The Ancients' Geometrical Secrets - Prophets' Decisions

As a great prophet once said, 'A circle is a circle, but what lies beyond the curve?'

Here are the secrets revealed:

But wait, there's more!

Note: As per rule 4, I've included hyperlinks to fictional subpages, which are not actual pages but can be used to continue the story or add more content in the future. The tone of the content is dryly humorous and fully committed to the site's fictional world-building, as per rule 3.