900 rhombi arranged to have 3 fold symmetry with blue-purple gradients.

Spent some time this evening relaxing playing in Tile Farm Studio and like this creation made out of 900 rhombi. Can you see factors of 900 in it?

#tilefarm #mathart #rhombi

Frankenstein pixel art.

We have some fun Halloween themed patterns you can collect in Tile Farm Harvest this week. Here is one built in Tile Farm Studio by a 2nd grader from Albuquerque, NM. It’s a beautiful design, but also has a lot of underlying math in it.

#TileFarm #iTeachMath #PixelArt #Halloween #Frankenstein

A bucket op popcorn where the popcorn kernels are based off of the hat tile aperiodic tiling.

I arguably spent too much time this morning trying to make a hat tile bucket of popcorn in Tile Farm Studio.

#iTeachMath #tessellation #tileFarm #hatTile

#MathPhoto25 #Symmetry Here’s a pair of shoes I designed in Tile Farm Studio. The underlying pattern relates to the subtraction of fractions, geometric series, and the Euclidean Algorithm, and is a highly symmetric 42 sided polygon, but I colored it asymmetrically. #iTeachMath #TileFarm

Made a Dodgers jersey using a simple cryptographic font (a=1 square, b=2 squares etc.). Designed in Tile Farm Studio, then used a cricut machine to cut the design with iron on vinyl.

#iTeachMath #cryptography #TileFarm #Cricut #Dodgers #MookieBetts

Working on a 50 states art collection that I’m curating from patterns made in Tile Farm studio. Students will be able to collect these. Can you tell what state this is for? If US based, what image or symbol would you want for your home state?

#iTeachMath #mathArt #geometry #tileFarm

Friday is a very special day as it is 5/9/2025 and 5^2 * 9^2 = 2,025. This image is that illustrated visually in Tile Farm Studio. Good question for you or your students: when was the last time the day squared times the month squared equaled the year?

#iTeachMath #Math #TileFarm #PerfectSquare

A diagram with two dodecagons made out of pattern blocks, and substitutions that can be used to transition between them.

#MathArtMarch day 31, “change”. Using the substitutions shown below, how can you get from dodecagon A to dodecagon B? It’s fun to try yourself, but a solution is shown in comments. Credit to my dad for coming up with the concept of “flipping pentagons”.

#tilefarm #patternblocks #iteachmath

#MathArtMarch day 28, “quadrilateral”. A favorite dodecagn you can make out of quadrilaterals with basic pattern blocks.

#TileFarm #iTeachMath

#MathArtMarch day 27: tangled. “Tangled Rectangles” made by Emily Bucholz using Tile Farm Studio as part of a polygon puns art series.

#TileFarm #iTeachMath

A chaotic image of multicolored dots.

#MathArtMarch day 25, “chaos”. Made with dotted squares in Tile Farm Studio. What’s your estimate for total number of dots?

#TileFarm #iTeachMath #Estimation

#MathArtMarch day 24, “equal”. A simple way of visualizing 7*8 = 8*7 in Tile Farm Studio.

#TileFarm #Multiplication #iTeachMath

#MathArtMarch day 22, “hexagon”. Here are some nice regular hexagons made out of 30-60-90 triangles.

#TileFarm #MathArt #Math #iTeachMath

#MathArtMarch day 21, “font”. Just in time for spring, here’s a honeycomb font made in Tile Farm Studio.

#TileFarm #MathArt #iTeachMath

A complex tessellation made out of right triangles.

#MathArtMarch day 20, “repetition”. A tessellation with both inward and translational repetition. This is a variation of the truncated hexagon tiling, but the dodecagons and triangles are made out of infinite geometric series of triangles, or “subtractagons” as we call them.

#TileFarm #MathArt

42 representations of the number 42

#MathArtMarch day 19, “42” (second submission because I just had to). 42 representations of the number 42 made by a bunch of different people in Tile Farm Studio.

#TileFarm #iTeachMath #Math #MathArt

#MathArtMarch day 19, “42”. Did you know a 42 sided polygon is the largest regular polygon that will fit around a vertex with other regular polygons (fits with 7 and 3 sided)? Here it is represented visually in Tile Farm Studio.

#TileFarm #iTeachMath

11 dodecagons with 11 different symmetries.

#MathArtMarch day 17, “symmetry”. Here are the 11 symmetries of regular dodecagons you can make with classic pattern blocks (D12, D6, C6, D4, C4, D3, C3, D2, C2, D1, C1).

#TileFarm #Dodecagon #PatternBlocks #iTeachMath #Symmetry

#MathArtMarch day 16, “connected”. This shows the connection between the snub squares Archimedean tiling and the Cairo tiling using the same grid of right triangles colored with different pallets.

#TileFarm #CairoTile #iTeachMath

A 72 sided polygon made out of thousands of isosceles triangles.

#MathArtMarch day 15, triangle. One favorite discovery in Tile Farm Studio is that you can make a regular polygon out of any two adjacent “fraction triangles”. Here is a 72 sided polygon made out of 1/8 and 1/9 fraction triangles. We call these shapes subtractagons.

#TileFarm #mathArt #triangle

A Fibonacci rectangle

#MathArtMarch day 14, “irrational”. From the highly rational adding of squares, comes the Fibonacci flag with an irrational aspect ratio (the golden ratio).

#TileFarm #MathArt #Rectangle #iTeachMath

#MathArtMarch day 13, “zero”. Here is an alternative cover for the hit single “Zero” from the Smashing Pumpkins 1995 Album “Mellon Collie and the Infinite Sadness”.

#SmashingPumpkins #Zero #Math #TileFarm

A tessellation of interlocking 3-way arrows.

#MathArtMarch day 13, “on an iso grid”. This is one of my favorite patterns from the Alhambra, recreated in Tile Farm Studio. It is super fun to make the seed tile, then see how they interlock together when you multiply it into a tessellation.

#tessellation #mathArt #TileFarm #Alhambra #iTeachMath

#MathArtMarch day 11, “proof”. This is a very simple visual proof that the thinner rhombus in classic pattern blocks is half the area of the square.

#TileFarm #iTeachMath #Pentagon #PatternBlocks

#MathArtMarch day 10, “Maps”. Here is a map of my mind (on music) made in Tile Farm Studio.

#TileFarm #MathArt #Brain

#MathArtMarch day 9, “growth”. Here is a seed of 9 “rainbow rhombi” multiplying and growing. This is also your multiples of 9 up to 9x12.

#TileFarm #Rhombus #Math #MathArt #iTeachMath

An Archimedean tiling pattern with dodecagons, squares, and hexagons

#MathArtMarch day 7, “how many?” This is a favorite yet trickier than it seems question: For every dodecagon in this Archimedean tiling pattern, how many squares and hexagons are there respectively?

#TileFarm #ArchimedeanTiling #Tessellation

A pink knotted structure.

#MathArtMarch day 6, “A single line”. I guess theoretically this isn’t a line, but in this world we inhabit, aren’t lines just a theoretical concept?

#TileFarm #Math #Knots #MathArt

This is a 42 sided polygon with 3 concentric rings with colors repeating every 2, 3, and 7 in the respective rings.

#MathArtMarch day 5, “discovery”. I was really happy when I discovered this visual representation of the prime factorization of 42 in Tile Farm Studio. This is a 42 sided polygon with 3 concentric rings with colors repeating every 2, 3, and 7 in the respective rings.

#math #mathArt #tilefarm #art

A rainbow road swirl.

#MathArtMarch day 4, swirly rainbow road made in Tile Farm Studio. This was made coloring a 42 sided polygon then zooming in and cropping.

#math #mathArt #tilefarm