Cute Geometry Proof

Math Online Tom Circle

Prove:  Any line L will cut a circle at most 2 points:

Let circle C (x,y) be unit circle defined by
C(x,y) : x² + y² = 1
 

Factorize C(x,y) : (x+iy) (x-iy) = 1 in the complex plane.
So C  = {L1} U {L2}
where L1 and L2 are two lines

L1= x+iy
L2= x – iy
L1 and L2 intersect at origin (0,0):
x+ iy = x-iy
We know that any line L will cut L1 at most 1 point, and L2 at most 1 point
Therefore,
L cuts the circle C at most (1+1=) 2 points. [QED]

View original post

Advertisements

About tomcircle

Math amateur
This entry was posted in Uncategorized. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.