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This formula involves the trace of the Frobenius on the étale cohomology, with compact supports, of ¯ with values in the field of -adic numbers, where is a prime coprime to . If X {\displaystyle X} is smooth and equidimensional , this formula can be rewritten in terms of the arithmetic Frobenius Φ q {\displaystyle \Phi _{q}} , which acts as ...
This ratio of densities, and other ratios (using four fundamental constants: speed of light in vacuum c, Newtonian constant of gravity G, reduced Planck constant ℏ, and Hubble constant H) computes to an exact number, 32.8·10 120. This provides evidence of the Dirac large numbers hypothesis by connecting the macro-world and the micro-world.
A mathematical coincidence often involves an integer, and the surprising feature is the fact that a real number arising in some context is considered by some standard as a "close" approximation to a small integer or to a multiple or power of ten, or more generally, to a rational number with a small denominator.
This is the formula for the relativistic doppler shift where the difference in velocity between the emitter and observer is not on the x-axis. There are two special cases of this equation. The first is the case where the velocity between the emitter and observer is along the x-axis. In that case θ = 0, and cos θ = 1, which gives:
The relation is: = +. where L is the light yield, S is the scintillation efficiency, dE/dx is the specific energy loss of the particle per path length, k is the probability of quenching, [1] and B is a constant of proportionality linking the local density of ionized molecules at a point along the particle's path to the specific energy loss; [1] "Since k and B appear only as a product, they act ...
Luck. Fate. Blessing. A glitch in the matrix. Or, if you’re more skeptical, just a coincidence.. It’s a phenomenon that, from a statistical perspective, is random and meaningless.
ζ(3) was named Apéry's constant after the French mathematician Roger Apéry, who proved in 1978 that it is an irrational number. [4] This result is known as Apéry's theorem . The original proof is complex and hard to grasp, [ 5 ] and simpler proofs were found later.
Some quite famous coincidences weren’t even mentioned in this list. For example, the one about the writer Mark Twain and the comet. He was born on November 30, 1835, when Halley’s comet came ...