Yesterday, I started reading a book on geometry for scientist and engineers. It covers affine, projective, and differential geometry to differing degrees, with an algorithmic mind-set. What I found surprising is that it claims that all geometries can be embedded in projective geometry, yet I’ve never even heard that much about it. I thought projective geometry was rather useless up to now.

Another interesting thing is the concept of a barycenter, which seems like the mathematical equivalent of a center of mass. Apparently a polynomial can be expressed as the set of barycenters of a finite number of points, something I would never have expected.

Possibly relevant posts:

• Solid Shape (9/11/2004)
• Differential Algebra (6/8/2005)
• Q: zero crossings and extrema of stationary Gaussian r.v.s (1/7/2008)