Tessellation

If you look at a tile floor, you will see that all the edges of tiles sit next to each other, with no gaps. This is tessellation, fitting polygons – shapes with at least three sides – next to each other in a pattern.

A football (or soccer ball) icon.

A football (or soccer ball) icon. (Photo credit: Wikipedia)

How would you like to make your own design, and then eat it afterwards?

This activity uses an oven, so it requires adult supervision.

Materials

  • Mixing bowl
  • Spoon for stirring batter and one for sieving powdered sugar
  • Small sieve
  • Rectangular baking pan (you can use a square one with your favorite brownie recipe, but this recipe makes enough for an 8×10 rectangular pan)
  • Toothpicks
  • Gloves or hot pads
  • Cooling rack
  • Paper towel
  • Flat-edged spatula or cake knife
  • ½ cup butter/1 stick (use the wrapper to grease the pan)
  • ½ cup orange juice
  • 1/3 cup cocoa
  • 2 eggs
  • 1 ½ cups sugar
  • ¼ teaspoon salt
  • 1 teaspoon vanilla
  • 1 cup flour, plus extra for pan
  • 1 teaspoon baking powder
  • ¼ cup powdered sugar

Instructions

  • Preheat the oven to 350 degrees Fahrenheit
  • Mix all ingredients in mixing bowl, except the powdered sugar, using the mixing spoon
  • Grease the pan with the butter remaining on the paper used to wrap it
  • Dust the pan with a spoonful of flour, tilting the pan around until the flour covers the bottom and sides
  • Spoon the dough into the pan; put the pan in the oven (the oven’s hot!)
  • Using gloves or hotpads, check the brownies after 12 minutes with a toothpick. If it comes out clean, they’re done. If not, continue to check until it’s been 15 minutes altogether.
  • Using gloves or hotpads, take the brownies out of the oven and let them set on the cooling rack for at least 15 minutes, until the pan is cool enough to touch
  • Turn the brownies out gently onto the cooling rack or a paper towel
  • Cut the block of  brownies in half. Dust half with powdered sugar
  • Cut all the brownies into squares (should make 24)
  • Cut all the squares in half, into triangles
  • Start making designs by putting one powdered triangle’s edge next to the edge of a plain triangle

What Should Happen?

The triangles, alternating by aligning the edges of those with plain and powdered sugar, will make squares. They can also, like quilt patterns, be made into artistic shapes, such as pinwheels, or the squares assembled into larger shapes, like fish.

Play around with the different designs and shapes you can make while lining up the edges of alternating plain and sugared triangles.

Why Is This Useful?

Tesselation is useful both as an artistic way to cover tiled floors or mosaic wall decorations, but also as an efficient way to cover a surface without gaps or overlaps.

Soccer balls are tessellated, with alternating 20 hexagons and 12 pentagons. Since the 1970s, when this design was introduced, they have been considered the closest to round, with the most predictable action in the air. The alternating black and white pattern was used so the ball would be more visible on what was then mostly black-and-white television sets. They are sometimes called “buckyballs,” after Buckminster Fuller, who developed a similar dome shape for buildings to reduce the amount of material required for construction.

Honeycombs are tessellated hexagons made out of wax.

Jigsaw puzzles are tessellated pieces that fit together flat.

Quilts are tessellated pieces of cloth sewn together to make a flat blanket.

Tessellation is used in computer graphics to make scenes look more realistic by breaking them down into triangles, so the data can be transmitted quickly.

Thanks to math educator, Ann McCallum, for this activity and the brownie recipe described in her book, Eat Your Math Homework: Recipes for Hungry Minds.

Listen to an interview with author McCallum below.

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You can order her book from amazon by clicking on the title, “Eat Your Math Homework.”

 

Carol Covin, Granny-Guru

Author, “Who Gets to Name Grandma? The Wisdom of Mothers and Grandmothers

http://newgrandmas.com

 

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