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For instance, an object located at position p at time t 0 can only move to locations within p + c(t 1 − t 0) by time t 1. This is commonly represented on a graph with physical locations along the horizontal axis and time running vertically, with units of t {\displaystyle t} for time and ct for space.
Seth Lloyd proposed an alternative approach to time travel with closed timelike curves (CTCs), based on "post-selection" and path integrals. [21] Path integrals are a powerful tool in quantum mechanics that involve summing probabilities over all possible ways a system could evolve, including paths that do not strictly follow a single timeline ...
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) ' shortest time '), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead ...
A tautochrone curve or isochrone curve (from Ancient Greek ταὐτό ' same ' ἴσος ' equal ' and χρόνος ' time ') is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve.
Angle notation can easily describe leading and lagging current: . [1] In this equation, the value of theta is the important factor for leading and lagging current. As mentioned in the introduction above, leading or lagging current represents a time shift between the current and voltage sine curves, which is represented by the angle by which the curve is ahead or behind of where it would be ...
In general relativity, a congruence (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime. Often this manifold will be taken to be an exact or approximate solution to the Einstein field equation.
The bathtub curve is a particular shape of a failure rate graph. This graph is used in reliability engineering and deterioration modeling. The 'bathtub' refers to the shape of a line that curves up at both ends, similar in shape to a bathtub. The bathtub curve has 3 regions: The first region has a decreasing failure rate due to early failures.
A "coin graph" is a graph formed by a set of circles, no two of which have overlapping interiors, by making a vertex for each circle and an edge for each pair of circles that kiss. The circle packing theorem , first proved by Paul Koebe in 1936, states that a graph is planar if and only if it is a coin graph.