On the volumes of balls, joint with Stephen Schanuel
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We prove the formula for the volume of an even-dimensional ball by exhibiting an explicit, locally volume-preserving (in fact symplectic) map from a polydisk.
On a Problem of H. N. Gupta, joint with Victor Pambuccian (Geom. Dedicata 61 (1996) 329--331)
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It is shown that the axiom "For any points x, y, and z such that y is between x and z, there is a right triangle having x and z as endpoints of the hypotenuse and y as foot of the altitude to the hypotenuse", when added to 3-dimensional Euclidean geometry over arbitrary ordered fields, is weaker than the axiom "Every line which passes through the interior of a sphere intersects that sphere".
Sperner Spaces and First-Order Logic, joint with Victor Pambuccian (Math. Logic Quarterly 49 (2003) 111-114)
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We study the class of Sperner spaces, a generalized version of affine spaces, as defined in the language of point-line incidence and line parallelity. We show that, although the class of Sperner spaces is a pseudo-elementary class, it is not elementary nor even L_{infty,omega}-axiomatizable. We also axiomatize the first-order theory of this class.