Look at David Stephenson's 24 images on his portfolio, taken from Heavenly Vaults.
What would have happened if the architects mixed up 90 degrees with 60 degrees? Disaster.
Now check out Vi Hart's Origami Proof on Youtube. Try it out!
At the very least, you'll have folded your paper with wonderful creases; they give you a working space for your next task.
Use your folded paper to create a design for a space that you'd like to see when you look upward. Imagine it painted on a ceiling. If you were to do that, you'd need to divide your space carefully, check your measurements (twice) and then begin painting.
Oh, and visit a chapel, or somewhere with a big roof space. Ladies, did you look upwards at King's?
And while we're wandering about here, you should know about this.
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