physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), or curve of fastest descent, is...

over the acceleration of gravity. The tautochrone curve is related to the brachistochrone curve, which is also a cycloid. It was in the left hand try-pot...

to variational problems, such as the brachistochrone and tautochrone questions, introduced properties of curves in new ways (in this case, the cycloid)...

curve of fastest descent under uniform gravity (the brachistochrone curve). It is also the form of a curve for which the period of an object in simple harmonic...

surface Elkies trinomial curves Hyperelliptic curve Classical modular curve Cassini oval Bowditch curve Brachistochrone Butterfly curve (transcendental) Catenary...

for a general introduction. Action (physics) Averaged Lagrangian Brachistochrone curve Calculus of variations Catenoid Cycloid Dirichlet principle Euler–Lagrange...

gravitational field. The catenary curve has a U-like shape, superficially similar in appearance to a parabola, which it is not. The curve appears in the design of...

century. He then used calculus of variations in his solving of the brachistochrone curve problem in 1697, which was posed by Johann Bernoulli in 1696, thus...

certain limits. Jakob Bernoulli and Johann Bernoulli solve the brachistochrone curve problem, the first result in the calculus of variations. unknown...

and thus more direct path than any point on the larger circle. Brachistochrone curve Coin rotation paradox Trochoid Drabkin, Israel E. (1950). "Aristotle's...

modular curve Erdős lemniscate Hurwitz surface Mandelbrot curve Polynomial lemniscate Sinusoidal spiral Superellipse Bowditch curve Brachistochrone Butterfly...

but not without friction. Their most bitter dispute concerned the brachistochrone curve problem, or the equation for the path followed by a particle from...

to the imaginary component of the index of refraction. Brachistochrone curve – Fastest curve descent without friction for a simple proof by Jacob Bernoulli...

The brachistochrone problem can be formulated and expressed as a variational problem, emphasizing the importance of finding the optimal curve that minimizes...

methods prior to the twentieth century. It was followed by the brachistochrone curve problem of Johann Bernoulli (1696), which Bernoulli solved, using...

prior to the twentieth century. This problem was followed by the brachistochrone curve problem raised by Johann Bernoulli (1696), which was similar to...

center of the Earth to commute between Western Europe and Australia. Brachistochrone curve Funicular Hyperloop Rail energy storage Schuler tuning Colonization...

engineering and parameter estimation in biochemical pathways. Brachistochrone curve Curve fitting Deterministic global optimization Goal programming Important...

Palimpsest Archimedes' use of infinitesimals Arithmetization of analysis Brachistochrone curve Chinese mathematics Cours d'Analyse Edinburgh Mathematical Society...

problems: to determine the brachistochrone curve between two given points not in the same vertical line to determine a curve such that, if a straight line...

anonymously submitted solution to Bernoulli's challenge regarding the Brachistochrone curve. tantum religio potuit suadere malorum to such heights of evil are...

Child Notable for Awards Johann Bernoulli L'Hôpital's rule catenary brachistochrone curve Daniel Bernoulli Bernoulli's principle Gamma function Farkas Bolyai...

Hypocyloid curves Animation of Epicycloids, Pericycloids and Hypocycloids Plot Hypcycloid — GeoFun Snyder, John. "Sphere with Tunnel Brachistochrone". Wolfram...

Sinusoidal spiral Superellipse Hurwitz surface Bowditch curve Brachistochrone Butterfly curve Catenary Clélies Cochleoid Cycloid Horopter Isochrone Isochrone...

Senftleben–Beenakker effect Carlo Beenakker Johann Bernoulli Catenary brachistochrone curve Daniel Bernoulli Bernoulli's principle Marcel Brillouin Léon Brillouin...

an application of the Beltrami identity is the brachistochrone problem, which involves finding the curve y = y ( x ) {\displaystyle y=y(x)} that minimizes...

In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points...

tautochrone curve, for which particles at different starting points always take equal time to reach the bottom, and the brachistochrone curve, the curve that...

tautochrone curve is the same as the brachistochrone curve for any given starting point. Johann Bernoulli posed the problem of the brachistochrone to the readers...

later lead to the studies of many other such curves, including the caustic, the brachistochrone, the sail curve, and the catenary. Additionally, his exacting...