Kids Math-Based Craft Project based on New Glassblowing Mold Design

I started work on a custom 6-sided steel glassblowing mold, based on a pyramid (faceted cone).

In the process I uncovered a quick and easy math-based craft project which you may find suitable for your elementary school (or older) children. My brother’s kids seemed to enjoy this project yesterday during Thanksgiving.

Basically, with only a protractor, scissors or paper cutter, ruler, and a few pieces of tape, you and your kids can create n-sided pyramids. In other words, 3, 4, 5, or 6-sided pyramids that are fun to make, and if decorated, can make some really nice paper hats, kind of like Wizard Hats! As well as perhaps teaching a little bit of math along the way!

This project started from the wonderful online article Compound Angles – Calculations and Jig for Making for N-sided Pyramids by Tony Beugelsdijk of the Albuquerque Woodworkers Association. I have an extra copy of that PDF stored
here (if you have a problem with the first link).

There is some really interesting math — algebra and trigonometry — which I’ll go over at the end of the article, if you are interested, but for now, here is a summary table if your goal is to have some math-based fun with a kids craft project, and make some hats!

I’m going to make the last one — a 5-sided hat which is 4 inches on each side and 11 inches tall.

1. Start with the protractor on the corner of a piece of standard letter-size paper, and place a dot at 10 degrees.
   
   
2. Draw a 5-inch line along the dot to the corner of the paper
   
   
3. Draw another line from the point where you ended to the other corner of the paper.
   
   
4. You will need to hold a stack of 5 pieces of paper, and cut out the isosceles triangles you just drew. This step is especially easy with a paper cutter
   
   
5. You will then hopefully have five identical triangles
   
   
6. Which you need to tape together their long sides.
   
   
7. Now (while flat) would be a good time to decorate the sides!
   
   
8. Tape the final edges together, you’ve got a beautiful hat!
   
   

If you would prefer a flat-topped hat, you could create a truncated pyramid (Pyramidal Frustum), using sides which look more like this (for a 6-sided two-inch-to-four-inch truncated pyramid).

How are the angles in the table above calculated? Glad you asked! Tony Beugelsdijk’s article gives worked-through examples of the math, and from those, I created this Excel spreadsheet (also available in Excel 97-2003 format) which looks like this (from the last example in the table, and the hat we made above):

In Excel 2007, typing the keyboard shortcut (toggle) ctrl+` (that is the “Grave Accent” key which is above the tab key), shows the formulas:

A1: n
B1: 5
C1: number of sides

A2: h
B2: 13.6
C2: vertical height of pyramid (not length of side)

A3: a
B3: 5
C3: base length

A4: Theta θ
B4: =ATAN(SQRT((2*h/a)^2+k^2))*(180/PI())
C4: or
D4: =90-theta
E4: degrees

A5: Phi Φ
B5: =ATAN((2*h)/(a*k))*(180/PI())
C5: first angle to be cut on the table saw

A6: b
B6: =SQRT(h^2+(a*k/2)^2)
C6: lenth of side (face altitude), this is a piece of legal-size paper

A7: k
B7: =TAN(PI()/2-PI()/n)
C7: used in various calculations