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The arithmetic plane
If you haven’t seen them already, you might want to read John Baez’s week205 and Lieven le Bruyn’s series of posts on the subject of spectra. I especially recommend that you take a look at the picture...
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Some quadratic reciprocity
In the previous post we showed that the splitting behavior of a rational prime in the ring of cyclotomic integers depends only on the residue class of . This is suggestive enough of quadratic...
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Ideals and the category of commutative rings
In this post I’d like to give a better (by which I mean category-theoretic) definition of the lattice of ideals than the standard one. We know that the lattice of ideals has meets and joins defined by...
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Heron’s formula
Heron’s formula for the area of a triangle with side lengths is where is the semiperimeter. Today I’d like to try to prove this using as little geometry as possible. The assumption If we assume that is...
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