I tried to find this online, and couldn't come up with clear directions and pictures together, so here's my attempt at explaining the construction of a card ball. And de-mystifying the trick of getting an equilateral triangle inside a circle is maybe the best part.
For my project I didn't use actual card stock, just scrapbook paper. I
chose five different but coordinating prints. I also used a 1 7/8"
circle punch, a glue stick, and took my lead from
HellomynameisHeather's Paper Globes.
I have to say, all that cutting of templates, pre-scoring your fold
lines and using special glue, etc. in her directions is not for me. I
mean, sure, if I was going to be published in ME's Home Companion, but
for Stay.See.Make.Do. the motto is Make.Do. - not
Make.Perfect.and.Make.Self.Crazy. (I think a lot of the Crazy would
come from the fumes from the E6000 glue she recommends. No offense
meant to Heather, I'm sure. Her stuff does rock.)
Start by making your template. You need a circle and a triangle. Heather kindly gives you a pattern to trace and/or cut out so that you can have an equilateral triangle that fits perfectly inside the circle. But that only works if you use her circles. Because I am lazy and did not want to cut twenty circles by hand after tracing hers, I decided to use a punch.
Having taken higher maths in college, I figured something in my trig/calc/geom/diff history would enable me to find the exact measurements to put an equilateral triangle inside a circle. This is a triangle and a circle, folks. My preschooler could tell me that much, so how tough could it be? Well, I struggled for five minutes with fractions (who chose a 1 and 7/8 punch?) and cross-multiplication (she's got two circles/triangles on her instructions) and pi (well, it is a circle after all) and realized that not only had most of my higher maths filtered out of my brain over the past (gasp!) 15 years, but that none of it was actually necessary. I put down my pencil and decided to rely on my much sharper origami skills.
Punch a circle out of scrap paper and fold it in half. Then match the fold lines and fold in half the other way to give yourself the center point.
Now here is the magic: fold one edge of the circle so that it touches the center point. Any edge anywhere on the circle will do.
Keep that fold, and do it again starting the next fold at the point of the fold you just made. Bring the edge to the center point. Okay, so I don't know how to explain it; look at the picture, please:
Do it one more time and...
There you have one nearly perfect equilateral triangle inside your circle.
****I should point out here that it looks like there is a big hole/space in the center (above) but that is only because the flaps are not lying down completely flat. When flat, there should only be about enough space to poke a tack through the center.****
No math, no stress.
My next post will be the rest of the construction of the paper ball. But if you can't wait, I'm sure you can figure it out from Heather's pdf (linked above).