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The Erdős Distance Problem consists of twelve chapters and three appendices. [5]After an introductory chapter describing the formulation of the problem by Paul Erdős and Erdős's proof that the number of distances is always at least proportional to , the next six chapters cover the two-dimensional version of the problem.
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 slides ...
According to Paul Virilio, time-space compression is an essential facet of capitalist life, saying that "we are entering a space which is speed-space ... This new other time is that of electronic transmission, of high-tech machines, and therefore, man is present in this sort of time, not via his physical presence, but via programming" (qtd. in ...
Daily time dilation (gain or loss if negative) in microseconds as a function of (circular) orbit radius r = rs/re, where rs is satellite orbit radius and re is the equatorial Earth radius, calculated using the Schwarzschild metric. At r ≈ 1.497 [Note 1] there is no time dilation. Here the effects of motion and reduced gravity cancel.
The first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1 2 = 4.9 m. After two seconds it will have fallen 1/2 × 9.8 × 2 2 = 19.6 m; and so on. On the other hand, the penultimate equation becomes grossly inaccurate at great distances.
A trivial example. In mathematics, the mountain climbing problem is a mathematical problem that considers a two-dimensional mountain range (represented as a continuous function), and asks whether it is possible for two mountain climbers starting at sea level on the left and right sides of the mountain to meet at the summit, while maintaining equal altitudes at all times.
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The horizontal axis is comoving distance, the vertical axis is conformal time, and the units have the speed of light as 1. For reference . The theory of cosmic inflation has attempted to address the problem by positing a 10 −32 -second period of exponential expansion in the first second of the history of the universe due to a scalar field ...