A Level Further Maths: Demystifying Polar Coordinates through Shapes

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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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