### A Level Further Maths: Demystifying Polar Coordinates through Shapes

The above shape is known as cardioid in mathematics. It is produced by the polar equation, r = a(1 + cos(Θ)), where a can be an integer. You can practise a cardioid with the following simulation and see how r and Θ do the magic to produce the shape. Rose Petals You can practise the creation of shapes with the following applet interactively: note the value of n, an odd number, and the number of petals. Fermat's Spiral The polar equation of Fermat's Spiral is as follows: r = a√Θ, where a > 0. Fermat's spiral is produced as follows: