Golden Sections

I was inspired by this short Randall Carlson episode to re-construct the diagram in Wolfram Mathematica.

It is a geometric construction of “the golden mean”, and then viewing it as a ratio, as the basis for a triangle, and as the basis for a pair of circles.

Here is a screenshot of that intermediate step:

For extra fun, there is a comparison of this ratio with a few interesting real-world … objects.

Here is a screenshot of that part:

But the real takeaway is how fluid it is to tinker with all this.

As I grow older, I really appreciate the “amateur joy” of all this 🙂

Here is the notebook published to the cloud, free to access publicly.

Yield curves

Playing around with Wolfram Mathematica again for a bit:

Notebook is viewable here.

Polar Primes

This “five minutes of Wolfram Language” exercise can be surprisingly therapeutic 🙂

I had come across something interesting today:

However, I then wanted to try it out on my own.

These days, the commonly available frameworks/libraries make it too hard to just up-and-sketch-something.

… which is where WolframLanguage comes in.

I was able to make a simple notebook for this in five minutes:

Using WolframLanguage to see the spiral pattern in which primes show up when plotted in polar cp-ordinates

… and have the satisfaction of seeing that yes, it is indeed true.

Seeing things on your own, making things on your own, is a really nice feeling.

Wolfram Language “dashboards”

Playing around with Mathematica for a few minutes.

Or rather, using it to play around.

I’m trying to figure out the “least B.S.” portions of “web3/defi/whatever”. So far, a limited goal is to follow along a couple of “stable, publicly used and usable” blockchains, and I picked Tezos and Cardano for this.

I built some probing views for each, as cloud notebooks:

Transactions within the last 20 Tezos blocks as of around 5:09pm on Mar 13, 2022
Transactions within the last 20 Cardano blocks as of around 5:09pm on Mar 13, 2022

Very elementary stuff, but it took a few minutes, and really shows how Wolfram (Mathematica) is a really great “computational explorer” right now.

P.S. eyeballing the two, at a very subjective, no-flame-war, just-this-instance level, Tezos seems to be stably handling about 2x transaction throughput compared to Cardano.