#MathArtChallenge 90: Sand Piles

The Challenge: Explore a toppling sand pile.

Here is my explanation (note, I’m pretty sure I have a mistake in toppling 20)

Here is a video that Numberphile put together describing them as well:

Reflection questions:

  • Is it possible for a pile to topple differently? Does it matter if different stages appear different or is it necessary for the toppling to be consistent?
  • What would an isometric (triangular) grid toppling looks like? How about a hexagonal one?
  • How might you meld this with computer programming?
  • Is there a less or more illuminative coloring for the sand piles? What kinds of coloring may make the sand pile structures more obvious or less?

#MathArtChallenge Day 65: Penrose Triangle

The Challenge: Create a penrose triangle.

Materials needed: Pencil, paper, etc.

#MathArtChallenge Day 15: Isometric Illusions

2020-03-30 07.52.09-1

THE CHALLENGE: Create an illusion using isometric lines.

MATERIALS NEEDED: Isometric Grid paper You can print some or you can create some (that just takes a bit of patience). Pencil and ERASER. This challenge is best done as an exercise in erasing, changing and play. You can see in my time lapse below just how much erasing I did and I’ve done this kind of thing many times before. Be gentle with yourself.

#MathArtChallenge Day 3: Isometric Cube Cutouts

Day3 MAC
Purple 3D looking cube with instructions for how to draw

Draw a cube by connecting 3 rhombi (see below). Then use only parallel lines to those in the rhombi to embellish the cube.

Materials Needed: Writing surface, writing utensil, straight edge, colors?
Math Concepts: Perspective, 3D projections
Day3 MAC teal
Green cube drawn with large patterned sections appearing to be “carved out”.

Depending on how you use this activity, you may engage with different standards. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

5.) Use appropriate tools strategically. How precise does one have to be in order for this to appear convincing? What tools make that more apparent? How can you make use of color?

6.) Attend to precision. Without attention to detail here, the visual falls apart.

7.) Look for and make use of structure. Can you create an “impossible” illusion? How so? What structure do you need to make use of to succeed in that?