Dude, I got TWO liberal arts degrees and I'm telling you it's trivial, if not "double-walled". This isn't even "real math" so much as it's "mock up scaling":
1) Measure the side and base of a face of each pyramid size.
2) Multiply those values by "X" where X is the scaling factor (x10, x20, x30 whatever).
3) Draw a triangle with those measurements:
3a) Draw a straight line for the base line
3b) Use a compass or a string and pencil to strike an arc from each end of the line, at the scaled side length.
3c) Where the arcs intersect is the peak: draw a line from the intersection to each end of the base line.
4) Cut out that bigger triangle--your "stencil".
5) Lay on material, outline, shift to line up with one side, outline, repeat two more times.
6) You now have four triangles, sharing edges with each other. Cut out outermost edge (two sides, four bases).
7) Fold and tape.
It has occurred to me that you MIGHT want to shorten your medium and small triangle stencil, once cut out and before your lay it out on the material (i.e. Step 4a), because your wall thickness will directly affect how high they stack on each other (nesting needn't be "perfect" to work). For instance, thin cardboard, done as above, stacked into a tree, would only show about an inch or so of the large and medium (assuming about a two-foot-high large) because the material is so thin it doesn't "stand off" the lower piece. That's why folks make double-walled mids out of cardboard.
BUT... with camping mat and larges about a foot high, I think the mat's thickness could provide stand-off. Or, as above, just shorten the medium and small stencil, which will exaggerate the tree stack (and, yes, make a nest stack "rattle" a bit--whatcha want for an afternoon's work?)
Anyhow, good luck... but I really think you'll spend more time hunting for a pattern with the right proportions than Steps 1 - 5 of the above procedure require;
-------- Original Message --------
Subject: Re: [Rabbits] Giant Pyramids
From: miyu <xmiyux@xxxxxxxxx>
Date: Wed, July 25, 2007 3:45 pm
To: "Rabbits Discussion List" <rabbits@xxxxxxxxxxxxxxxxxxxx>
All good ideas.
One thing though, while I am a teacher, I have a liberal arts degree. This means the last time I did geometry or any real mat was in high school. :lol: