Arithmetic – 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 99: Quilts & the Underground Railroad

A quilt containing 6 of the blocks mentioned below as having possibly been used as a code in the underground railroad.

The Challenge: Learn a bit about the code discussed below, and then have yourself or students create some or all of the quilt blocks discussed.

Materials needed: Certainly you can make these as actual quilt pieces. You can also just use a square piece of paper and work on construction within that using paper and pencil.
Math concepts you could explore with this challenge: angles, arithmetic, geometry, philosophy on math, polygons, symmetry, tessellations.

#MathArtChallenge 95: Magic Squares

Overhead view of lego towers arranged in a 3×3 grid.

The Challenge: Create a magic square. Bonus points if you make it a physical thing.

Materials Needed: Legos, blocks or coins all work well for making these towers. Could also be pen/pencil & paper, of course.
Math Concepts: Algebra, arithmetic, counting, proportions/ratios, structure, sum of 1-n integers

#MathArtChallenge 90: Sand Piles

The Challenge: Explore a toppling sand pile.

Materials Needed: Paper, pencil, and probably a good eraser. You could also do this using a whiteboard or other writing surface.
Math concepts you could explore with this challenge: algebra, arithmetic, counting, fractals, functions isometric, proportions/ratios

#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 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

#MathArtChallenge Day 37: Pascal’s Triangle Patterns

The Challenge: Start by making (or use mine below) a Pascal’s Triangle. Then shade in some sequence of values. I suggest starting with even/odd numbers, and then perhaps multiple of 3, 4 etc.

Materials Needed: Pascal’s triangle. You can print one or you can create your own!
Math concepts you could explore with this challenge: algebra, arithmetic, combinations & permutations, counting, functions, proportions/ratios, sequences, symmetry

#MathArtChallenge Day 32: Megan’s Spirals

A spiral created by connecting sequence values on a spiral chart of 1089 numbers.

The Challenge: Color a spiral of numbers. Or 3. Or fifty. (This one gets quite addictive.)

Materials Needed: A spiral chart. Two pdf versions are shown below.
Math concepts you could explore with this challenge: algebra, arithmetic, counting, functions, lines, sequences, symmetry

#MathArtChallenge Day 18: Celtic Knots

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.

#MathArtChallenge Day 16: Mondrian Puzzles

Day16 MAC — One large rectangle colored in pale yellow, blue and pinks below multiple other rectangles split into many rectangles.

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 concepts you could explore with this challenge: arithmetic, geometry, proportions/ratios