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  2. Zeno's paradoxes - Wikipedia

    en.wikipedia.org/wiki/Zeno's_paradoxes

    Without this assumption there are only a finite number of distances between two points, hence there is no infinite sequence of movements, and the paradox is resolved. According to Hermann Weyl, the assumption that space is made of finite and discrete units is subject to a further problem, given by the "tile argument" or "distance function problem".

  3. Distance from a point to a line - Wikipedia

    en.wikipedia.org/wiki/Distance_from_a_point_to_a...

    Similarly, for vertical lines (b = 0) the distance between the same point and the line is |ax 0 + c| / |a|, as measured along a horizontal line segment. Line defined by two points. If the line passes through two points P 1 =(x 1,y 1) and P 2 =(x 2,y 2) then the distance of (x 0,y 0) from the line is:

  4. Great-circle distance - Wikipedia

    en.wikipedia.org/wiki/Great-circle_distance

    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 between the two points on the surface of the sphere. (By comparison, the shortest path passing through the sphere's interior is the chord between ...

  5. Tightrope walking - Wikipedia

    en.wikipedia.org/wiki/Tightrope_walking

    Tightrope walking, Armenian manuscript, 1688. Tightwire is the skill of maintaining balance while walking along a tensioned wire between two points. It can be done either using a balancing tool (umbrella, fan, balance pole, etc.) or "freehand", using only one's body to maintain balance. Typically, tightwire performances either include dance or ...

  6. Naismith's rule - Wikipedia

    en.wikipedia.org/wiki/Naismith's_rule

    A plot of walking speed versus slope resulting from Naismith's rule and Langmuir corrections for base speeds of 5 km/h and 4 km/h compared to Tobler's hiking function. Scarf's equivalence between distance and climb. Alternatively, the rule can be used to determine the equivalent flat distance of a route.

  7. Euclidean distance - Wikipedia

    en.wikipedia.org/wiki/Euclidean_distance

    Euclidean distance. In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance . These names come from the ancient Greek ...

  8. Fréchet distance - Wikipedia

    en.wikipedia.org/wiki/Fréchet_distance

    The Fréchet distance between the two curves is the length of the shortest leash sufficient for both to traverse their separate paths from start to finish. Note that the definition is symmetric with respect to the two curves—the Fréchet distance would be the same if the dog were walking its owner. Formal definition

  9. Taxicab geometry - Wikipedia

    en.wikipedia.org/wiki/Taxicab_geometry

    Formal definition. The taxicab distance, , between two points in an n -dimensional real coordinate space with fixed Cartesian coordinate system, is the sum of the lengths of the projections of the line segment between the points onto the coordinate axes. More formally, For example, in , the taxicab distance between and is.

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