Cylindrical coordinates
Cylindrical coordinates are interesting to represent cylindrical shaped surfaces with short equations. They can be seen as an extension of the polar coordinates that are used in the polar equation of a curve. The cylindrical coordinates of a point in space are determined by the modulus r, the argument u and the height z, defined as follows:
- The modulus r is the distance of the point to the z-axis;
- The argument u is the angle measured from the x-axis to the vertical plane through the point and the z-axis;
- The height z is the height of the point with respect to the xy-plane.
With an equation of the surface in cylindrical coordinates, we mean an equation in which the modulus is expressed with respect to the argument and the height. A cylinder around the z-axis with radius 2 for example obtains the simple equation r=2, where u and z can be chosen arbitrarily.
Here we see an illustration of cylindrical coordinates, with both the side and upper view given. The surface shown here has equation r = u with u between 0 and 2*pi and z between 0 and 5. A vertical plane is added to make the cylindrical coordinates more clear.
