Posts Tagged ‘skewers’

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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.    

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2. Wooden skewers

make-hyperbolic-paraboloid-using-skewers.w654

You will find full instructions at the Mathscraft blog.

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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.

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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.

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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