The Challenge: Can you figure out all of the ways that 3 circles can overlap and intersect with each other?
Materials Needed: Curiosity and patience. Whatever medium you like! Please watch ONLY the first 1 minute and 20 seconds of the video below. If you watch more, the answer will be given away! Don’t ruin it for yourself! It’ll be so satisfying if you do it yourself!
Math concepts you could explore with this challenge: circles, combinatorics & permutations, vertices/intersections, radii
Note: This is a first foray for the #mathartchallenge into Islamic Geometry. I would be a fool to not take this opportunity to teach you about Samira Mian. Her online courses are fantastic, and her tutorials are great. So are is her instagram!
The Challenge: Construct an 8-pointed star, and possibly tile it?
Materials needed: Straight edge, writing utensils, paper, compass? (There are tutorials for both compass and no compasses below.)
Math concepts you could explore with this challenge: angles, circles, geometric construction, Islamic geometry, symmetry, tessellations, vertices/intersections
The Challenge: Draw a large shape. Then place a large circle inside that shape, touching at least one edge of the original shape. Then draw the next largest circle you can, and repeat drawing the next largest circle you can. (See video below for examples.)
Materials Needed: Writing utensil, paper.
Math concepts you could explore with this challenge: : Ratios, radius, tangency (tangent circles), proportions, area, perimeter, fractals, geometry
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
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
The Challenge: Draw a cube by connecting 3 rhombi (see below). Then use lines parallel to those of the rhombi to embellish the cube.
Materials Needed: writing surface, writing utensil, straight edge, colors
Math concepts you could explore with this challenge: geometric construction, isometric grids, lines, perspective, polygons, polyhedra, topology, vertices/intersections
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
The Challenge: Draw as many connected triangles as you can. Goal is to have as many vertices with 7 triangles as possible.
Materials Required: Writing surface, writing utensil
Math concepts you could explore with this challenge: angles, counting, exponents, fractals, functions (exponential), triangles, geometry, graph theory, hyperbolic geometry, lines, polygons, sequences, intersections/vertices
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