Tusi-couple

The Tusi-couple is a mathematical device in which a small circle rotates inside a larger circle twice the radius of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle. It was developed by the 13th-century Persian astronomer and mathematician Nasir Al-Din Tusi as an alternative to the problematic equant introduced over a thousand years earlier in Ptolemy's "Almagest".

Some modern commentators also call the Tusi couple a "rolling device" and describe it as a small circle rolling inside a large fixed circle. However, Tusi himself described it differently:

:"if two coplanar circles, the diameter of one of which is equal to half the diameter of the other, are taken to be internally tangent at a point, and if a point is taken on the smaller circle—and let it be at the point of tangency—and if the two circles move with simple motions in opposite direction in such a way that the motion of the smaller [circle] is twice that of the larger so the smaller completes two rotations for each rotation of the larger, then that point will be seen to move on the diameter of the larger circle that initially passes through the point of tangency, oscillating between the endpoints." [Translated in F. J. Ragep, "Memoir on Astronomy" II.11 [2] , pp. 194, 196.]

The term "Tusi couple" is a modern one, coined by Edward Kennedy in 1966. [E. S. Kennedy, "Late Medieval Planetary Theory," p. 370.] It is one of several late Islamic astronomical devices bearing a striking similarity to models in "De revolutionibus orbium coelestium", including his Mercury model and his theory of trepidation. Historians suspect that Copernicus or another European author had access to an Islamic astronomical text, but an exact chain of transmission has not yet been identified. [E. S. Kennedy, "Late Medieval Planetary Theory," p. 377.]

There are hints that the "Tusi-couple" was known in Paris by the middle of the 14th Century. In his "questiones" on the "Sphere" (written before 1362), Nicole Oresme described how to combine circular motions to produce a reciprocating linear motion. The description is unclear and it is not certain whether this represents an independent invention or an attempt to come to grips with a poorly understood Arabic text. [Claudia Kren, "The Rolling Device," pp. 490-2.] Since the Tusi-couple was used by Nicolaus Copernicus in his reformulation of mathematical astronomy, there is a growing consensus that he became aware of this idea in some way. It has been suggested both by a historian of Medieval European astronomy [Claudia Kren, "The Rolling Device," p. 497.] and by a historian of Arabic astronomy [George Saliba, "Whose Science is Arabic Science in Renaissance Europe?" [http://www.columbia.edu/~gas1/project/visions/case1/sci.1.html] ] that the idea of the Tusi couple may have arrived in Europe leaving few manuscript traces, since it could have occurred without the translation of any Arabic text into Latin. One possible route of transmission may have been through Byzantine science, which translated some of al-Tusi's works from Arabic into Byzantine Greek. Several Byzantine Greek manuscripts containing the Tusi-couple are still extant in Italy. [cite web|author=George Saliba|title=Islamic Science and the Making of Renaissance Europe|date=April 27, 2006|url=http://www.loc.gov/today/cyberlc/feature_wdesc.php?rec=3883|accessdate=2008-03-01]

Notes

References

* Di Bono, Mario. "Copernicus, Amico, Fracastoro and Tusi's Device: Observations on the Use and Transmission of a Model." "Journal for the History of Astronomy" 26 (1995):133-154.
* Kennedy, E. S. "Late Medieval Planetary Theory." "Isis" 57 (1966):365-378.
* Kren, Claudia. "The Rolling Device of Nasir al-Din al-Tusi in the "De spera" of Nicole Oresme." "Isis" 62 (1971): 490-498.
* Ragep, F. J. "The Two Versions of the Tusi Couple," in "From Deferent to Equant: A Volume of Studies in the History of Science in Ancient and Medieval Near East in Honor of E. S. Kennedy", ed. David King and George Saliba, Annals of the New York Academy of Sciences, 500. New York Academy of Sciences, 1987. ISBN 0-89766-396-9 (pbk.)
* Ragep, F. J. "Nasir al-Din al-Tusi's "Memoir on Astronomy," Sources in the History of Mathematics and Physical Sciences,12. 2 vols. Berlin/New York: Springer, 1993. ISBN 3-540-94051-0 / ISBN 0-387-94051-0.

External links

* Dennis W. Duke, [http://www.csit.fsu.edu/~dduke/models Ancient Planetary Model Animations] includes two links of interest:
** [http://people.scs.fsu.edu/~dduke/tusi.html An interactive Tusi couple]
** [http://people.scs.fsu.edu/~dduke/arabmars.html Arabic models for replacing the equant]
* George Saliba, [http://www.columbia.edu/~gas1/project/visions/case1/sci.2.html "Whose Science is Arabic Science in Renaissance Europe?"] Discusses the model of Nasir al-Din al-Tusi and the interactions of Arabic, Greek, and Latin astronomers.