I have a question regarding how you go about constructing a proof of an idea. I'm not familiar with very many examples - Pythagoras's proof, Euclid's proof that sqrt(2) is irrational, and a handful of others I know.
I'm trying to 'prove' something that seems intuitively true, but I know that's not enough in the world of maths.
So, take 2 coordinates on an x,y graph and join them with a line. Take the midpoint of that line and construct a perpendicular line. Taking the center of a circle to be anywhere along this line is there an infinite number of circles that pass through our original coordinates.
(x−h)^2+(y−k)^2=r^2 describes a generic circle and if (h,k) is the center of the circle.
So, as i've said this seems intuitively true and i'm able to show that it is true for certain circles, but how do I extend that into being true for an infinite number of circles?