Question

What is a geodesic? Explain with reference to the book "A briefer history of time".

Answer 1

it is shortest route between two points of earth
it isshortest path between two points in a curved space can be found by writing the equation for the length of a curve (a function f from an open interval of R to the manifold and then minimizing this length using the calculus of variations. This has some minor technical problems, because there is an infinite dimensional space of different ways to parameterize the shortest path. It is simpler to demand not only that the curve locally minimizes length