The Challenge: How many 2 link knots can you find? See the examples above to help you get started.
Materials Needed: knot materials (these could be crocheted like I have, or shoe laces, or electrical cords which you can plug into themselves)
Math concepts you could explore with this challenge: combinations & permutations, graph theory, knot theory, topology, vertices/intersections.
The Challenge: Inspired by this tweet (below), the goal here is to make a knot surface*.
Materials Needed: Can be done with tape and paper, also through crochet.
Math concepts you could explore with this challenge: Knot theory, topology
The Challenge:
Materials needed: whiteboard?, pencil/paper?
Math concepts you could explore with this challenge: circles counting, knot theory, topology, vertices/intersections
The Challenge: Can you find the 4, 5 and 6 crossing knots?
Materials needed: Patience, creativity, paper, pencil, maybe some strips of t shirts and a safety pin?
Math concepts you could explore with this challenge: Combinatorics & permutations, counting, graph theory, knot theory, topology, vertices/intersections
The Challenge: Play with chirality. Chirality refers to the rotation of a specific object. The knots above have opposite chirality.
Materials Needed: This is wide open. Spinning video? Knots? Twisted candy? Be creative!
Math concepts you could explore with this challenge: knot theory, pespective, topology, vertices/intersections
The Challenge: If you have a math friend in your life, they’ve probably introduced you to Möbius strips. If you haven’t been introduced, my apologies, on behalf of all math teachers, for having failed you this far. Please, follow instructions below to create and then deconstruct a möbius strip.
Materials Needed: Strips of paper, possibly a zipper (note! If you choose to use a zipper, make sure it is completely detachable. Meaning that the two sides can actually separate. Some zippers are permanently connected at the bottom and will not work for this task.)
Math concepts you could explore with this challenge: knot theory, sequences, topology.
The Challenge: Build a set of 3, 4, or even 5 Brunnian links.
Materials Needed: Your call. Joey already did the 3 link one with straws. I used crocheted yarn. Shoelaces?
Math concepts you could explore with this challenge: Combinations & Permutations, counting, knot theory, vertices/intersections
The Challenge: Dave Richeson came up with a brilliant extension for Day 14
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 concepts you 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 concepts you could explore with this challenge: arithmetic, combinations & permutations, counting, knot theory, proportions/ratios.
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