physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), or curve of fastest descent, is...
37 KB (6,015 words) - 17:21, 23 June 2024
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...
16 KB (2,976 words) - 16:15, 16 July 2024
Cycloid (category Roulettes (curve))
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...
26 KB (3,771 words) - 22:19, 30 June 2024
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...
12 KB (1,399 words) - 21:30, 13 September 2023
The brachistochrone problem can be formulated and expressed as a variational problem, emphasizing the importance of finding the optimal curve that minimizes...
23 KB (2,775 words) - 11:01, 8 August 2024
Palimpsest Archimedes' use of infinitesimals Arithmetization of analysis Brachistochrone curve Chinese mathematics Cours d'Analyse Edinburgh Mathematical Society...
1 KB (130 words) - 17:01, 21 April 2022
medium has nothing different from that in a lossless medium. Brachistochrone curve – Fastest curve descent without friction for a simple proof by Jacob Bernoulli...
28 KB (4,073 words) - 18:39, 28 August 2024
but not without friction. Their most bitter dispute concerned the brachistochrone curve problem, or the equation for the path followed by a particle from...
16 KB (1,474 words) - 15:31, 20 June 2024
and thus more direct path than any point on the larger circle. Brachistochrone curve Coin rotation paradox Trochoid Drabkin, Israel E. (1950). "Aristotle's...
14 KB (1,746 words) - 20:05, 27 July 2024
to variational problems, such as the brachistochrone and tautochrone questions, introduced properties of curves in new ways (in this case, the cycloid)...
25 KB (3,648 words) - 22:31, 26 August 2024
modular curve Erdős lemniscate Hurwitz surface Mandelbrot curve Polynomial lemniscate Sinusoidal spiral Superellipse Bowditch curve Brachistochrone Butterfly...
8 KB (206 words) - 01:55, 24 July 2024
Semicubical parabola (category Cubic curves)
tautochrone curve, for which particles at different starting points always take equal time to reach the bottom, and the brachistochrone curve, the curve that...
8 KB (1,377 words) - 12:04, 12 June 2024
certain limits. Jakob Bernoulli and Johann Bernoulli solve the brachistochrone curve problem, the first result in the calculus of variations. unknown...
2 KB (143 words) - 16:45, 16 June 2024
center of the Earth to commute between Western Europe and Australia. Brachistochrone curve Funicular Hyperloop Rail energy storage Schuler tuning Colonization...
11 KB (1,737 words) - 19:20, 26 January 2024
Catenary (redirect from Chain curve)
Solution to the equations discussed. The straight line, the catenary, the brachistochrone, the circle, and Fermat Unified approach to some geodesics. Ira Freeman...
51 KB (6,927 words) - 11:17, 31 May 2024
for a general introduction. Action (physics) Averaged Lagrangian Brachistochrone curve Calculus of variations Catenoid Cycloid Dirichlet principle Euler–Lagrange...
987 bytes (80 words) - 12:21, 5 April 2022
Hypocycloid (category Roulettes (curve))
Hypocyloid curves Animation of Epicycloids, Pericycloids and Hypocycloids Plot Hypcycloid — GeoFun Snyder, John. "Sphere with Tunnel Brachistochrone". Wolfram...
11 KB (1,342 words) - 14:33, 14 May 2024
with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). It immediately occupied...
56 KB (9,263 words) - 19:21, 15 April 2024
anonymously submitted solution to Bernoulli's challenge regarding the Brachistochrone curve. tantum religio potuit suadere malorum to such heights of evil are...
14 KB (196 words) - 07:39, 20 August 2024
surface Elkies trinomial curves Hyperelliptic curve Classical modular curve Cassini oval Bowditch curve Brachistochrone Butterfly curve (transcendental) Catenary...
7 KB (528 words) - 02:32, 24 July 2024
engineering and parameter estimation in biochemical pathways. Brachistochrone curve Curve fitting Deterministic global optimization Goal programming Important...
52 KB (6,012 words) - 10:08, 25 August 2024
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...
42 KB (5,836 words) - 12:44, 19 May 2024
an application of the Beltrami identity is the brachistochrone problem, which involves finding the curve y = y ( x ) {\displaystyle y=y(x)} that minimizes...
6 KB (1,070 words) - 15:17, 18 March 2024
Sinusoidal spiral Superellipse Hurwitz surface Bowditch curve Brachistochrone Butterfly curve Catenary Clélies Cochleoid Cycloid Horopter Isochrone Isochrone...
47 KB (3,580 words) - 17:01, 29 June 2024
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...
27 KB (3,671 words) - 23:40, 3 May 2024
Fontenelle and gave solutions to the problems of the tautochrone curve, the brachistochrone curve and orthogonal trajectories. He was elected a member of the...
3 KB (257 words) - 17:51, 25 March 2021
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...
82 KB (10,146 words) - 15:54, 15 May 2024
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...
15 KB (1,852 words) - 10:16, 10 August 2024
Trochoid (category Roulettes (curve))
Aristotle's wheel paradox Brachistochrone Cyclogon Cycloid Epitrochoid Hypotrochoid List of periodic functions Roulette (curve) Spirograph Trochoidal wave...
6 KB (1,028 words) - 23:51, 5 April 2024
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...
11 KB (1,232 words) - 11:11, 21 August 2024