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I would like to know if there are some topics that could be covered in an undergraduate first-term course about analytic geometry, but related to Computer Science.

I know that, for example, the simple equation for the line can be used for explaining linear regression or other topics in elliptic cryptography (too advanced for an initial course).

Any suggestion of topics?

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Computer graphics is applied analytic geometry, and showing how games do their computations might be exactly the kind of motivating subject matter you are looking for.

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is there any other topic apart of Computer Graphics? – Layla Jan 26 '13 at 12:06
Typography, the current definition of letter shapes by curves might qualify. A program handling the techniques underlying Metafont but with a much more approachable syntax is – vonbrand Jan 26 '13 at 14:02

One other topic that could be covered is numerical methods and algorithms. Efficient way of visualizing the multidimensional graphs, functions,....

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