Q: The shortest distance between any two points on the globe is along?

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You get a curve. If you join them along the shortest [Euclidean] distance between them, you get a straight line.

It is the shortest distance between the conductors measured along with the surface of insulators.

There is not a converse, as such, but there are other metrics that may be applicable in different circumstances. One such is the Manhattan distance (deeloped by Minkovsky) which uses the grid pattern of roads as a way to measue distances. On the non-planar surface, such as that of the earth, the shortest distance between two points will be along the "Great Circle" passing through the two points. In some situations people may be interested in the fastest route between two points even if it is not the shortest straight line distance.

If the two lines are parallel, then the shortest distance between them is a single, fixed quantity. It is the distance between any point on one line along the perpendicular to the line.Now consider the situation where the two lines meet at a point X, at an angle 2y degrees. Suppose you wish to find points on the lines such that the shortest distance between them is 2d units. [The reason for using multiples of 2 is that it avoids fractions].The points are at a distance d*cos(y) from X, along each of the two lines.

If they are in the same plane then it is the length of the straight line joining them. If they are not in a plane then things get complicated. On the surface of the earth (a sphere), the shortest distance is an arc along the great circle. The great circle is a circle whose centre is the centre of the earth and which passes through the two places. This is why New York to Tokyo flights go over the Arctic region. With polyhedra, one way to find the shortest distance is to mark the two points on a net the shape. If you can draw a straight line between the points such that all of it is on the net, then that is the shortest distance. You may need to play around with different nets.

It is simply called the distance between the two points - simple as that. How that distance is measured will depend on the nature of the surface on which the two points are located as well as on the metric for measuring distance that is defined on that space.The common metric in Euclidean space is the Pythagorean distance while on the surface of a sphere (like the Earth, for example), distances are measured along the great arc.

It is provided by the markings on a ruler which can be laid along the line.

Across the shortest distance along the english channel from England to France its about 34 km.

Every so-called "great circle" is (more or less) the longest circumference of the Earth that includes any two points. The great circle includes the shortest distance between the two points for travel along the Earth's surface.

Assuming the earth to be a perfect sphere, the shortest distance is an arc of the great circle. The two places and the centre of the earth define a plane. The great circle is the circle formed by the intersection of that plane and the surface of the earth. The shortest route between the two places is the smaller of the two arcs along that circle.

Yes.

The shortest distance between two paralle lines is the length of the line that is perpendicular to both line and intersects both.