What is...an Euclidean domain?

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Goal.
Explaining basic concepts of (a classical course in) algebra in an intuitive way.

This time.
What is...an Euclidean domain? Or: Generalizing division with remainder.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.

Material used.

Euclidean algorithm.

Euclidean algorithm for polynomials.

Z[sqrt(d)], Q[sqrt(d)] is or is not Euclidean.

Mathematica.

#algebra
#galoistheory
#mathematics
  1. VisualMath
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very nice visual illustration of why the euclidean algorithm for gcd works. The second illustration (maybe on purpose) is actually in the ratio of the Fibonacci numbers! Connecting the corners of the squares (in a slightly different order), one would get the fibonacci spiral.

RahulMadhavan