## Maths Mystery Box 8: JUNK FOOD

February 16, 2015**Middle School Maths Challenge**

**Make a 3D graph or Make Like a Pringle**

Pringles are mathematically yummy because each Pringle is a little 3D graph called a Hyperbolic Paraboloid or – YeeHa! – it’s a saddle.. You will find information about Hyperbolic Paraboloid at the fab **Math Jokes 4 Mathy Folks blog** here and here.

You may have drawn 2D graphs. Bar graphs, Pie Charts and Linear Graphs.

A linear graph will have the equation

**y = mx + c**

You might have looked at quadratic equations such as the parabola:

**Y = ax ^{2 }+ bx + c**

So what could a 3D graph of a saddle look like? Well, you have to add a z so that you have an x-axis, y-axis and a z-axis.

More info here.

# The BIG challenge

Can you make a hyperbolic paraboloid? The most mathematically amazing feature of the hyperbolic paraboloid is that it can be constructed from straight lines.

Here’s How:

### 1. Cardboard and wool:

**You need:**

***** cereal box

*wool

*ruler & scissors.

**Instructions:**

Cut a 15cm x 15 cm square out of the cereal box.

Fold it diagonally.

Cut slots at 1cm interval.

Thread wool into opposite slots as shown (below).

NB: The thread should be a straight line.

Detailed instructions here.

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### 2. Wooden skewers

You will find full instructions at the Mathscraft blog.

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### 3. Cardboard only

Here is another way to make a hyperbolic paraboloid using cardboard. You will find full instructions including a video at Mathscraft.

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# 4. Bubble

You will find more about the geometry of soap films here.

More intriguing information about all sorts of geometric bubbles here at The Wonderful World of Soap Bubbles.

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## The Hyperbolic Paraboloid in Construction

The structure is often used today for rooves.

Too funny! Thanks for the mention, Kerry. I’ve been thinking about you. I’m a lead for the “Popularization of Mathematics” TSG at ICME 13, and I think you’d be a good candidate to submit a paper. Check out http://wp.me/pQxa7-1ni, and send me a note at patrick@mathjokes4mathyfolks.com.

by venneblock February 16, 2015 at 3:09 pmAWesome Patrick, I’m onto it. Cheers Mathspig

by mathspig February 18, 2015 at 1:38 am[…] 8. Maths Mystery Box 8: JUNK FOOD […]

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by MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig …………………………………………………. with Kerry Cue | Mathspig April 25, 2015 at 8:58 am[…] 8. Maths Mystery Box 8: JUNK FOOD […]

by MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig …………………………………………………. with Kerry Cue | Mathspig April 25, 2015 at 8:59 am