Chris’ Corner: Monaspace
I’m a sucker for a new coding font. I generally don’t think what coding font you use affects productivity in any significant way (unless it’s distracting) so farting around and switching it up is just a fun little thing to do. Like pushing around the furniture in your room or
Read morePeriod of a nonlinear pendulum
The term “nonlinear pendulum” is analogous to a retronym, a new name for an old thing to distinguish it from a new variation. For example, once upon a time a guitar was just a guitar. Now such a guitar is called an acoustic guitar to distinguish it from an electric
Read moreKepler triangle
A Kepler triangle is a right triangle whose sides are in geometric progression. That is, if the sides have length a < b < c, then b/a = c/b = k. All Kepler triangles are similar because the proportionality constant k can only take on one value. To see this,
Read moreDecoupling formal theorem proving effort
Terence Tao has been experimenting with formal theorem proving using Lean and writing about his experience. Here’s something Tao said on Mathstodon that I thought was interesting. It is remarkable how much “decoupling” is achieved by the Lean+Blueprint combo. Contributors can work locally on proving a lemma, without necessarily fully
Read morePartitioning dots and dashes
Given a set of dots and dashes, how many ways can they be partitioned into a set of Morse code letters? There is at least one way, since you could take each dot to be an E and each dash to be a T. If you have a sequence of n
Read moreSchwarz lemma, Schwarz-Pick theorem, and Poincare metric
Let D be the open unit disk in the complex plane. The Schwarz lemma says that if f is an analytic function from D to D with f(0) = 0, then for all z in D. (The lemma also says more, but this post will focus on just this portion of
Read moreFactored random numbers
A couple days ago Michael Nielsen posted an image of a one-page paper that gives an algorithm for generating factored random numbers, uniformly distributed from 1 to some designated N. The algorithm does not generate random numbers then factor them. It’s more efficient than that, generating the factorization along with
Read moreDICOM image data
The previous post discussed EXIF data embedded in a digital photo. DICOM files are analogous medical images. You can think of a DICOM image as a JPEG with medical metadata. Strictly speaking a DICOM file is a sort of database, and one of the fields in the database contains
Read morePersonal information in digital photos
Is it possible to identify the people in the photo above? Maybe. Digital images potentially contain a large amount of metadata that could reveal the photographer’s identify and location. There may also be a surprising number of clues in the photo itself. EXIF metadata The standard format for image metadata
Read moreWhat can you learn from a phone number?
What can someone learn about you from your phone number? The answer depends on what other information someone has. Identifiers always depend on context. To a naked man in a tree [1] the phone number doesn’t carry any information. But to someone with a list of names and phone numbers,
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