Interactive · 2 questions
Definition: A geometric object is convex if, for any two points and in the object, the segment lies entirely in the interior of the object.
Is a square convex?
Correct! If you join any two points inside a square, the resulting segment will still be in the square.
Is a circle convex?
Nice! Using the definition, we can see that if you connect any two points in a circle, the resulting segment should be in the circle.
As a bonus, here's another way to think about convexity intuitively. A fun exercise would be to convince yourself why this intuition is true.
Intuition: An object in 2D space is convex if it is "always curving inwards".