0 < Beta < 1

the square root of ( 1 - beta squared) is a rational number

and beta is a rational number

Beta does not equal 1

Beta does not equal 0

Beta is a real number

Beta can equal 0.8 and Beta can equal 0.6

Are there any other solutions that use rational numbers and give rationoal numbers?

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Square root of (1 -( pythagorean triple / pythagorean triple ) squared ) = pythagoeran triple / pythagorean triple

(1 - ( a/c )^2)^(1/2) = b/c

where a, b and c are pythagorean triples

en.wikipedia.org/wiki/Pythagor

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