The great-circle distance is the shortest distance between two points along the surface of a sphere. It is formed by the intersection of a plane and the sphere through the center point of the sphere. A great circle (also orthodrome) of a sphere is the largest circle that can be drawn on any given sphere. The haversine formula works by finding the great-circle distance between points of latitude and longitude on a sphere, which can be used to approximate distance on the Earth (since it is mostly spherical). In the haversine formula, d is the distance between two points along a great circle, r is the radius of the sphere, П• 1 and П• 2 are the latitudes of the two points, and О» 1 and О» 2 are the longitudes of the two points, all in radians. The haversine formula can be used to find the distance between two points on a sphere given their latitude and longitude: There are a number of ways to find the distance between two points along the Earth's surface. Given the two points (1, 3, 7) and (2, 4, 8), the distance between the points can be found as follows: d =Дistance between two points on Earth's surface Like the 2D version of the formula, it does not matter which of two points is designated (x 1, y 1, z 1) or (x 2, y 2, z 2), as long as the corresponding points are used in the formula. Where (x 1, y 1, z 1) and (x 2, y 2, z 2) are the 3D coordinates of the two points involved. The distance between two points on a 3D coordinate plane can be found using the following distance formulaД = в€љ (x 2 - x 1) 2 + (y 2 - y 1) 2 + (z 2 - z 1) 2 For example, given the two points (1, 5) and (3, 2), either 3 or 1 could be designated as x 1 or x 2 as long as the corresponding y-values are used: The order of the points does not matter for the formula as long as the points chosen are consistent. Where (x 1, y 1) and (x 2, y 2) are the coordinates of the two points involved. The distance between two points on a 2D coordinate plane can be found using the following distance formula

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