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So, for example, if a route is 20 kilometres (12 mi) with 1600 metres of climb (as is the case on leg 1 of the Bob Graham Round, Keswick to Threlkeld), the equivalent flat distance of this route is 20+(1.6×8)=32.8 kilometres (20.4 mi). Assuming an individual can maintain a speed on the flat of 5 km/h, the route will take 6 hours and 34 minutes.
(The distance can be measured by taking the absolute value of the function.) The three green lines represent the values for acceleration at different points along the curve. The expressions given above apply only when the rate of change is constant or when only the average rate of change is required.
The two dimensional Manhattan distance has "circles" i.e. level sets in the form of squares, with sides of length √ 2 r, oriented at an angle of π/4 (45°) to the coordinate axes, so the planar Chebyshev distance can be viewed as equivalent by rotation and scaling to (i.e. a linear transformation of) the planar Manhattan distance.
That is (unlike road distance with one-way streets) the distance between two points does not depend on which of the two points is the start and which is the destination. [12] It is positive, meaning that the distance between every two distinct points is a positive number, while the distance from any point to itself is zero. [12]
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
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