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The statement "A property of the Tusi couple is that points on the inner circle that are not on the circumference trace ellipses" is not correctly stated. There can not be any points on the inner circle that are not on its circumference, because, by construction, all points on a circle lie on the circumference of that circle. What is meant would be correctly expressed if we are talking about all points of a disk that is co-rotating with the inner circle. Only then is it true that there can be points of the disk not on the circumference of the circle, and that those points not on the circle's circumference trace ellipses. Suggested replacement would be:
"A property of the Tusi couple is that all points of a disk of any radius co-rotating with the inner circle trace out ellipses. Points on the circumference of the circle or at the center of the circle trace out degenerate ellipses (straight line and circle, respectively.)"
173.243.178.98 ( talk) 20:44, 24 January 2020 (UTC)
Dear Duythai25,
I like the division of information and everything looks fleshed out now. Maybe you could add more about epicycles and how Western theories using them were different than Arab counterparts. SebCoyle ( talk) 16:33, 16 April 2014 (UTC)
The opening lines "The Tusi-couple ... (Sotiroudis and Paschos 1999, p. 60; Kanas 2003)" are taken verbatim from [1], without citation (and without giving the full form of the references cited there).
I have removed Maestlin's sentence "The large circle rotates in the opposite direction at half the speed, carrying the small circle with it." since the two animations of the Tusi Couple in the external links both have the small circle rotating within a fixed outer circle. There is also a way to depict the Tusi couple in which two circles of the same size rotate in opposite directions, but this is not the one in the animations or in the diagram from the Vatican manuscript of Tusi's invention. Di Bono's article in JHA discusses the various ways to depict the Tusi couple.
-- SteveMcCluskey 00:14, 20 June 2006 (UTC)
Well, here we go again. Its an Arabic thing... but actually appears in commentaries on Euclid more than 500 years earlier. Major rephrasing is required. I suspect the hand of Jagged William M. Connolley ( talk) 20:05, 21 April 2011 (UTC)
Anyway, there is no source for It was developed by the 13th-century Persian astronomer and mathematician Nasir al-Din al-Tusi as an alternative to the problematic equant. Who says it is an alternative to the equant? William M. Connolley ( talk) 21:20, 21 April 2011 (UTC)
@ MichaelFrey: The recently added section on technical usage anachronistically suggests that the hypocycloid Straight-line Mechanism is historically related to the Tusi couple. Although they may be geometrically equivalent, the material presented suggests that the nineteenth-century inventors were credited for creating a new mechanism for producing reciprocating straight line motion rather than applying al-Tusi's discovery.
I don't feel this discussion belongs in this article on the Tusi couple, perhaps it could be added to the article Straight line mechanism under the heading Hypocycloid straight-line mechanism (Tusi couple). If retained in this article, the discussion should make it clear that we have a nineteenth-century discovery of an equivalent mechanism to the Tusi couple for which no historical connection has been demonstrated. -- SteveMcCluskey ( talk) 18:41, 5 January 2017 (UTC)
That reference seems to be the only mention of this on the Internet, and it says nothing about it being invented by Goodman, nor being named after Goodman, only that he made a video of some gears. Is there any info to the contrary?
The "Goodman couple" appears to be at least 5 centuries old as it was described by Cardano in the 16th century, now known as the "Cardan straight line mechanism." I personally suspect it can be traced to ancient Greece, and will attempt to prove it.