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Pythagorean Theorem Roots by Parker Emmerson © 2009-2010.nb
b Ø ArcSinB
4 p r q - r q2 4 p2
SolveBArcSinB
4 p r q - r q2 4p
::r Ø
2p
H4 p - qL q
F = ArcSinB
2
F
2p
F == ArcSinB
H4 p - qL q 2p
F, rF
H4 p - qL q H4 p - qL q
>>
ü A quick calculation: 2 p r2 +
2p
4p-
r4 -r2 h2
2 p r2 +
r2
r4 -r2 h2 r2
SolveBr ==
, hF 2 p r2 +
4p-
r4 -r2 h2
2 p r2 +
r2
r4 -r2 h2 r2
88h Ø - 1<, 8h Ø 1<<
2 p r2 +
2p
4p-
r4 -r2 h2
2 p r2 +
r2
r4 -r2 h2 r2
SolveBr ==
, rF 2 p r2 +
4p-
r4 -r2 h2
2 p r2 +
r2
r4 -r2 h2 r2
8<
2p
p2 - p2 Sin@bD2
4p-2 p+
p2 - p2 Sin@bD2
2 p+
SolveBr ==
, bF 4p-2 p+
2
2
p - p Sin@bD
2
2 p+
2
2
p - p Sin@bD
1 1 ::b Ø - ArcSinB F>, :b Ø ArcSinB F>> r r
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