FieldofBase20

#mathart #mathober2025 #mathober #mathober24 #NumberFields #design #Base20

Blogpost: https://blog.illestpreacha.com/mathober2025numberfields

For my 19th sketch of Mathober2025 (curated by @fractalkitty ) coded in #P5js @processing ( remixed of a previous sketch), FieldofBase20 takes the 24th prompt of “Number Field” and makes a grid of Base20 numbers which are part of the field of rational numbers.

#Poetry

Numbers Field
Numbers Grid
Numbers wheel
Numbers Feel
Numbers Filled

#creativecoding #coding
#newmedia #scifi #animation
#math #numerical #numbers

I still think my answer here is cleaner and much tidier than all of the others: https://math.stackexchange.com/a/3188720/664348

I demand a karma recount!

#NumberFields #Algebra

#NumberFields #NumberTheory Does anyone have good references other than Milne for CM fields? I'm up to my ears in them and a few basic properties in a citation-friendy format would go a long way.

It's really frustrating when I should be able to re-derive what I need, but get muddled along the way every time. This should be already done stuff.

Ie. I'm pondering a quandary.

#NumberTheory #Algebraic #NumberFields #cm

Let F CM over ℚ with max real subfield K then α generate F over K, α totally imaginary unit. Take the partial norm of α by the Galois group of K lifted over F; I assert that since it is a generator of an extension, its norm should NOT collapse into ℚ. Thus being a unit it must have its partial norm also a unit, and being totally imaginary in a quadratic extension this must be i.