A Level Further Maths: Demystifying Polar Coordinates through Shapes


Cardioid: polar coordinates for further maths

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

Polar equations - 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:

Polar equations- Fermat's Spiral


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