Рет қаралды 47,921
We find a differential equation whose solutions are exactly the set of circles in R^2. After finding a differential equation satisfied by all circles, we then solve it to verify that its solutions only include circles. The constraints r﹥0, |x - a| ≤ r, and |y - b| ≤ r, arise naturally during the solution.
Separation of variables: en.wikipedia.org/wiki/Separat...
Implicit function theorem: en.wikipedia.org/wiki/Implici...
00:00 Intro
00:31 Some technical points
01:28 Deriving the differential equation
04:45 Solving the differential equation