Category Archives: Uncategorized

Spectra of atoms

Why is a sodium lamp yellow? How can we determine the elemental composition of the sun? How does a Helium-neon laser can work? To some degree all of these questions require knowing the spectra of atoms, which can in theory … Continue reading

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Regular expressions, automata and monoids

In formal language theory the task is to specify, over some given alphabet, a set of valid strings. This is useful in searching for structures textual data through files (e.g. via grep), for specifying the syntactic structure of programming languages … Continue reading

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DVI by example

The Device Independent File Format (DVI) is the output format of Knuth’s TeX82; modern TeX engines (pdfTeX, luaTeX) output straight to Adobe’s Portable document format (PDF). However TeX82 and DVI still work as well today as they did when they … Continue reading

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Algorithms for finding the real roots of polynomials

Given an degree n polynomial over the real numbers we are guaranteed there are at most n real roots by the fundamental theorem of algebra; but how do we find them? Here we explore the Vincent-Collins-Akritas algorithm. It uses Descartes’ … Continue reading

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Non-desarguesian projective planes

There are two main constructions of a projective space.

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Geometry and topology of division rings

Following from my last post (and Veblen and Young’s Projective Geometry) consider a projective plane satisfying the axioms: Given two distinct points there is a unique line that both points lie on Each line has at least three points which … Continue reading

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Geometry of division rings

It is fairly easy to construct a geometry from algebra: given a division ring K we form an n-dimensional vector space, the points being the elements of the field and a line being a translation of all (left) multiples of a … Continue reading

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