• Thumbnail for Brachistochrone curve
    physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), or curve of fastest descent, is...
    37 KB (6,096 words) - 19:29, 4 July 2025
  • Thumbnail for Tautochrone curve
    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...
    17 KB (3,136 words) - 14:13, 18 February 2025
  • Thumbnail for Curve
    to variational problems, such as the brachistochrone and tautochrone questions, introduced properties of curves in new ways (in this case, the cycloid)...
    26 KB (3,656 words) - 15:31, 1 April 2025
  • Thumbnail for Cycloid
    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...
    27 KB (3,936 words) - 22:12, 21 April 2025
  • surface Elkies trinomial curves Hyperelliptic curve Classical modular curve Cassini oval Bowditch curve Brachistochrone Butterfly curve (transcendental) Catenary...
    7 KB (530 words) - 16:34, 2 December 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
  • Thumbnail for Catenary
    Catenary (redirect from Chain curve)
    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...
    51 KB (7,011 words) - 09:18, 7 July 2025
  • Thumbnail for Isaac Newton
    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...
    175 KB (18,745 words) - 12:28, 9 July 2025
  • 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
  • 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
  • modular curve Erdős lemniscate Hurwitz surface Mandelbrot curve Polynomial lemniscate Sinusoidal spiral Superellipse Bowditch curve Brachistochrone Butterfly...
    8 KB (206 words) - 01:51, 1 May 2025
  • Thumbnail for Johann 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...
    16 KB (1,502 words) - 06:38, 19 April 2025
  • Thumbnail for Snell's law
    to the imaginary component of the index of refraction. Brachistochrone curve – Fastest curve descent without friction for a simple proof by Jacob Bernoulli...
    27 KB (3,946 words) - 08:30, 24 June 2025
  • Thumbnail for Daubechies wavelet
    The brachistochrone problem can be formulated and expressed as a variational problem, emphasizing the importance of finding the optimal curve that minimizes...
    23 KB (2,825 words) - 20:22, 24 May 2025
  • methods prior to the twentieth century. It was followed by the brachistochrone curve problem of Johann Bernoulli (1696), which Bernoulli solved, using...
    55 KB (6,755 words) - 21:18, 6 July 2025
  • prior to the twentieth century. This problem was followed by the brachistochrone curve problem raised by Johann Bernoulli (1696), which was similar to...
    58 KB (9,530 words) - 08:36, 5 June 2025
  • Thumbnail for Gravity train
    center of the Earth to commute between Western Europe and Australia. Brachistochrone curve Funicular Hyperloop Rail energy storage Schuler tuning Colonization...
    11 KB (1,723 words) - 23:42, 1 February 2025
  • Thumbnail for Mathematical optimization
    engineering and parameter estimation in biochemical pathways. Brachistochrone curve Curve fitting Deterministic global optimization Goal programming Important...
    53 KB (6,155 words) - 14:53, 3 July 2025
  • 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
  • Thumbnail for Later life of Isaac Newton
    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...
    43 KB (5,837 words) - 03:14, 8 June 2025
  • anonymously submitted solution to Bernoulli's challenge regarding the Brachistochrone curve. tantum religio potuit suadere malorum to such heights of evil are...
    14 KB (181 words) - 12:48, 3 October 2024
  • Child Notable for Awards Johann Bernoulli L'Hôpital's rule catenary brachistochrone curve Daniel Bernoulli Bernoulli's principle Gamma function Farkas Bolyai...
    5 KB (246 words) - 17:57, 20 May 2025
  • Thumbnail for Hypocycloid
    Hypocycloid (category Roulettes (curve))
    Hypocyloid curves Animation of Epicycloids, Pericycloids and Hypocycloids Plot Hypcycloid — GeoFun Snyder, John. "Sphere with Tunnel Brachistochrone". Wolfram...
    12 KB (1,382 words) - 20:52, 12 May 2025
  • Sinusoidal spiral Superellipse Hurwitz surface Bowditch curve Brachistochrone Butterfly curve Catenary Clélies Cochleoid Cycloid Horopter Isochrone Isochrone...
    46 KB (3,547 words) - 00:42, 27 May 2025
  • Senftleben–Beenakker effect Carlo Beenakker Johann Bernoulli Catenary brachistochrone curve Daniel Bernoulli Bernoulli's principle Marcel Brillouin Léon Brillouin...
    5 KB (148 words) - 06:03, 29 June 2025
  • 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 (1,076 words) - 07:12, 21 October 2024
  • Thumbnail for Geodesic
    In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points...
    32 KB (4,304 words) - 17:43, 5 July 2025
  • Thumbnail for Semicubical parabola
    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 (1,404 words) - 23:26, 13 May 2025
  • Thumbnail for List of Dutch discoveries
    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
  • Thumbnail for Horologium Oscillatorium
    later lead to the studies of many other such curves, including the caustic, the brachistochrone, the sail curve, and the catenary. Additionally, his exacting...
    29 KB (3,157 words) - 05:10, 30 June 2025