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Hart’s theorem says If a triangle be formed by the arcs of three circles, the inscribed and the three escribed circles are all tangent to a new circle or line. Here “triangle” means a three-sided figure whose sides are portions of a circle. The inscribed circle is the largest circle that can fit inside the […]

The post Hart’s theorem first appeared on John D. Cook.

Disclaimer: Anything can happen at anytime in the market; I don’t give stock picks, and as the saying goes, the market can remain irrational longer than you can remain solvent.

This post will reveal the connection between my two previous posts: one on the Star Trek lemma and one on Pythagorean triples. In the process of writing the latter, I looked at the Wikipedia article on Pythagorean triples and noticed this curious paragraph. In every Pythagorean triangle, the radius of the incircle and the radii of the […]

The post Incircles and Excircles of Pythagorean triangles first appeared on John D. Cook.

I wrote the following piece for IFP’s Transit Abundance Playbook, a collection of 15 ideas to improve transit delivery in the US.

Finding the vulnerabilities is the easy part

In this post we find all Pythagorean triples that contain consecutive numbers, all Pythagorean triples (a, b, c) such that a + 1 = b or b + 1 = c. a + 1 = b George Osborne wrote a paper [1] addressing the question of when the squares of two consecutive numbers is also a square. Geometrically this is asking […]

The post Consecutive Pythagorean triangle sides first appeared on John D. Cook.

Today's links Jailbreaking isn't theft: It wasn't progress when they did it, it's not piracy when we do it back to them. Hey look at this: Delights to delectate. Object permanence: Major AI breakthrough; Disney v Pooh tombstone; Vancouver riot kiss; Farage admits Brexit lies;...

I was reading an article this evening and saw a footnote to a book by Arthur Baragar [1]. This caught my eye because he was my officemate at UT for a year. I found his book on Archive.org and was surprised to see “The Star Trek Lemma” in the table of contents. What could this […]

The post The Star Trek lemma first appeared on John D. Cook.

simonw/browser-compat-db Inspired by Mozilla's new MDN MCP service - source code here - I decided to try converting their comprehensive mdn/browser-compat-data repository full of browser compatibility data into a SQLite database. This new GitHub Repo includes a Claude Code f...

Capital won't save you from disempowerment.

In the last few months, I've started to see [job applications] that were clearly cowritten by an LLM, link to an LLM-generated portfolio site, which then links to LLM-generated GitHub projects, with purely LLM-generated commit messages. [...]

My other reaction is that I don't know anything about these people.

They haven't put themselves out there. They haven't said anything true. [...]

The perfected, generated, prompted resume is generic and impersonal. It tells me nothing about this person, other than that they use particular tools.

— Tom MacWright, Accidental anonymity

Tags: careers, ai, tom-macwright, ai-misuse

In the hours following the release of CVE-2026-55200 for the project libssh2, site reliability workers and systems administrators scrambled to desperately rebuild and patch all their systems to fix an out-of-bounds write in ssh2_transport_read() due to a missing upper...

What happens if I just point a git server at an object storage bucket? Back when I was porting agent sandboxes to Go, I built everything on top of billy, a filesystem abstraction for Go. The whole trick of the project was teaching a Ti...

I've been following WisdPi's development of various 5 Gbps and 10 Gbps Ethernet adapters for the past couple years.

They use newer Realtek Ethernet chips, which sometimes have performance quirks—most frequently encountered under Linux.

In today's video, I tested the new WisdPi 10G Ethernet Expansion Card for Framework computers. It fits in any available Framework Expansion slot—even on the Framework Desktop.

But Expansion Cards use USB-C for their connection to the mainboard—and therein lies the rub...

John Gruber writes about those annoying popups every website seems to have now and while he does a great job tearing into these ubiquitous, user-hostile patterns, one of the things that stood out to me about his piece was this meta commentary on blogging. Here’s John: If yo...

I find it baffling just how poorly documented most big projects are. Auth0 by Okta has a fair bit of cash, lots of customers, and almost completely absent documentation. Here's how to successfully authenticate a JWT supplied by Auth0. Once your user has authenticated with Auth0, they will be given an accessToken and an idToken. Only the idToken is needed for our purposes. It will look…

I know enough about home cinema audiovisual to know there's a lot I don't know. It's conscious incompetence, if you like, which is different to the unconscious incompetence most people have on the topic. That's not to sound derogatory (it's

The most frustrating aspect of regular expressions is that implementations vary. Features supported in one tool may not be supported at all in another tool, or they may be supported with slightly different syntax. I learned regular expressions in the context Perl, a maximalist regex environment. This led to frustration when features I expect to […]

The post Regular expressions that work “everywhere” first appeared on John D. Cook.

One aspect of strategy that’s been largely lost in the tech industry in recent years is how to compete against platforms, since the major tech companies have gotten so big that markets are no longer competitive. However, the AI market is still early enough, and users and soc...

Release: datasette 1.0a35 I'll write more about this one tomorrow, but it's a big release. Three highlights from the release notes: New "Create table" interface in the database actions menu, backed by the /<database>/-/create JSON API. It can define columns, ...