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The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
The first general equation of motion developed was Newton's second law of motion. In its most general form it states the rate of change of momentum p = p(t) = mv(t) of an object equals the force F = F(x(t), v(t), t) acting on it, [13] : 1112. The force in the equation is not the force the object exerts.
Friction of distance. Friction of distance is a core principle of geography that states that movement incurs some form of cost, in the form of physical effort, energy, time, and/or the expenditure of other resources, and that these costs are proportional to the distance traveled. This cost is thus a resistance against movement, analogous (but ...
Great-circle navigation. Great-circle navigation or orthodromic navigation (related to orthodromic course; from Ancient Greek ορθός (orthós) 'right angle' and δρόμος (drómos) 'path') is the practice of navigating a vessel (a ship or aircraft) along a great circle. Such routes yield the shortest distance between two points on the globe.
The map, initially utilized by Edward Lorenz in the 1960s to showcase irregular solutions (e.g., Eq. 3 of [1]), was popularized in a 1976 paper by the biologist Robert May, [2] in part as a discrete-time demographic model analogous to the logistic equation written down by Pierre François Verhulst. [3] Mathematically, the logistic map is written
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
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 time–distance diagram is a chart with two axes: one for time, the other for location. The units on either axis depend on the type of project: time can be expressed in minutes (for overnight construction of railroad modification projects such as the installation of switches) or years (for large construction projects); the location can be (kilo)meters, or other distinct units (such as ...