Graph Theory – arbitrarilyclose

#MathArtChallenge 100: Balloon Polyhedra

In the first, allow me to thank each and every one of you who has participated in the #MathArtChallenge in the last few months. This is my “last” post. Meaning, I don’t promise to make more Math Art Challenges, but there’s always the chance that something will come up…

All of the #MathArtChallenge-s will continue to be up on this blog, and I really hope that you’ll make use of them in your classes or in your fun time or however brings you joy.

The Challenge: Today, you get Balloon Polyhedra. There’s actually several papers written about this, so go check them out.

Materials needed: Twisting balloons, pump, patience
Math concepts you could explore with this challenge: angles, arithmetics, counting, geometry, graph theory, polygons, polyhedra, symmetry, vertices/intersections

#MathArtChallenge 96: Not so much rational tangles as… a 2 link challenge.

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.

#MathArtChallenge 93: Archimedean Solids from Vertex descriptions

The Challenge: Using a vertex description, build yourself one, two… up to all 13 of the Archimedean solids.

Materials needed: Card stock and tape (painter’s tape is great, or masking. Other stuff will work, but I’ve had more success with the paper-y tapes.) OR Magnatiles, but those can get pretty pricey.
Math Concepts: structure, polyhedra, angles, 3D structure

#MathArtChallenge 79: Knot Surfaces & “Why” Diversity

The Challenge: Inspired by this tweet (below), the goal here is to make a knot surface*.

One of the most important ideas for studying knots is to consider "nice surfaces whose boundaries are the given knots". These are called Seifert surfaces, and I finished crocheting one for the trefoil knot last night! pic.twitter.com/E4ezi8FrYp
— Shintaro Fushida-Hardy 🐌 (@FushidaHardy) May 20, 2020

Materials Needed: Can be done with tape and paper, also through crochet.
Math concepts you could explore with this challenge: Knot theory, topology

#MathArtChallenge Day 71: Sona Drawings

Given what’s happening in my community right now, I felt it was necessary to highlight some Black brilliance today.

The Challenge: (Re)create a Sona drawing. I did a couple hours of research yesterday (which is totally insufficient to fully understand it), but what I can tell you is that these drawings originate with the Chokwe people in southwestern Africa, specifically Angola and the southern part of the Democratic Republic of the Congo. The drawings are told in conjunction with a story, and the goal of most is to draw them in as unbroken a line. Please check out some of the resources below, and if you have others to add, I’d love to see them and link them here.

Materials Needed: grid, pencil, paper, perhaps graphing software.
Math concepts you could explore with this challenge: angles, counting, geometry, graph theory, proportions/ratios, slope, symmetry, vertices/intersections

#MathArtChallenge Day 66: Venn Diagrams

A complete 3 set Venn diagram, and an incomplete 4 set Venn diagram.

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

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

#MathArtChallenge Day 51: KNOTS (Finally)

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

#MathArtChallenge Day 43: Sprouts!

The ~~Challenge~~ Game: This one really isn’t a challenge – it’s a sweet game, you should play with whomever you’re sequestered at home with. Or by yourself. I clearly played myself.

Materials Needed: writing utensil, writing surface
Math concepts you could explore with this challenge: graph theory, proportions/ratios, vertices/intersections

#MathArtChallenge Day 40: Flexagons

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

#MathArtChallenge Day 20: Origami Icosahedron

Day20 Icosahedron — A spinning icosahedron made from origami paper.

The Challenge: Fold 30 identical pieces of paper to put together as an icosahedron.

Materials Needed: 30 square pieces of paper. No problem if it’s not origami paper, you can use regular paper (and you can decorate it if you want!)
Math concepts you could explore with this challenge: Geometry, graph theory, origami, polygons, polyhedra, symmetry, vertices/intersections