等时降线 Tautochrone curve
（重定向自Tautochrone）
![等时降在线的四个质点释放位置不同，但到达最低点的时间相等。](/Images/godic/202502/15/Tautochrone_curve3649.gif")
![Esquema de un péndulo cicloidal.](/Images/godic/202502/15/CyloidPendulum3649.png")
![Representación esquemática de cinco péndulos cicloidales isócronos, es decir que poseen la misma frecuencia independientemente de sus amplitudes.](/Images/godic/202502/15/Isochronous_cycloidal_pendula3650.gif")
等时降线(tautochrone curve或isochrone curve)是一种曲线，将一质点放置在此曲在线任一点使其自由下滑(不计阻力)至最低点所需的时间皆相等。此曲线的解是摆线，而下滑所需的时间与摆线绕转圆的半径平方根成正比，与重力场强度的平方根成反比。
tautochrone
/'tɔ:təukrəun/
英汉-汉英词典
n. 等时曲线,等时降落轨迹
词组 | 习惯用语
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- diachronic adj. 历时的
- dodecahedron n. 十二面体
- enthrone vt. 使登基；立…为王；任为主教；崇拜 vi. 热心
- cautioner n. 担保人,警告者
tautochrone n. 等时降落轨迹，[数] 等时曲线
网络短语:
tautochrone u 等时曲线
tautochrone E 等时曲线
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Tautochrone curve 等时降线
（重定向自Tautochrone）
![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.](/Images/godic/202502/15/Tautochrone_curve3650.gif")
![Schematic of a cycloidal pendulum.](/Images/godic/202502/15/CyloidPendulum3650.png")
A tautochrone or isochrone curve (from Greek prefixes tauto- meaning same or iso- equal, and chrono 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. The curve is a cycloid, and the time is equal to π times the square root of the radius over the acceleration of gravity. The tautochrone curve is the same as the brachistochrone curve for any given starting point.