Tessellations -- those gapless, mesmerizing mosaics of defined shapes -- pop up everywhere once you know what you're looking for. You can find them under microscopes, radiating from sunflowers and even in the hallowed halls of art museums. What can you tell us about these awesome repeating patterns?

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Question 1 of 20

### Let's kick off this quiz with a little etymology. The word "tessellation" derives from the word for what?

A tiny constellation

A small mosaic tile

The word "tessellation" comes from tessella, the diminutive form of the Latin word tessera, an individual tile in a mosaic.

Tess of the d'Urbervilles

Question 2 of 20

### Tessellations and polygons need one another like popcorn needs butter. What's a polygon again?

Any two-dimensional, closed shape with three straight sides or more

Triangles, squares, rectangles, rhomboids -- any closed shape with three straight sides or more will qualify as a polygon. Sorry, circles. You and your curved sides can't join the polygon party.

Any two-dimensional, closed shape with four straight sides or more

A polygon? Isn't that another name for a pentagon?

Question 3 of 20

### Which of the following would NOT be an example of a tessellation?

A honeycomb

A rack of billiard balls

Unlike a rack of billiard balls, a tessellation must have no gaps.

A grid

Question 4 of 20

### If you head into the wild, you'll find that some animals incorporate tessellations on their skin. What would NOT qualify as a tessellation?

Zebra stripes

Zebra stripes are striking, but they don't qualify. Turtle shells and the bony bumps (scutes) on crocodile skin do though.

Turtle shells

Crocodile scutes

Question 5 of 20

### If you're devoted to this hobby, you encounter tessellations all the time.

Rock climbing

Baking

Quilting

We suppose you could encounter tessellations while scaling massive boulders and putting the finishing touches on a lemon tart, but quilters frequently deal with tessellations when they're crafting their masterpieces.

Question 6 of 20

### What sport likes tessellations so much that it plastered one on its ball?

Golf

Soccer

The iconic black-and-white pattern of a soccer ball qualifies as a semiregular tessellation. Take that, all you golf and Skee-ball fans.

Skee-ball. Of course.

Question 7 of 20

### If you're going to wow everyone with your knowledge of tessellations, you'll want to mention this famous 14th century palace that's renowned for its incorporation of intricate tessellated patterns. What's it called?

The Alhambra

While Windsor Castle may keep royal company and Castle Frankenstein may have inspired author Mary Shelley, it's the Alhambra that's synonymous with intricate tessellations.

Windsor Castle

Castle Frankenstein

Question 8 of 20

### OK, now you know what the famous landmark is called, but can you tell us where it's located?

Saudi Arabia

Egypt

Spain

After you're done checking out Gaudi's Parc Guell in Barcelona and the Prado Museum in Madrid, you may want to venture out to see the Alhambra in Granada, Spain.

Question 9 of 20

### Which famous artist featured tessellations heavily in his work?

Pablo Picasso

M.C. Escher

The famous left-handed graphic artist M.C. Escher reigns as the acknowledged master of tessellations. Escher is also well-known for his trippy works like "Metamorphosis I" and "Metamorphosis II."

Claude Monet

Question 10 of 20

### In what country was M.C. Escher born?

The Netherlands

Maurits Cornelis Escher was born in the Netherlands on June 17, 1898.

The United States

Belgium

Question 11 of 20

### What was M.C. Escher's connection to the Alhambra?

It inspired him to take up tessellations.

Escher was inspired to take up tessellation after visiting the fortress in Spain as a young man.

He helped design it.

No connection at all. We're tricky like that.

Question 12 of 20

### Enough with the easy questions. Let's get into the nitty-gritty of tessellation. Which of the following regular polygons does NOT tessellate with itself in two dimensions?

Square

Pentagon

Regular pentagons don't tessellate in two dimensions, although certain irregular pentagons do.

Equilateral triangle

Question 13 of 20

### Can you tessellate a plane by combining regular and semiregular polygons?

Yes

Not satisfied with regular polygons in your tessellation? You can combine regular and semiregular polygons to make one as well. You can do it. We believe in you!

No

Question 14 of 20

### Is it true that any four-sided polygon will tessellate?

Yes, if placed back-to-back

Any four-sided shape tessellates if placed back-to-back, forming a hexagon, because any hexagon will tessellate.

Yes, under any circumstances

No, that's crazy talk.

Question 15 of 20

### When you're talking tessellations, a wallpaper group is another name for a two-dimensional repetitive pattern. How many are there?

37

17

All two-dimensional planes with repetitive patterns fall into one of 17 wallpaper groups or symmetry types (although not all tessellations are symmetrical).

7

Question 16 of 20

### How many wallpaper groups can you glimpse in the mosaics of the Alhambra?

13

The Alhambra's famed mosaics feature 13 of the 17 symmetry groups.

1

17

Question 17 of 20

### Which of the following is NOT an example of a Voronoi-like tessellation?

Soap bubbles in a foam

Lichen on a rock

Chipped beef on toast

Like other tessellations, Voronoi tessellations pop up repeatedly in nature, because any phenomenon involving point sources growing together at a constant rate, like lichen spores on a rock, will produce such a pattern. Collections of connected bubbles form 3-D examples of Voronoi-like polygons. Researchers take advantage of this similarity to model foams.

Question 18 of 20

### Which of the following is NOT another name for a Voronoi tessellation?

Dirichlet tessellation

Thiessen polygons

Archimedean tessellation

Voronoi tessellations, named for mathematician Georgy Voronoi, are also known as Dirichlet tessellations or Thiessen polygons.

Question 19 of 20

### What kind of polygons do you get with a Delaunay tessellation?

Skinny squares

Fat triangles

Delaunay tessellations always produce fat triangles, which makes them handy for modeling terrain.

Rotund rhomboids

Question 20 of 20

### Why might a mathematician or statistician find Delaunay tessellations useful?

Estimating an answer when a full calculation is impossible

Delaunay tessellations allow number crunchers to make valid estimations when calculations are otherwise impossible, such as when a formula must be applied to every point in space (an infinite number).

Testing for homoscedasticity

Coming up with an equitable way to divide a pizza

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