Diff — Pi
Revision #624 → #1472 · back to history
addedDefinition of π as ratio of circumference to diameter7bcbdcaa88ac
addedWeierstrass integral definition of π246504211afa
addedBaltzer–Landau definition via cosine027aa9277de6
addedDefinition via complex exponential5f45fa7c4463
addedπ is irrationalcdf0a8bbf435
addedNormality conjecture for πd1fe6260a94c
addedπ is transcendental (Lindemann–Weierstrass)bce0d39f8c50
addedImpossibility of squaring the circled7b284cb00d0
addedSimple continued fraction of πf6a5f2cbbb47
addedBest rational approximations from continued fraction5ba3a9ed255a
addedPolar representation of complex numbers3c222c7e735b
addedEuler's formula0c241b396672
addedEuler's identitya4d9bf6fa653
addednth roots of unity29e06f85ec1f
addedArchimedes' polygon bounds on πdf05695ea478
addedViète's formulaa417f2a0f4e1
addedWallis product1c3f3d474750
addedGregory–Leibniz arctangent series2067f4f533eb
addedMachin's formula0d92827c8e60
addedNewton's accelerated arctan series01fe28105f37
addedGregory–Leibniz series for π36bdd715574c
addedNilakantha's series for π188389c560ad
addedBasel problem solution (ζ(2) = π²/6)e4b2b16656f2
addedLambert's proof that π is irrational2eebfe571f8e
addedLegendre: π² is irrational4b179b5eac59
addedLindemann's proof that π is transcendental2929e137a90e
addedGauss–Legendre iterative algorithm2a6dd49584ec
addedRamanujan's series for π016e97eb4da5
addedChudnovsky formulac9a858312f5e
addedPlouffe's PSLQ template formulaec63db3157d67
addedBuffon's needle approximation of π3bf9ec905cab
addedDots-in-square Monte Carlo method314a9e74915d
addedRandom walk computation of πbe3838200914
addedBBP digit extraction formula4b7575f17ab8
addedCircumference of a circle8abdcbfd87f8
addedArea of a circledf0d52829101
addedArea of an ellipse3f1d88722c91
addedVolume of a sphere24e638e88e85
addedSurface area of a spheread524f02f940
addedBarbier's theoremf04b65981169
addedIntegral for area of semicircle5c90cead6eb6
addedRadian measure with π694b771f5055
addedPeriodicity of sine and cosineffee7ae44fc7
addedVibrating string eigenvalue problem9212584aa7a5
addedWirtinger's inequalityae2d1d64cfd6
addedIsoperimetric inequality0d7b5829d229
addedCritical Sobolev inequality in two dimensionsee88c2b2cc50
addedPoincaré inequality with π as best constant598628b8fb64
addedFourier transforma9206f4d904c
addedHeisenberg uncertainty principledf66e1676d38
addedGaussian function (normal distribution density)e81eeca7d730
addedGaussian integral441712d2bb3d
addedGaussian is its own Fourier transforma58383a45d9e
addedGauss–Bonnet formula3947fbbc5b2d
addedCauchy's integral formula8f887c859d56
addedCauchy's integral formula (general form)174a1e9169c0
addedResidue theorem86b2ee3b7c9f
addedTwo-dimensional Newtonian potential29c7cf0eeaab
addedThree-dimensional Newtonian potential6408f6455283
addedTotal curvature of a smooth plane curve8c446ca12c61
addedTotal curvature of closed curve equals 2πN2dba0b15769b
addedGamma function at half-integers contains πaeb999dd32fc
addedWeierstrass product for the gamma function3b27e1e0b8b2
addedVolume of n-ball and surface area of (n−1)-sphere4a266a232f52
addedStirling's approximationc2ba4cb99cba
addedEhrhart's volume conjecture85af4a8355d3
addedBasel problem: ζ(2) = π²/650523ed5a67a
addedProbability two random integers are coprime376ac25d0202
addedRiemann's functional equation293e361b9265
addedDerivative of zeta function identity04bdcf1e2ad7
addedCharacters of the circle groupe671eba4ee06
addedBourbaki's definition of πf8e558d815bf
addedJacobi theta functionab93a196c671
addedTheta function automorphic transformation0f00f6d77c31
addedCauchy distribution4f21bf5c5168
addedShannon entropy of the Cauchy distribution662f6a0aa33b
addedHilbert transformbadf3b9c4ffa
addedπ in the Mandelbrot set2a86352563b1
addedPeriod of a simple pendulum4962890e6eb9
addedHeisenberg's uncertainty principle (quantum mechanics)00e8a2a0ffac
addedOrthopositronium inverse lifetime91659a2f3305
addedEuler's buckling formulad9ab5093fd71
addedStokes' lawec4a68753d6e