Trigonometry is one of those topics that seems completely cut-and-dried, yet continues to offer-up new and fascinating results.
As my company logo will attest, I’m particularly fond of (what I’ve dubbed) the Complete Triangle figure above. (See my post “(Almost) Everything you need to remember about trig…”.) Strictly speaking, this diagram isn’t new to mathematics, but it’s disappointingly unfamiliar to mathematics teachers. My mission seems to be to proselytize this figure for the betterment of mathematical education.
And then there are other dabblings, as later posts will show. The now-decades-long dabblings in the “dimensionally-enhanced” trigonometry of tetrahedra have become so significant as to warrant their own subject category, Hedronometry.