#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

Continue reading “#MathArtChallenge 90: Sand Piles”

#MathArtChallenge 88: the Recamán Sequence

The Challenge: Create a visual (or audio?) of the Recamán sequence, created by a Colombian mathematician, Bernardo Recamán Santos (who seems to have very little biographical information out there??). I was first introduced through Alex Bellos and Edmund Harris’s book.

Materials Needed: Straight edge, maybe a compass, maybe a ruler. Paper, riting utensil.
Math concepts you could explore with this challenge: algebra, circles, counting, functions, proportions/ratios, randomness, sequences

Continue reading “#MathArtChallenge 88: the Recamán Sequence”

#MathArtChallenge Day 37: Pascal’s Triangle Patterns

Blank Pascal's Triangle

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

Continue reading “#MathArtChallenge Day 37: Pascal’s Triangle Patterns”

#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

Continue reading “#MathArtChallenge Day 32: Megan’s Spirals”

#MathArtChallenge Day 24: Polygon Midpoints

2020-04-08 08.13.50
4 polygons with multiple iterations of midpoints connected inside the shape.

The Challenge: Draw a polygon. Then mark the midpoint of each side. Connect the midpoints of each side to make a new polygon. Repeat. (Don’t sleep on the quadrilaterals here. They do something rather surprising and beautiful!)

Materials Needed: Paper & pencil or online graphing software like Geogebra or Desmos
Math concepts you could explore with this challenge: angles, fractals, functions, geometry, lines, polygons, proportions/ratios, slope symmetry, vertices/intersections.

Continue reading “#MathArtChallenge Day 24: Polygon Midpoints”

#MathArtChallenge Day 12: DRAGONS

An iteration of the dragon fractal drawing on grid paper.

(Props to Kate Nowak who suggested this.)

The Challenge: Create as many iterations of the Dragon Fractal as you can. See below for my attempts and videos to help.

Material Needed: There are a couple options here:
-Paper and marker (sharpie?). Maybe grid paper, preferably paper that is thin enough to see through (notebook paper is normally thin enough)
-Strips of paper to fold it
-Whiteboard marker and whiteboard/window
-??? I bet you have better ideas than I do.
Math concepts you could explore with this challenge:  fractals, functions, geometry, proportions & ratios, sequences

Continue reading “#MathArtChallenge Day 12: DRAGONS”

#MathArtChallenge Day 7: Cardioids!

Day7 MAC Cardiod
4 different cardioids created using different ratios

The Challenge: Create cardioid images by marking the circumference of a circle with equally spaced tick marks, then connecting them at various ratios.

Materials Needed: Paper, circle to trace (yogurt or oatmeal lid?), writing utensil, straight edge (doesn’t have to be a ruler, could just be a piece of cardboard cut straight or any other number of things.
Math Concepts: sequences, modular arithmetic, angles, geometric construction, ratios, circles, functions, vertices/intersections

Continue reading “#MathArtChallenge Day 7: Cardioids!”

#MathArtChallenge Day 4: Hyperbolic Geometry

Day4 MAC hyperbolic planes
5 differently colored origami hyperbolic planes

The Challenge: Fold your very own Hyperbolic Plane from a simple piece of paper!

Materials Needed: A square piece of paper. Youtube instructional video below!
Math concepts you could explore with this challenge:  Algebra (how many folds per stage?), angles, counting, exponents, functions, geometry, Hyperbolic planes, proportions/ratios, sequences, symmetry, topology, vertices/intersections

Continue reading “#MathArtChallenge Day 4: Hyperbolic Geometry”

#MathArtChallenge: Day 2 Looping Colors

Day2 MAC
A looping line, with created spaces alternating blue and red in color.

The Challenge: Draw a long, looping, self-intersecting line that meets back with itself at the start. Avoid having any 3 lines cross at the same intersection (although after a bit it may be fun to play with this). Then, select a color, and start coloring in the spaces created by your line’s intersections.
Can you color it such that you end with every section alternating colors?

Materials Needed: writing utensil, writing surface
Math concepts you could explore with this challenge: counting, functions, geometry, knot theory, vertices/intersections

Continue reading “#MathArtChallenge: Day 2 Looping Colors”