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 along a diameter of the larger circle. It was developed by the 13th-century astronomer and mathematician Nasir Al-Din Tusi as an alternative to the problematic equant introduced over a thousand years earlier in the 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 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 astronomyClaudia Kren, "The Rolling Device," p. 497. and by a historian of Arabic astronomyGeorge Saliba, "Whose Science is Arabic Science in Renaissance Europe?" ^* 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.

See also

• Antikythera mechanism

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.
• Ragep, F. J. Nasir al-Din al-Tusi's "Memoir on Astronomy." 2 vols. New York: Springer, 1993.

External links

• Ancient Planetary Model Animations includes three links of interest:
  • An interactive Tusi couple
  • Arabic models for replacing the equant
  • An article by George Saliba discussing the model of Nasir al-Din al-Tusi and the interactions of Arabic, Greek, and Latin astronomers

History of astronomy | History of mathematics | Islamic Science