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That is, 7.92 units of distance are equivalent to 1 unit of climb. For convenience an 8 to 1 rule can be used. 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).
A random walk is a discrete fractal (a function with integer dimensions; 1, 2, ...), but a Wiener process trajectory is a true fractal, and there is a connection between the two. For example, take a random walk until it hits a circle of radius r times the step length.
The discrete Fréchet distance, also called the coupling distance, is an approximation of the Fréchet metric for polygonal curves, defined by Eiter and Mannila. [6] The discrete Fréchet distance considers only positions of the leash where its endpoints are located at vertices of the two polygonal curves and never in the interior of an edge.
Assuming a perfect sphere with no terrain irregularity, the distance to the horizon from a high altitude transmitter (i.e., line of sight) can readily be calculated. Let R be the radius of the Earth and h be the altitude of a telecommunication station. The line of sight distance d of this station is given by the Pythagorean theorem;
Mean squared displacement. In statistical mechanics, the mean squared displacement (MSD, also mean square displacement, average squared displacement, or mean square fluctuation) is a measure of the deviation of the position of a particle with respect to a reference position over time. It is the most common measure of the spatial extent of ...
The public transport accessibility level (PTAL) is a method sometimes used in United Kingdom transport planning to assess the access level of geographical areas to public transport. PTAL is a simple, easily calculated approach that hinges on the distance from any point to the nearest public transport stop, and service frequency at those stops.
Lévy flight. A Lévy flight is a random walk in which the step-lengths have a stable distribution, [1] a probability distribution that is heavy-tailed. When defined as a walk in a space of dimension greater than one, the steps made are in isotropic random directions. Later researchers have extended the use of the term "Lévy flight" to also ...
Both methods require the user to know the relationship between the paces walked, and the distance traveled. [3] There are two main ways to use the beads. One is to represent the distance a person has walked, and the other is to represent the distance they need to walk. In the latter, beads may be used to count down the distance to a destination.
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