# sin(N): What is it?

A Mathematical Droodle

What if applet does not run? |

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Copyright © 1996-2017 Alexander Bogomolny

### A few words

The applet depicts the values of sin(N mod 2p), for integer N, or plain sin(N) with the horizontal scale chosen accordingly. In the former case, we see that the sequence {N mod 2p} is dense on the unit circle.

What is the nature of the periodic pattern observed in the latter case?

The applet also shows a no less curious behavior of tan(N).

In February 2011, Scott Brodie has drawn my attention to the fact that a relevant topic has been discussed by Norman Richert for which the starting point were two pictures on the cover of G. Strang's *Calculus* text. The pictures are the ones that are displayed by the applet with the "Modulo 2*Pi" box unchecked in scales 1280 and 10240.

### References

- N. Richert,
__Strang's Strange Figures__,*The American Mathematical Monthly,*Vol. 99, No. 2 (Feb., 1992), pp. 101-107 - G. Strang,
*Calculus*, Wellesley-Cambridge Press, Wellesley, Mass., 1991.

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Copyright © 1996-2017 Alexander Bogomolny

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