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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?