The Challenge: Draw an alternating knot. Then see if there’s any way to draw a looping line that cannot be turned into an alternating knot.

Materials needed: Pencil & eraser, or whiteboard, or markers? Math conceptsyou could explore with this challenge: counting, graph theory, knot theory, vertices/intersections.

The Challenge: Create a Celtic knot, and do some wondering about why you got the number of links that you did. Can you predict how many links you’ll get? (I wrote another blog post on this a while ago, but only go there if you need more examples, because I reveal a lot of the good stuff in it: Knots, Links, & Learning)

Materials Needed: Paper, pencil. If you have grid paper, that might help, and here is some special grid paper you can use courtesy of Justin Aion. Day18 11×15 Celtic Knot Grid Day18 MAC 16×22 Celtic Knot Grid (or you can just rotate grid paper 45 degrees like I do in the video below) Math conceptsyou could explore with this challenge: arithmetic, combinations & permutations, counting, knot theory, proportions/ratios.

The Challenge: Create your very own order 4 Permutohedron (see video below).

Materials Needed: Paper, pencil, patience, and if you want to go 3D, you sure can. Post-it notes work pretty well when playing with this. Math conceptsyou could explore with this challenge: angles, combinations & permutations, geometric construction, geometry, graph theory, polyhedra, sequences, vertices/intersections.

The Challenge: Create a Mondrian artwork (maybe with a goal of getting the lowest score?) Here’s a Math Pickle article to get you started.

Materials Needed: Writing utensil and paper. (This would be fun with chalk on a sidewalk!) Math conceptsyou could explore with this challenge: arithmetic, geometry, proportions/ratios

The Challenge: Create an illusion using isometric lines.

Materials Needed: Isometric Grid paper You can print some or you can create some (that just takes a bit of patience), pencil and ERASER. This challenge is best done as an exercise in erasing, changing and play. You can see in my time lapse below just how much erasing I did and I’ve done this kind of thing many times before. Be gentle with yourself. Math conceptsyou could explore with this challenge: Angles, geometric construction, geometry, isometric grids, perspective

The Challenge: Using grid paper, assign each row/column a 0 or a 1. Then “stitch” both ways. You could assign the 0s and 1s as you prefer, or with a coin, or you could code something in binary!

Materials Needed: Grid/dot paper (You can print some or make some without too much trouble), or if you have the stitching materials… Math conceptsyou could explore with this challenge: binary numbers, randomness, probability, symmetry

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

The Challenge: Create as many iterations of the Dragon Fractal as you can. See below for my attempts and videos to help.

Material Needed: There are a couple options here: -Paper and marker (sharpie?). Maybe grid paper, preferably paper that is thin enough to see through (notebook paper is normally thin enough) -Strips of paper to fold it -Whiteboard marker and whiteboard/window -??? I bet you have better ideas than I do. Math conceptsyou could explore with this challenge: fractals, functions, geometry, proportions & ratios, sequences

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: Create an array with materials around your house. What do you notice? What do you wonder?

Materials needed: Go wild. Anything can work here: origami butterflies, shoes, paperclips, cereal, pencils… Math conceptsyou could explore with this challenge: arithmetic (multiplication), counting, proportions/ratios, sequences, symmetry