The challenge: Create a complete (all 16 spaces) 4 set venn diagram.

Materials needed: Pencil, paper, other?? Math conceptsyou could explore with this challenge: circles, combinations & permutations, graph theory, probability, vertices/intersections

The challenge: Create a rainbow and get it reflected in a curved surface to reveal a rectangle. All credit here to Woolly Thoughts! (They have wonderful things for you to play with there.)

Materials needed: I crocheted mine, which was a fun puzzle to get an even rainbow. They have knitting instructions on their website, but you could just as easily draw this with markers. I used tinfoil as my reflective surface wrapped around a nail polish remover bottle. I bet you all get more creative than myself. Math conceptsyou could explore with this challenge: circles, geometry, perspective, proportions/ratios

The Challenge: Build yourself a wobbler. Wobblers are 2 circle (or 2 ellipse!) constructions that have a constant center of mass. Or rather, a center of mass that doesn’t move up and down as the wobbler rolls. Thus, resulting in a satisfyingly continuous “wobble”.

Materials Needed: cardboard, ruler, boxcutter or scissors Math conceptsyou could explore with this challenge: algebra, angles, circles, geometry, proportions/ratios, symmetry, vertices/intersections

A 10 petal flower made with compass and straight edge.

The Challenge: I’m seeing the trees start blossoming around here (MN) so this felt like a good time for this one. I used Samira Mian‘s instructions. If you’re interested in Islamic Geometry, I cannot recommend her enough. Here is my creation, followed by her youtube video.

Materials required: Compass, straight edge, pencil. Math conceptsyou could explore with this challenge: circles, geometric construction, Islamic geometry, symmetry, vertices/intersections

The Challenge: With a compass or with tech like Geogebra or Desmos Geometry, to recreate the Lotfallah Mosque Dome design.

Materials Needed: compass, straight edge, colors. You could also use graphing software for this. Math conceptsyou could explore with this challenge: angles, circles, geometric construction, geometry, Islamic geometry, lines, polygons, proportions/ratios, symmetry, vertices/intersections

Materials Needed: Compass, increasingly large circles to trace or graphing technology. Math conceptsyou could explore with this challenge: Circles, geometric construction, geometry, symmetry, vertices/intersections

The Challenge: Can you figure out all of the ways that 3 circles can overlap and intersect with each other?

Materials Needed: Curiosity and patience. Whatever medium you like! Please watch ONLY the first 1 minute and 20 seconds of the video below. 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! Math concepts you could explore with this challenge: circles, combinatorics & permutations, vertices/intersections, radii

Construction (compass and straight edge) of a tessellation of 8 pointed stars.

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 conceptsyou could explore with this challenge: angles, circles, geometric construction, Islamic geometry, symmetry, tessellations, vertices/intersections

The Challenge: Draw a large shape. Then place a large circle inside that shape, touching at least one edge 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 conceptsyou could explore with this challenge: : Ratios, radius, tangency (tangent circles), proportions, area, perimeter, fractals, geometry

4 different cardioids created using different ratios

The Challenge: Create cardioid images by marking the circumference of a circle with equally spaced tick marks, then connecting them at various ratios.

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 arithmetic, angles, geometric construction, ratios, circles, functions, vertices/intersections