The Museum of Mathematics in NYC created this hyperbolic paraboloid sliceform. It is amazing to see the form take place as you put it together. It lies flat after you put it together! You have to love it!
My daughter loved the fact that when the parabola lies flat it shows the integrals for the area under the curve...a good sliceform to show to a calculus class. For the less mathematical people, the area under the curve can be explained as...what is the area of this three dimensional parabola? The area of multiple two dimensional rectangles added together will result in the approximation of the total area of this 3 D parabola.
Here is the link to the pdf of this sliceform. http://momath.org/wp-content/uploads/Hyperbolic_Parabola_Model_85by11.pdf
If you have a Cameo Silhouette, you are in luck because I created a .Studio file for this sliceform so you do not have to do any of the cutting by hand.
Here are the two .Studio files. Make one copy of each.
After cutting the file, there might be some confusion as to how to put the pieces together. I hope this explanation helps...otherwise...try to label the pieces according to the pdf file. The pieces slide together in the following order. Pair up the pieces of file #1. Do the same for File #2. There should be one piece that does not pair up - a rectangle. Take the two rectangles and slide them together in the middle. All the other pieces are now trapezoid shapes. There should be six of them for File #1. Slide the pieces together from the outside in starting with the smallest length trapezoid using the middle slit. The highest points will be on the opposite sides. Repeat with pieces of File #1. Do the same for File #2 pieces. The opposite sides will have the tallest side on the outside.