Square root factorial
What factorial is closest to the factorial of 2024? A good guess would be 1012, based on the idea that √(n!) might be near (n/2)!. This isn’t correct—the actual answer is 1112—but it’s not wildly off. Could it be that (2n)! is asymptotically (n!)²? No, Gauss’ duplication formula shows that
Read moreBuild Your Own AI Tools in Python Using the OpenAI API
Learn how to integrate the OpenAI/ChatGPT API into your Python scripts, from initial setup to real-world, practical examples of using it. Continue reading Build Your Own AI Tools in Python Using the OpenAI API on SitePoint.
Read moreTry these apps to reach your New Year’s resolutions in 2024
As the new year approaches, many of us are reminded of all the things we accomplished this year — getting a promotion, being more productive or even showing up to places on time — as well as things we failed to do. (There may or may not be a barely
Read moreClimate tech might be the hot job market in 2024
While much of the tech world has been besieged by layoffs, climate tech continued to hire. Next year looks no different. © 2023 TechCrunch. All rights reserved. For personal use only.
Read moreComputing square root floor
Given an integer n, suppose you want to compute ⌊√n⌋, the greatest integer less than or equal to the square root of n. One reason you may want to compute ⌊√n⌋ is to know when you can stop trial division when factoring n. Similarly, ⌊√n⌋ gives you a starting point
Read moreGroups of order 2024
This time last year I wrote about groups of order 2023 and now I’d like to do the same for 2024. There are three Abelian groups of order 2024, and they’re not hard to find. We can factor 2024 = 8 × 11 × 23 and so the Abelian groups
Read moreWeak encryption and surveillance
Two of the first things you learn in cryptography are that simple substitution ciphers are very easy to break, and that security by obscurity is a bad idea. This post will revisit both of these ideas. Security depends on your threat model. If the threat you want to protect against
Read moreWhat a long, strange year it’s been in enterprise tech news
Looking back at the top enterprise news stories of the year, it's clear that generative AI dominated, but it wasn't the only news. © 2023 TechCrunch. All rights reserved. For personal use only.
Read moreI guess I’m a projector person now?
I’ve been one of the those “I don’t own a TV” people for a long time. Really my entire adult life, excepting those times when I shared my living space with someone who brought their own to the party. My exact motivation is a bit hazy all these years later,
Read moreAmazon Echo Frames review, MrBeast jumps the shark and the Apple Watch gets un-banned
Hey, folks, and welcome to Week in Review (WiR), TechCrunch’s regular newsletter recapping the week that was in tech. Typically, the stretch between Christmas and New Year’s tends to be on the sleepier side — but that wasn’t the case in 2023. Fortunately, the TC crew was around to document
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