Imagine the field isn't flat, but 200 yards high. Would you still walk over the grass? This is basically what it is about in spaces with curvature: a giant heap in the middle. Or take the earth. There is no way directly through it. Masses bend spacetime and thus it has a curvature and the shortest way isn't a straight line anymore.ChrisisC said:
Have you ever seen a map showing intercontinental airplane routes? Why do you think the airlines use curved routes if not because they are shorter and therefore save money.ChrisisC said:
Good idea! (black is the shortest way, grey the direct line - it shows at least the principle)Dale said:
What exactly are you referring here? The concept of geodesics was not introduced by Einstein.ChrisisC said:
A.T. said:
Could also mean the pseudo-Euclidean line interval in Minkowski space time.ChrisisC said:
A curved line is a line that deviates from a straight path. It can be represented by a mathematical equation and can take on various shapes such as circles, ellipses, and parabolas.
The shortest distance between two points on a curved line is important because it allows us to find the most efficient path between those two points. This is useful in many fields including engineering, transportation, and navigation.
The shortest distance between two points on a curved line can be calculated using the shortest distance formula, which takes into account the curvature of the line. This formula involves using calculus and can be solved using various methods such as differentiation or integration.
Yes, the shortest distance between two points on a curved line can be shorter than the straight-line distance. This is because the curved line may take a more direct path between the two points, even though it may appear to be longer when graphed on a two-dimensional plane.
Yes, there are many real-life applications of calculating the shortest distance between two points on a curved line. Some examples include finding the most efficient flight path for airplanes, determining the optimal route for a train, and designing curved roads for transportation systems.