Talk:Cycloid

message: There's a theorem that states that a tangent line to any point on the cycloid passes through a point, which can be defined in terms of t, located at the top of its corresponding rolling circle. I was told that this is Descartes' theorem, but it doesn't appear to be. Thus far, I've been unable to find any record of the theorem online. Has anyone heard of it? --Ketsuekigata 19:06, 8 May 2007 (UTC)
thread_title: Descartes' Theorem?

message: Are there any excamples of cycloids in nature or engineering?
:Every time something round rolls in a straight line, there's a cycloid. --Ketsuekigata 20:54, 16 June 2007 (UTC)
thread_title: Uses

message: Quoting Article:
The cycloid through the origin, generated by a circle of radius r, consists of the points (x, y) with
    x = r(t - \sin t)\,
    y = r(1 - \cos t)\,
where t is a real parameter, corresponding to the angle through which the rolling circle has rotated, measured in radians (not degrees). For given t, the circle's centre lies at x = rt, y = r.
---
It would seem that you could use degrees, as long as you made 0 < t < 360.  The statement that t is measured in degrees is dubious, unless there is a statement saying 0 < t < 2*pi.
Am I missing something? jheiv (talk) 16:37, 5 May 2009 (UTC)
replies: text: I edited the article to correct what I thought was wrong / confusing. jheiv (talk) 16:41, 5 May 2009 (UTC)

text: Yes, you're missing something. t has to be in radians, irrespective of any bounds. The bounds you've given just mean that you get one arch of the cycloid, which is not unreasonable I guess.  —Preceding unsigned comment added by 81.152.169.12 (talk) 20:58, 11 May 2009 (UTC)
thread_title:  "Radians (not degrees)" 

message: hey I've seen the cycloid pendulum somewhere and i would like to give an illustration.
http://commons.wikimedia.org/wiki/File:Cycloid_pendulum.png
But I don't know how to use svg editors.
I hope someone can help to create an svg image or make a thumbnail of my image and then add it to the related part.  —Preceding unsigned comment added by Kimkim0513 (talk • contribs) 12:19, 20 February 2010 (UTC)
replies: text: That would be nice but that picture is completely wrong I'm afraid. The cycloidal jaws are of two cycloids side by side and the support point is at the cusp. +the length should be half the length of the cycloid curve. The path of the pendulum is another cycloid of the same size from the lowest point of the two cycloids. There should be some picture accessible from google somewhere. Dmcq (talk) 13:30, 20 February 2010 (UTC)
replies: text: Oh...You pointed out the key facts! thanks for teaching me~ Kimkim0513 (talk) 16:42, 22 February 2010 (UTC)
thread_title:  Cycloid pendulum 

message: The cycloid has been called "The Helen of Geometers" as it caused frequent quarrels among 17th-century mathematicians.
This is a teaser and the reference to a text book doesn't enlighten. What quarrels? Who called it Helen? And who, for that matter, is Helen (for those who don't know their Greek mythology)?  — Preceding unsigned comment added by 92.25.9.36 (talk) 07:31, 30 April 2013 (UTC)
thread_title:  Quarrels? 

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thread_title:  External links modified 

message: It seems like we could profitably cut several sentences about speculative attributions that were later shown to be wrong. This might be in scope for some deep dive or historiography study, but doesn't really seem that helpful to readers of this encyclopedia article. –jacobolus (t) 07:32, 1 April 2023 (UTC)
thread_title:  does the history section really need to describe the history of wrong attributions?