KnowraSmall-angle approximationLinked fromLinked fromThe 12 pages that link to Small-angle approximation, each with the reason it gives.All 12Broader topic 3Related 8Compared with 1Taylor seriesBroader topic: The sine Taylor series explains why these approximations work and how their errors grow.ParallaxRelated: It simplifies the geometry of distant objects with tiny measured shifts.AngleCompared with: It treats angles as approximations in calculations rather than exact geometric measures.Rayleigh criterionRelated: It converts the diffraction angle into the familiar ratio of wavelength to diameter.Paraxial approximationRelated: The paraxial model uses this expansion to simplify wave-vector relations.Taylor polynomialBroader topic: These familiar formulas are low-degree Taylor polynomials around zero.Simple pendulumRelated: It turns the pendulum’s nonlinear equation into the simple harmonic oscillator equation.Linear approximationBroader topic: These familiar trigonometric estimates are linear and constant Taylor approximations at zero.Binomial seriesRelated: Binomial expansions approximate expressions such as \((1-x)^{1/2}\) that arise in geometric derivations.MilliradianRelated: It explains why one milliradian spans about one unit per thousand units of range.Legendre's theorem on spherical trianglesRelated: The theorem’s accuracy relies on the triangle being small relative to the sphere.StadimeterRelated: At ordinary viewing distances, this makes distance approximately proportional to target height divided by angular height.