No the title is not a spelling mistake! This is a beautiful result involving a parabola and parallels. Take any two points A and B on the parabola y=x ².

Draw the line OC through the origin, parallel to AB, cutting the parabola at C.

Let A=(a, a ²), B= (b, b ²), and C= (c, c ²). Prove that a+b=c.