The Tusi couple is a 2-cusped hypocycloid obtained by rolling a circle of radius inside a circle of radius .
The result is a line segment (Steinhaus 1999, p. 145;
Kanas 2003), as noted by the Persian astronomer and mathematician Nasir Al-Din al-Tusi
(1201-1274) (Sotiroudis and Paschos 1999, p. 60; Kanas 2003).
Al-Tusi described the construction in his astronomical works, including his Memoir on Astronomy (al-Tadhkira fi 'ilm al-hay'a) (Ragep 1993). A manuscript
copy cataloged as British Library Add MS 23394 contains a diagram of the construction
on folio 27r (British Library 2025).
inside a circle of radius 
.
The result is a line segment (Steinhaus 1999, p. 145;
Kanas 2003), as noted by the Persian astronomer and mathematician Nasir Al-Din al-Tusi
(1201-1274) (Sotiroudis and Paschos 1999, p. 60; Kanas 2003).
