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

cycloid) 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...

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...

half-pipe if friction is neglected. It is then called a brachistochrone curve. Such a curve in its pure form has infinitely short verts and is π times...

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

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

medium has nothing different from that in a lossless medium. Brachistochrone curve – Fastest curve descent without friction for a simple proof by Jacob Bernoulli...

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

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

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

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

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

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

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

Solution to the equations discussed. The straight line, the catenary, the brachistochrone, the circle, and Fermat Unified approach to some geodesics. Ira Freeman...

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

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

with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). It immediately occupied...

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

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

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

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...

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

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

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

Fontenelle and gave solutions to the problems of the tautochrone curve, the brachistochrone curve and orthogonal trajectories. He was elected a member of the...

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...

descent of a rolling ball in fact follows a curve) alludes to Galileo's investigation of the brachistochrone (in the context of the quickest descent from...

Aristotle's wheel paradox Brachistochrone Cyclogon Cycloid Epitrochoid Hypotrochoid List of periodic functions Roulette (curve) Spirograph Trochoidal wave...

the solutions to the brachistochrone problem, and the discovery of a turning point singularity on the involute of a plane curve near an inflection point...