Aditi Kar is in the final year of her MA in Mathematics at St. Stephen's College, Delhi. Over the past few years, she has worked on projects on 'Groups and Symmetry', Lie Groups and differential geometry at the CMS, Delhi. This article was written during a visit to ISI, Bangalore in June 2002

Consider the unit circle T in the Euclidean plane. If it is rotated like a stationary wheel, in an anti-clockwise direction by 45 degrees, then the `spoke of the wheel' joining the centre (0,0) to the point (1,0) (call it v ) gets mapped to the spoke joining the centre to the point (Cos 45, Sin 45). We shall think of points on the plane as complex numbers when convenient.

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Aditi Kar
18/4 Northern Avenue
Kolkata 700 037, India.