Chapter1: Intro

Question 1

Curves can be

Answer 1

• trajectories of particles in space;
• world-lines of events in space-time;
• configurations of pieces of string, cable, or DNA;
• graphs of functions.

Question 2

Surfaces and curvature useful for

Answer 2

• computer graphics;
• medical imaging;
• image recognition;
• general relativity;
• calculating soap bubble shapes.

Question 3

Accurate maps>

Answer 3

The curvature of the Earth means that each way of drawing it on a plane will
involve compromises.

some maps correctly represent bearings
(i.e. angles), and some maps correctly represent areas.

No map correctly
represents both, nor correctly represents distances! We will prove this using curvature of surfaces.