The great-circle distance or orthodromic distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior).The distance between two points in Euclidean space is the length of a straight line between them, but on the sphere there are no straight lines.
"The shortest distance between two points is a..." - Archimedes quotes from BrainyQuote.com
The shortest distance between two points ? It is a straight line in 3 Dimensional world. In 2 Dimensional world, it can be a very long distance. Consider your living room, What is the shortest distance between a point A at the center of floor and a point B at the ceiling fan directly above it .
So, if we define a straight line to be the one that a particle takes when no forces are on it, or better yet that an object with no forces on it takes the quickest, and hence shortest route between two points, then walla, the shortest distance between two points is the geodesic; in Euclidean space, a straight line as we know it.
In plain geometry, the shortest distance between two points is a straight line, or, more precisely, the line segment connecting point A to point B.
There are two parts of the exercise; 1: to have the student prove that the shortest distance between two points is a straight line and 2: to have the student prove that by using the Pythagorean Theorem they will accurately calculate the shortest distance. Understand tracking vertically and horizontally on a coordinate grid
The resolution of an optical microscope is defined as the shortest distance between two points on a specimen that can still be distinguished by the observer or camera system as separate entities.
(The distance between two points is the shortest distance along any path). Such a distance function is known as a metric. Together with the set, it makes up a metric space. For example, the usual definition of distance between two real numbers x and y is: d(x,y) = | x − y |.
Proving that the shortest distance between two points is indeed a straight line:. Now to Prove: (well known equation for a straight line in Cartesian coordinates) 1) Distance between two points is "L", which in turn is the following integral: