In mathematics there is a concept known as ‘Conformal Mapping’ which allows you convert a given shape to a completely different one by making a transformation.
In the joukowski transform you take all the points on a circle and apply the following transform:
And the resulting transformed points resemble an aerofoil shape. Pretty cool huh ?
** Conformal mappings are a really cool topic in complex analysis but also equally extensive. If you want to know more about them click here
I forgot to mention that the transformation of a circle into an aerofoil is a very special case and the transformation of other shapes would yield distinct shapes. ( very different from an aerofoil )
Here’‘s what i mean:
Source : AT&T Archives
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