The unit ball in Rn is defined as the set of points (x1,…,xn) such that x12 + … + xn2 <= 1. What...

Continue reading...# multivariable calculus

## Impossible Integral?

The following integral may be problematic for a freshman calculus student, even if armed with a list of antiderivatives: INTEGRAL0...

Continue reading...## Polyhedral Face Vectors

A polyhedron is any closed region of 3-space cut out by a finite set of planes. Take any polyhedron and do the...

Continue reading...## Spherical Bands

Take any sphere and slice it up by parallel knives 1 inch apart. The areas of the spherical bands between the cuts...

Continue reading...## Right Double Cone

Take a solid cylinder of radius R and height 2R. Remove the right “double cone” which passes through the center...

Continue reading...