



 
Hi Silvan, The answer to your question relies on what is perhaps the best known result in all of mathematics called the Theorem of Pythagoras. The theorem states that
Said algebraically the theorem is
The converse is also true
Pythagoras lived from 570 to 495 BC but there is considerable evidence that this result was known much earlier. Why does this have any connection to your question? Let me draw a picture of a circular clock face with centre at (0, 0) and with a point (x, y) on the circumference. Next draw a vertical line segment from (x, y) to the xaxis and a line segment from (x, y) to (0, 0). What I see now is a right triangle with sides of length x, y and r where r is the radius of the circle. Hence by the Theorem of Pythagoras, x^{2} + y^{2} = r^{2}. The converse of the Theorem of Pythagoras implies that if (x, y) is any point in the plane and x^{2} + y^{2} = r^{2} then (x, y) must lie on the circumference of the circle with center (x, y) and radius r. This then gives you the answer to your question.
Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 