 Avicenna’s mathematical-style critique of Kalām atomism frequently appeal to issues associated with incommensurability. In this vein he argues that such geometrical commonplaces as diagonals and circles would be impossible on the assumption of conceptually indivisible atoms. For example, in the pixilated atomism of the Kalām, the atoms might be thought to form a three-dimensional Cartesian coordinate system with each atom corresponding to some ordered triplet on this space. A two-dimensional plane, then, would look something like a chessboard. Avicenna now has us describe a right isosceles triangle on this chessboard, setting the two equal sides, for instance, at 3 units. Given the Pythagorean Theorem, A2 + B2 = C2, we should be able to solve for the length of the hypotenuse, which is √18 ≈ 4.25. Avicenna, next observes that assuming Kalām atomism, the hypotenuse of our triangle must fall either well below the solution given by the Pythagorean theorem—namely, it would be 3 units if one just counts the 3 squares along the diagonal of a 3x3 chessboard—or significantly exceed it—for instance 6 units, if the atoms can somehow be stair stepped. Alternatively, one might consider units smaller than the atoms, but such a move is to give up atomism. Kalām atomism, then, cannot even approximate the answer of the Pythagorean Theorem, and yet the Pythagorean Theorem is arguably the most well-proven theorem in the history of mathematics. Given the choice between a dubious physical theory and our best mathematics, Avicenna sides with Euclidean geometry and its assumption of continuous  magnitudes.[5] 