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!
|Number of Sides||Width (inches) of Base Side||Height of Pyramid (hat)||Angle to be Measured|
|4 sides||6 inches||11 inches (letter-size paper)||15 degrees|
|6 sides||5.5 inches||11 inches (letter-size paper)||14 degrees|
|6 sides||4 inches||11 inches (letter-size paper)||10 degrees|
|5 sides||5 inches||11 inches (letter-size paper)||13 degrees|
|5 sides||4 inches||11 inches (letter-size paper)||10 degrees|
I’m going to make the last one — a 5-sided hat which is 4 inches on each side and 11 inches tall.
- Start with the protractor on the corner of a piece of standard letter-size paper, and place a dot at 10 degrees.
- Draw a 5-inch line along the dot to the corner of the paper
- Draw another line from the point where you ended to the other corner of the paper.
- 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
- You will then hopefully have five identical triangles
- Which you need to tape together their long sides.
- Now (while flat) would be a good time to decorate the sides!
- 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:
C1: number of sides
C2: vertical height of pyramid (not length of side)
C3: base length
A4: Theta θ
A5: Phi Φ
C5: first angle to be cut on the table saw
C6: lenth of side (face altitude), this is a piece of legal-size paper
C7: used in various calculations