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: Crochet your very own Hyperbolic Plane (or Pseudosphere?)
Materials Needed: Crochet hook, yarn.
Math concepts you could explore with this challenge: exponents, hyperbolic geometry, proportions/ratios, topology
The Challenge: Build your own Hyperboloid
Materials needed: Skewers, Tiny rubber bands (I was able to get skewers at the grocery store and polybands from Target)
Math concepts you could explore with this challenge: Angles, geometric construction, lines, symmetry, 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: Make yourself a MathArtChallenge sketchbook
Materials Needed: Paper (10 or so sheets), scissors.
Math concepts you could explore with this challenge: topology
The Challenge: Make you very own flexagon. Inspired today by this from @ayliean. Instructions from her below.
Materials Needed: Strips of paper, cloth, or some other foldable strip.
Math concepts you could explore with this challenge: graph theory, polygons, sequences, symmetry, topology
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: Crochet 2 möbius strips, of opposite chirality. Then sew their edges together to get your very own Klein bottle! (A Klein bottle has no obvious inside or outside.)
Materials Needed: Crochet or knitting skills, yarn.
Math concepts you could explore with this challenge: topology
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