Vertices/Intersections – 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 94: Twelvefold Islamic Geometric Rosette from Samira Mian

The Challenge: Make yourself a 12-fold Islamic Geometric Rosette.

Materials needed: Compass, straight edge, paper, pencil, colors
Math Concept: angles, circles, geometric construction, geometry, Islamic geometry, lines, polygons, symmetry, tessellations, 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 89: Voronoi diagrams

The Challenge: Throw some random points (or carefully selected ones!) on a plane. Identify the parts of the plane that are closest to each of those points.

Materials Needed: Paper, ruler, writing utensil.
Math concepts you could explore with this challenge: algebra, arithmetic, geometry, lines, proportions/ratios, slope, tessellations, vertices/intersections.

#MathArtChallenge 87: Burr Puzzle Origami

An origami stellated polyhedra made from origami

The Challenge: Fold yourself a 6 piece puzzle that comes together as a 3D star shape. You’ll need 6 pieces of paper.

Materials Needed: 6 square pieces of paper.
Math concepts you could explore with this challenge: angles, geometry, origami, polygons, polyhedra, vertices.

#MathArtChallenge 76: Decagon & Pride Flag

The Challenge: Create this decagon using the symmetries visible in the piece. The central images are rhombi.

Materials Needed: compass or ruler, could also use graphing software (see below!)
Math concepts you could explore with this challenge: angles, circles, geometric construction, geometry, polygons, symmetry, vertices/intersetions.

#MathArtChallenge Day 74

The Challenge: Create the above tessellation using compass and straight edge or isometric grid paper.

Materials Needed: compass, straight edge, grid paper, possibly isometric paper. Math concepts you could explore with this challenge: angles, circles, geometric construction, geometry, Islamic geometry, lines, symmetry, vertices/intersections.

#MathArtChallenge Day 73: More Islamic Design

The Challenge: Create the tessellation above using a compass and straight edge.

Materials Needed: Compass, straight edge, possibly grid paper
Math concepts you could explore with this challenge: angles, circles, geometric construction, geometry, Islamic geometry, lines, symmetry, vertices/intersections.

#MathArtChallenge Day 72: Stars

The Challenge: Create all of the possible “stars” given a certain number of vertices.

Materials Needed: Pencil/paper
Math concepts you could explore with this challenge: angles, arithmetic, circles, combinations & permutations, lines, proportions/ratios, symmetry, vertices/intersections