# M.C. Escher – Math Search for All Ages

Image source: Kerry Randolf on Flickr!

Dutch graphic artist M.C. Escher was not a mathematician. After he finished school, he never studied math. Oh, and while in school, his grades were pretty bad (except in art classes). Yet he created amazing math-rich art.

If you are at the Worlds of M.C. Escher exhibit: walk around the exhibit and discover it using the clues on this card. There’s a no photography rule at the exhibit, but you (or an adult you’re with) can write down the titles of the works you find and look them up online.

If you are NOT at the Worlds of M.C. Escher exhibit: get an album with his work from the library (or a bookstore) or search online.

Here’s the printer-friendly PDF (no images) with the challenges, so you can take it with you to the exhibit.

Can you figure out all the hints?

SYMMETRY

Image source: Ron Wiecki on Flickr!

Many of the artworks in the exhibit show symmetry. It’s easier to notice in some works; harder in others. Can you find a print that shows reflection (line) symmetry? If you only had one half of an artwork and put a mirror to it, would you see an entire print? [Hint: “Magic Mirror” on the wall, is this art the most symmetrical of all?]

TESSELLATIONS

Image source: Eric Gjerde on Flickr!

M.C. Escher loved playing with tessellations or, as he called them, regular divisions of the plane. A plane here doesn’t mean an airplane, but a flat surface, like a wall or a floor (can you think of an example of another large flat surface?) He filled these large flat surfaces with shapes that interlocked like pieces of a jigsaw puzzle – without empty spaces or overlapping each other. M.C. Escher used birds, animals and other creatures in his tessellations, but he always started with regular polygons – triangles, squares or hexagons.

Tessellations Search 1 – Squares

Find a tessellation that starts as a bunch of squares. What creatures do the squares change into?

Tessellation Search 2 – Hexagons

Find a tessellation that starts as a bunch of hexagons. What creatures do the hexagons change into?

Tessellation Search 3 (1+2) – Squares and Hexagons

Find a tessellation that changes from squares to hexagons and maybe even back to squares. [Hint: The title of the piece is the name of a process known as “nature’s ultimate transformer”]

INFINITY

Image source: castgen on Flickr!

Have you ever played a game where whoever calls the largest number wins? You say “one hundred” and your friend says “one thousand” and then the two of you make your way to a million, a billion, a quintillion, and a googol. Some smarty-pants might try to call “infinity”, but that’s not a number. What is infinity then? Instead of trying to describe infinity with words, let’s find infinity in M.C. Escher’s art!

Infinity Search 1 – To Infinity! To infinity?

It takes a very, VERY long time to reach an infinitely large number. It’s kind of like trying to walk up to and touch the horizon. Can you  ever get to the edge of space? Or would your patience reach the LIMIT [that’s a hint, by the way]

Infinity Search 2 – Tiny Infinity

What would happen, if instead of looking for the largest number, you and your friend looked for the smallest number? You’d get to infinity again! It’ll be a very tiny infinity. Can you find it in Escher’s work called “Snakes”? Where else can you find tiny infinity?

SPACE CONFUSION

Image source: NASA Goddard Space Flight Center on Flickr!

Space Confusion Search 1 – What goes up…

Space can be disorienting. Just ask anyone who’s been to, well, space. In Space there’s no up and no down. What if here, on Earth, there was no up or down? Or up was down and down was up? Find a lithograph called “Up and Down”. But why stop here?. After all, what is “up” and what is “down”? Here on Earth there’s gravity to help you decide. But up in space, it’s all RELATIVE [yes, that’s another hint]

Space Confusion Search 2 – Two sides to every story?

Now imagine you are an ant out to explore the world around you. You crawl on top a strip of paper. Your slowly make your way along the top of the strip. Or is it the bottom of the strip? Surprise – it’s both! You are on a strip of paper that has only one side! It’s hard to believe until you see it for yourself. So hurry up and find a print with big ants on it.

IMPOSSIBLE CONSTRUCTIONS

Image source: Anne Worner on Flickr!

Do you know that your brain plays tricks on you every single day? Every time you look at photographs (or, say, play Minecraft), you look at a picture on a flat surface of photo paper or a computer screen. But your brain makes you believe that you see your cat or an Enderman (from Minecraft) in three dimensions. That’s pretty cool, right? Artists noticed this ability of our brains a long time ago and started using it in their work. M.C. Escher was no exception. Check out his prints of Italian towns.

But some of the structures M.C. Escher drew are impossible to build. Here are two of the most famous examples of impossible constructions. Your mission is to figure out why they are impossible.

Impossible Constructions Search 1 – Belvedere

Check out one of the most famous of M.C. Escher’s impossible constructions, the Belvedere. If you are at the exhibit, there’s also a 3D model of it that you simply can’t miss. Why can’t you build this in real life? [Hint: In the print, find the boy on the bench. In his hands is the key to the answer.]

Impossible Constructions Search 2 – Waterfall

Why wouldn’t this waterfall, well, fall? [Hint: If you thought the right triangle was annoying, this one is absolutely IMPOSSIBLE!]

It took me many hours of research, writing and testing to put together this math scavenger hunt. If you enjoyed it and found it valuable, please consider supporting the development of future scavenger hunts (and other cool ideas) with a one-time donation.