:: deftheorem Def8 defines FanS JGRAPH_4:def 8 :
for s being Real
for q being Point of (TOP-REAL 2) holds
( ( (q `1) / |.q.| >= s & q `2 < 0 implies FanS (s,q) = |.q.| * |[((((q `1) / |.q.|) - s) / (1 - s)),(- (sqrt (1 - (((((q `1) / |.q.|) - s) / (1 - s)) ^2))))]| ) & ( (q `1) / |.q.| < s & q `2 < 0 implies FanS (s,q) = |.q.| * |[((((q `1) / |.q.|) - s) / (1 + s)),(- (sqrt (1 - (((((q `1) / |.q.|) - s) / (1 + s)) ^2))))]| ) & ( ( not (q `1) / |.q.| >= s or not q `2 < 0 ) & ( not (q `1) / |.q.| < s or not q `2 < 0 ) implies FanS (s,q) = q ) );