Recent content by AlephOmega

Awesome! Cool formula and cool solving meathod.

I can use half-angle formulas to get it to √((1-cos(pi/5))/2)

Addition formulas (ex: sin(a+b) = sina cosb + cosa sinb ) Power reducing formulas (sin(a)^2 = (1-cos 2a)/2 ) Half and double angle formulas (derived from the above two formulas) Sum to product formulas ( sina + sinb = 2sin((a+b)/2)cos((a-b)/2) ) and product to sum formulas ( cosa * sinb =...

Oops sorry it should be (1/4)(√5 - 1) and I got it from wolfram alpha

I have learned a lot of formulas for converting trigonometric values, but when I looked up sin(pi/10) I got the exact answer (1/4)(√5 +1). I tried to arive at this using formulas, but I couldn't. How is this found? What other angles can be found exactly. Ps. I already know about how taylor...

I don't think anyone can explain it, but does anyone know what is up with this news about neurtinos going faster than the spead of light? I can feal all of physics crumbling around me whenever I think about it!

Oh. Fun stuff.

Can't you make a set out of anything? I already know the ordinals are uncountably infinite, so I just want it one step farther, "how" uncountably infinite. PS. I mean the set of the numbers themselves, not the sets they describe.

Does anyone happen to know what the cardinality of the set of ordinal number (transfinite and otherwise) is? A simplified proof would also be much appreciated. Recently I have been very interested in transfinite numbers and the logically gorgeous proofs involved :D