coordinate systems

Plane

1. Cartesian coordinates

2. Polar coordinates

${ℝ}^3$

1. Cartesian coordinates (http://planetmath.org/CartesianCoordinates)

2. Spherical coordinates

3. Cylindrical coordinates

Sphere $S^2$

1. Stereographic projection

2. Mercator projection

3. ..

Miscellaneous

1. Barycentric coordinates

2. Homogeneous coordinates $(x,y,t)$ in plane, $(x,y,z,t)$ in ${ℝ}^3$

Differential geometry

1. Normal coordinates (http://planetmath.org/RiemannNormalCoordinates) in Riemann geometry

2. Darboux coordinates (http://planetmath.org/DarbouxsTheoremSymplecticGeometry) in symplectic geometry

3. Gaussian coordinates

4. Fermi coordinates for a submanifold

5. Boundary coordinates

Coordinate transformations

1. affine transformations (http://planetmath.org/AffineTransformation)

2. continuous transformations (http://planetmath.org/HomotopyOfPaths) in algebraic topology (homotopy theory)

3. Lorentz group transformations

4. Cartesian-to-polar coordinate transformations

5. Cartesian-to-spherical coordinate transformations

6. A.

7. B.