about 565 miles
about 565 miles
The longest distance across a circle is its diameter and the shortest distance is a minor chord
The two points and the centre of the earth define a plane, and the intersection of this plane with the surface of the earth is a circle - the "Great Circle". The shortest distance between the two points is the smaller of the two arcs on this circle.
In plane geometry, the shortest distance between two points is a line. In spherical geometry, the shortest distance between two points is a segment of a great circle. The distance between one point and another is known as the displacement.
In plane geometry, the shortest distance between two points is a line. In spherical geometry, the shortest distance between two points is a segment of a great circle. The distance between one point and another is known as the displacement.
about 70 miles
a circle
The answer lies in Non-Euclidean geometry (spherical geometry). Florida, the Philippines, and Alaska are three collinear points on a great circle, a great circle is the equivalent to a line in Euclidean(2-D) geometry. A great circle is also classified as the shortest distance from one point to another around a circle. Because the earth is round, the distance seen on a flat map is a lot further than the distance on a globe, due to distortion. Therefore, following the great circle that goes through the three collinear points of Florida, the Philippines, and Alaska, it is a shorter distance to fly over Alaska
Great circle (shortest direct) = 315 miles (506 km)
Great circle (shortest direct) = 539 miles
radius
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.