**The Challenge**: Create a penrose triangle.

*Materials needed:* Pencil, paper, etc. *Math concepts* *you could explore with this challenge: *angles, isometric grids, perspective, vertices/intersections

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# Category: 2D

## #MathArtChallenge Day 65: Penrose Triangle

## #MathArtChallenge Day 64: Anamorphic Raintangle (from woollythoughts.com)

## #MathArtChallenge Day 63: Super Tic-Tac-Toe

## #MathArtChallenge Day 61: Hilbert Curve

A Hilbert Curve
## #MathArtChallenge Day 60: Triangle Incenters ala Matt Henderson

An orange triangle with a large number of folds and lines drawn on it.
## #MathArtChallenge Day 59: Cellular Automata

6 different iterations of random assignment automata
## #MathArtChallenge 57: Islamic Geometry – Sheikh Zayed Masjid

A 10 petal flower made with compass and straight edge.
## #MathArtChallenge Day 54: Permutations

## #MathArtChallenge Day 52: Crossing Lines

Multiple lines crossing
## #MathArtChallenge Day 51: KNOTS (Finally)

**The Challenge**: Create a penrose triangle.

*Materials needed:* Pencil, paper, etc. *Math concepts* *you could explore with this challenge: *angles, isometric grids, perspective, vertices/intersections

**The challenge: **Create a rainbow and get it reflected in a curved surface to reveal a rectangle. All credit here to Woolly Thoughts! (They have wonderful things for you to play with there.)

*Materials needed:* I crocheted mine, which was a fun puzzle to get an even rainbow. They have knitting instructions on their website, but you could just as easily draw this with markers. I used tinfoil as my reflective surface wrapped around a nail polish remover bottle. I bet you all get more creative than myself.*Math concepts* *you could explore with this challenge: *circles, geometry, perspective, proportions/ratios

**The challenge:** This is another game (like sprouts). Great to play with a friend, can even be challenging for you to play against yourself! Lots of variety of how you decide who “wins”.

*Materials needed*: paper, pencil/pen*Math concepts* *you could explore with this challenge: *probability

*Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the **8 mathematical practices**. Feel free to add your own suggestions in the comments! *

1.) Make sense of problems and persevere in solving them. *What strategy will most likely end with you winning? Do you want to start or go second? *

8.) Look for and express regularity in repeated reasoning. *If you play until all boards are filled, what is the expected number of 3 in a row? *

**The challenge:** Create a Hilbert curve.

*Materials needed:* Paper and pencil. Grid paper is helpful.*Math concepts* *you could explore with this challenge: *exponents, fractals, geometry, sequences, symmetry, tessellations

**The Challenge: **Create your own version of Matt Henderson’s triangle incenters.

*Materials needed:* Paper? Pencil? Origami? Graphing software? (There are lots of options here.) *Math concepts* *you could explore with this challenge: *angles, geometry, polygons, symmetry, vertices/intersections

**The Challenge:** Using rules from the “above row”, create a new row below.

*Materials needed:* grid (can be home made!) paper, pencil/pen.*Math concepts* *you could explore with this challenge: *Probability, randomness, expected value

**The Challenge:** I’m seeing the trees start blossoming around here (MN) so this felt like a good time for this one. I used Samira Mian‘s instructions. If you’re interested in Islamic Geometry, I cannot recommend her enough. Here is my creation, followed by her youtube video.

*Materials required:* Compass, straight edge, pencil.*Math concepts* *you could explore with this challenge: *circles, geometric construction, Islamic geometry, symmetry, vertices/intersections

**The Challenge:** Represent a pattern of permutations

*Materials Needed*: ??? There are so many options here. I used paint, but you could draw, use yarn, legos… anything. *Math concepts* *you could explore with this challenge: *combinations & permutations, counting

**The Challenge: **Drawing only straight lines where all lines must cross all other lines, how many can you draw?

*Materials Needed: *Paper, pencil, maybe a ruler.*Math concepts* *you could explore with this challenge: *angles, calculus, lines, slope

**The Challenge:** Can you find the 4, 5 and 6 crossing knots?

*Materials needed: *Patience, creativity, paper, pencil, maybe some strips of t shirts and a safety pin?*Math concepts* *you could explore with this challenge: *Combinatorics & permutations, counting, graph theory, knot theory, topology, vertices/intersections