Let the unit circle and integer point P = (-1,0) and line L with real slope m which passes through p.
i) For every real number m, L_{m} will intersect circle at the 2nd point Q_{m}. For what range of m will Q_{m} be interior of first quatrant such that x > y?
ii) Illustrate that if Q_{m} is the rational point then m should be too.
iii) Illustrate that if m = u/v is rational number in D then Q_{m} will be rational point of form (a/c, b/c) with a >= b. Determine the formula for each of numbers a, b, c in terms of m.
iv) Illustrate there is no rational number for which a = b
v) Illustrate that if the gcd = (a,c) = 1 then gcd(b,c) = 1 and under what conditions on m=u/v will gcd(a,c) = 1?