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Isochrone map
![Francis Galton's]] first known isochronic map published for the ''Proceedings of the Royal Geographical Society'', 1881. It shows the travel times in 1881 from [[London]], [[United Kingdom]] to different parts of the world in days. It assumes that there are favourable travel conditions and that travel arrangements over land have been made in advance. It assumes travelling methods of the day within a reasonable cost.](https://commons.wikimedia.org/wiki/Special:FilePath/Isochronic Passage Chart Francis Galton 1881.jpg?width=200 "Francis Galton's]] first known isochronic map published for the ''Proceedings of the Royal Geographical Society'', 1881. It shows the travel times in 1881 from [[London]], [[United Kingdom]] to different parts of the world in days. It assumes that there are favourable travel conditions and that travel arrangements over land have been made in advance. It assumes travelling methods of the day within a reasonable cost.")
![An early isochrone map of [[Melbourne]] rail transport travel times, 1910-1922](https://commons.wikimedia.org/wiki/Special:FilePath/Map of Melbourne and environs minimum railway or tramway time zones.jpg?width=200 "An early isochrone map of [[Melbourne]] rail transport travel times, 1910-1922")
MAP SHOWING AREAS RELATED TO ISOCHRONES BETWEEN DIFFERENT POINTS
Isodapane; Isochrone plan; Isochrone diagram
An isochrone map in geography and urban planning is a map that depicts the area accessible from a point within a certain time threshold. An [(iso = equal, chrone = time) is defined as "a line drawn on a map connecting points at which something occurs or arrives at the same time".
Stellar isochrone
CURVE ON THE HERTZSPRUNG-RUSSELL DIAGRAM
In stellar evolution, an isochrone is a curve on the Hertzsprung-Russell diagram, representing a population of stars of the same age but with different mass.
Tautochrone curve
![Schematic of a [[cycloidal pendulum]]](https://commons.wikimedia.org/wiki/Special:FilePath/CyloidPendulum.png?width=200 "Schematic of a [[cycloidal pendulum]]")
![Horologium oscillatorium sive de motu pendulorum]]'', 1673](https://commons.wikimedia.org/wiki/Special:FilePath/Huygens - Horologium oscillatorium, sive De motu pendulorum ad horologia aptato demonstrationes geometricae, 1673 - 869780.jpeg?width=200 "Horologium oscillatorium sive de motu pendulorum]]'', 1673")
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
Tautochrone problem; Tautochrone; Tautochrone Problem; Abel's mechanical problem; Abel's integral equation; Abel integral equation; Abel problem; Isochrone curve; Isochronous curve; Tautochrone curves; Isochrone curves
A tautochrone or isochrone curve (from Greek prefixes [meaning same or iso-] equal, and [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.
