A History of Mathematics From Mesopotamia to Modernity

(nextflipdebug2) #1

Islam,Neglect andDiscovery 129


Fig. 10Al-K ̄ash ̄i’s table. (Numbers are written using Arabic letters, cf fig. 5.)

value 42 25 35. Was the same method used?] Above (Fig. 10) is the table which al-K ̄ash ̄i gives of
the regular solids.


Exercise 10.Take a tetrahedron with vertices


(1, 1,− 1 ),(1,−1, 1),(−1, 1, 1),(−1,−1,− 1 )

(half the vertices of a cube).


(1) Why is this a regular tetrahedron?
(2) What is the length of a side?
(3) What is the diameter of the circumscribed sphere?Verify the relation which al-K ̄ash ̄i gives.
(4) What do his other statements mean, and can you check them?


Can you do any of this without using coordinates?

Free download pdf