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Maths Mystery Box 8: JUNK FOOD

February 16, 2015
Maths Mystery BOX 8

Middle School Maths Challenge

Make a 3D graph or Make Like a Pringle

pic 0 pringles hyperbolic paraboloid

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 = ax2 + 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.

pic 1 eqn

pic 2 graph_hyperbolic_paraboloid    mathinsight

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). 

pic 3 hyperbolic paraboloid  with wool

                  NB: The thread should be a straight line.

                  Detailed instructions here.    

 …………………………………………………………………

2. Wooden skewers

make-hyperbolic-paraboloid-using-skewers.w654

You will find full instructions at the Mathscraft blog.

 …………………………………………………………………

3. Cardboard only

hyperbolic-paraboloid

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

 …………………………………………………………………

4. Bubble

pic 4a saddle bubble

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

pic 4b hyperbolic paraboloid bubble 1

 

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

 ………………………………………………………………… 

The Hyperbolic Paraboloid in Construction

The structure is often used today for rooves.

 

pic 5

Not everyone is happy with Pringles:

pic 6 pringles joke

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5 comments

  1. 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.


    • AWesome Patrick, I’m onto it. Cheers Mathspig



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