Florian KEPLER
31.9K posts
Florian KEPLER
@AurelienEinst
Mégalodon en Physique, Littérature & Sciences...
France Bergabung Nisan 2013
1.1K Mengikuti364 Pengikut
Random events at a constant average rate produce waiting times that follow the exponential distribution.
Its probability density function is f(x) = λe^{-λx} for λ > 0 and x ≥ 0, with mean μ = 1/λ and variance σ² = 1/λ². The cumulative distribution function is F(x) = 1 - e^{-λx}.
It is used to model the time between successive customer arrivals at a service counter.
English
The shortest distance between two points isn't a straight line - it’s a Haversine curve.
The Haversine formula calculates the "great-circle" distance between two coordinates on a sphere using their latitudes (φ) and longitudes (λ).
It is the fundamental math powering every GPS calculation, flight path, and maritime route on our curved planet.
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@mathemetica La perception énergétique (quark tangentiel) 🌦️
Français
Binomial expansions work for any real power, not just whole numbers.
Newton’s theorem gives the infinite series for (x + y) raised to a real exponent a, valid when |x| < |y|:
(x + y)^a = ∑_{k=0}^∞ [a(a-1)(a-2)⋯(a-k+1)/k!] x^{a-k} y^k
The generalized binomial coefficient is that falling product divided by k!.
It is used to derive series approximations for the Lorentz factor in special relativity.
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Florian KEPLER me-retweet
Most people see a rocket. I see an operating system. SpaceX did not become extraordinary because it built rockets. It became extraordinary because it built a system capable of learning, adapting, and improving faster than most organizations thought possible. Vertical integration.
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