Tusi couple

The Tusi couple (also known as Tusi's mechanism^[1]^[2]^[3]) is a mathematical device in which a small circle rotates inside a larger circle twice the diameter 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. The Tusi couple is a 2-cusped hypocycloid.

The couple was first proposed by the 13th-century Persian astronomer and mathematician Nasir al-Din al-Tusi in his 1247 Tahrir al-Majisti (Commentary on the Almagest) as a solution for the latitudinal motion of the inferior planets^[4] and later used extensively as a substitute for the equant introduced over a thousand years earlier in Ptolemy's Almagest.^[5]^[6]

^ Roshdi Rashed (ed.). Encyclopedia Of The History Of Arabic Science.
^ Saliba, George (2002-07-01). "Greek astronomy and the medieval Arabic tradition: the medieval Islamic astronomers were not merely translators. They may also have played a key role in the Copernican revolution". American Scientist. 90 (4): 360–368. doi:10.1511/2002.27.360.
^ Nosonovsky, Michael (2018-08-14). "Abner of Burgos: The Missing Link between Nasir al-Din al-Tusi and Nicolaus Copernicus?". Zutot. 15 (1): 25–30. doi:10.1163/18750214-12151070. ISSN 1571-7283. S2CID 135358186.
^ George Saliba (1995), "A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam", pp. 152–155.
^ "Late Medieval Planetary Theory", E. S. Kennedy, Isis 57, #3 (Autumn 1966), 365–378, JSTOR 228366.
^ Craig G. Fraser, "The cosmos: a historical perspective", Greenwood Publishing Group, 2006 p. 39.

[1] Roshdi Rashed (ed.). Encyclopedia Of The History Of Arabic Science.

[2] Saliba, George (2002-07-01). "Greek astronomy and the medieval Arabic tradition: the medieval Islamic astronomers were not merely translators. They may also have played a key role in the Copernican revolution". American Scientist. 90 (4): 360–368. doi:10.1511/2002.27.360.

[3] Nosonovsky, Michael (2018-08-14). "Abner of Burgos: The Missing Link between Nasir al-Din al-Tusi and Nicolaus Copernicus?". Zutot. 15 (1): 25–30. doi:10.1163/18750214-12151070. ISSN 1571-7283. S2CID 135358186.

[4] George Saliba (1995), "A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam", pp. 152–155.

[5] "Late Medieval Planetary Theory", E. S. Kennedy, Isis 57, #3 (Autumn 1966), 365–378, JSTOR 228366.

[6] Craig G. Fraser, "The cosmos: a historical perspective", Greenwood Publishing Group, 2006 p. 39.

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