Curve for which the time to roll to the end is equal for all starting points
Four balls slide down a cycloid curve from different positions, but they arrive at the bottom at the same time. The blue arrows show the points' acceleration along the curve. On the top is the time-position diagram.Objects representing tautochrone curve
A tautochrone curve or isochrone curve (from Ancient Greek ταὐτό (tauto-) 'same', ἴσος (isos-) 'equal', and χρόνος (chronos) 'time') is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve. The curve is a cycloid, and the time is equal to π times the square root of the radius (of the circle which generates the cycloid) over the acceleration of gravity. The tautochrone curve is related to the brachistochrone curve, which is also a cycloid.
A tautochronecurve or isochrone curve (from Ancient Greek ταὐτό (tauto-) 'same', ἴσος (isos-) 'equal', and χρόνος (chronos) 'time') is the curve for...
posed by Johann Bernoulli in 1696. The brachistochrone curve is the same shape as the tautochronecurve; both are cycloids. However, the portion of the cycloid...
the curve does not depend on the object's starting position (the tautochronecurve). In physics, when a charged particle at rest is put under a uniform...
Café Seven bridges of Königsberg Spectral theory Synthetic geometry Tautochronecurve Unifying theories in mathematics Waring's problem Warsaw School of...
of finding the tautochronecurve, which in turn helped him construct an isochronous pendulum. This was because the tautochronecurve is a cycloid, and...
variational problems, such as the brachistochrone and tautochrone questions, introduced properties of curves in new ways (in this case, the cycloid). The catenary...
theory Noether's theorem Path integral formulation Plateau's problem Prime geodesic Principle of least action Soap bubble Soap film Tautochronecurve...
the development of the concept of moment of inertia. A tautochrone or isochrone curve is the curve for which the time taken by an object sliding without...
Isochrone Isochrone of Huygens (Tautochrone) Isochrone of Leibniz[1] Isochrone of Varignon[2] Lamé curve Pursuit curve Rhumb line Sinusoid Spirals Archimedean...
the tautochronecurve, for which particles at different starting points always take equal time to reach the bottom, and the brachistochrone curve, the...
same amount of time, regardless of its starting point; the so-called tautochrone problem. By geometrical methods which anticipated the calculus, Huygens...
starting point; the so-called tautochronecurve. By a complicated method that was an early use of calculus, he showed this curve was a cycloid, rather than...
Fontenelle and gave solutions to the problems of the tautochronecurve, the brachistochrone curve and orthogonal trajectories. He was elected a member...
the same time and thereby experimentally shows that the cycloid is the tautochrone 1668 - John Wallis suggests the law of conservation of momentum 1673...
The Whewell equation of a plane curve is an equation that relates the tangential angle (φ) with arc length (s), where the tangential angle is the angle...
In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the...
and wood, few of them now survive, though one for demonstrating the tautochronecurve of a cycloid and another for parabolic motion do remain. Many small...
resistance problem Solution to the brachistochrone problem Solution to the tautochrone problem Solution to isoperimetric problems Calculating geodesics Finding...
Lagrange in connection with their studies of the tautochrone problem. This is the problem of determining a curve on which a weighted particle will fall to a...
to fall. This in effect shows the solution to the tautochrone problem as given by a cycloid curve. In modern notation: ( π / 2 ) √ ( 2 D / g ) {\displaystyle...
1690, James Bernoulli showed that the cycloid is the solution to the tautochrone problem; and the following year, in 1691, Johann Bernoulli showed that...
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