WildTrig4: Five main laws of rational trigonometry

Hi, Dr. Wildberger. You're probably getting sick of me, but I'm stuck on algebra here again. (I'm a grad student; this is embarrassing.)

At 5:05 you use the Triple-Quad Formula in the form (P3+Q2-P1)^2=4(P3)(Q2), but the largest quadrance of three in the diagram is Q2. When I watch you derive the TQF in another video, it seems clear to me that the odd sign in the squared term has to go on the large quadrance. If I'm making a bad assumption here, could you point me in the right direction please?

Well, guess what: I worked through it with side-lengths and found out once again that you were right and I was wrong. (But in my defense, I would never have intuitively guessed you could rearrange it like that and still have it be true.) Sorry for bothering you with my feats of ineptitude. Keep up the good work.

The general Triple Quad Formula has the form (x+y-z)^2=4xy and the important thing is that the two variables involved in the right hand side occur with the same sign in the left hand side. Perhaps it's easier to remember in the equivalent form (x+y+z)^2=2(x^2+y^2+z^2).

you kind of lost me on the cross law, a bit more examples wouldve been useful

Trigonometry without a calculator! I won't be able to use these techniques in my school exams though... pity

Hello wildberger. I like you work a lot...
I'd like to ask: is there a development of the Rational Trigonometry laws for R^3 ? is it straight-forward?
Thank you!

Rational trig can also be developed in R^3 but it is theoretically more work. It turns out that also one needs some additional concepts, basically the idea of a `solid spread' to replace `solid angles'.