It is a very interesting term. More so, for word buffs, enthusiast of Physics, Mathematics , Engineering and like.
You might have come across, the word ‘Tautology’(and may-be Pleonasm too)— Tautology stands for some truth statements. You may have worked with Truth tables in Mathematics and Physics.
Root ‘tauto’ means truth or exact.
Chrone is a much used root for words like chronic, chronology, monochromic, polychromic, synchronous, asynchronous and so on. It gives a sense of time or color.
Tautochrone is a special type of curve. A curve which is a Cycloid. You know cycloid. Don’t you?
Cycloid, epicycloids and hypocycloid are curves created as the locus of the point which is situated on the circumference of a circle and moves along with the movement of the circle on its circumference.
[For example: If you draw the locus of a point situated on the rim of a tyre , as it moves, you will get a cycloid]
Why Tautochrone is special?
Tautochrone is special for watchmakers. Classically pendulums were used for making watches but the swing of the pendulum was not an exact movement to be relied upon for the measurement of time. Huygens came up with the idea of the Tautochrone. If you have a curve like Tautochrone and you drop a particle from any point of it, it takes exactly similar time to reach to the bottom. This was the reason for its being more suitable for making watches, compared to the pendulums.
Do let me know of your ideas about Tautochrone and similar shapes.
Image source: Pendulum