Tradition dictates that each Carnival of Mathematics begin with a riff about the number of the carnival. Since this is the 50th carnival, and the Roman numeral representation of 50 is L, I’ll start with a short riff on a few uses of “L” in math.
- In tiling, “L” is for L-polyominos, like that look like the letter “L.”
- In analysis, “L” is for Lp spaces, named after Henri Lebesgue. These are spaces of functions whose pth powers are Lebesgue-integrable.
- In statistics, “L” is for L-estimators. These are robust estimators formed by taking linear combinations of order statistics. I suppose in this case, “L” is for “linear.” The median is the simplest example of an L-estimator. Another simple L-estimator is John Tukey’s trimean.
- In number theory, “L” is for L-functions. First, there were Dirichlet’s L-functions. Then came, in order of increasing generality and abstraction, Hecke’s L-functions, Artin’s L-functions, and Weil’s L-functions. I don’t know where the “L” came from in this case. I suppose Dirichlet arbitrarily chose it and his successors followed his convention.
And now, on to recent math posts from around the web.
Richard Elwes classifies polyhedra in Passing Platonic Solids. He starts with the most restrictive definition of regularity, which gives the five platonic solids. He then discusses which solids are possible as each of the criteria are removed.
Continuing with the historical theme, Michael Croucher from Walking Randomly presents Full versions of historical mathematical texts (for free!).
Cariel Montalban presents Basics of Linear Vector Spaces posted at Quantum Science Philippines, a blog for science students in the Philippines. Vector spaces are fundamental to quantum mechanics because wave functions reside in Hilbert spaces, vector spaces with inner products.
- Given a square matrix A and a particular sparsity pattern, how can we find if it is possible to factorize A into N square factor matrices (where N is finite) whose sparsity pattern is the specified one?
- If such factorization is possible, how can we compute each factor, and how can we find the value of N?
The next Carnival of Mathematics will be somewhere on March 13.