or why not?

7.) Look for and make use of structure. Let’s say you start with a circle of radius 5 units. What’s the largest radius you can use for your circles centered on the torus? What’s the minimum?