The mathematical mechanic : using physical reasoning to solve problems / Mark Levi.

The Pythagorean theorem
Minima and maxima
Inequalities by electric shorting
Center of mass : proofs and solutions
Geometry and motion
Computing integrals using mechanics
The Euler-Lagrange equation via stretched springs - -Lenses, telescopes, and Hamiltonian mechanics
A bicycle wheel and the Gauss-Bonnet theorem
Complete variables made simple(r)
Physical background.