Pythagorean Theorem Found On Clay Tablet 1,000 Years Older Than Pythagoras
"The conclusion is inescapable. The Babylonians knew the relation between the length of the diagonal of a square and its side: d=square root of 2," mathematician Bruce Ratner writes in a paper on the topic.
I gave my geometry students some ChatGPT-generated "proofs" this week to review. There were several examples, each designed to illustrate a different point. One was a "proof" that the diagonals of a rectangle are congruent, which contained several errors. I was proud that several students immediately identified how dangerous it was: "It sounds like it is correct, until you look more closely at it."
The first episode of Coding History: 3D from Mode7 to DOOM is live now! It explains how to rotate points in 2D space and why the rotation formula so often used in game development is the way it is: https://www.youtube.com/watch?v=JC5IMfK7Yfw
Please go check it out and boost this post if you want to support an educational video series about old school 80s and 90s 3D 🙏
Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī was born ~780. He not only revolutionized algebra, but his contributions in mathematics, astronomy & geography have been central to hundreds of years of scientific advances.
I think this is interesting and welcome, especially on mobile devices. It is not without problems to want to quickly check some fact on your phone, download the PDF, go to landscape mode, find the right location in the paper, zoom in, etc.
1/4
I don't understand how lace is made, but looking at the #bobbins and pins and patterns ... listen buddy I know math when I see it. This is A #Math Thing. Obviously.
Right away I want to know: Can I encode information in lace?
How much of an expert must one be to make your own patterns?
What about the creation of surfaces?
#Knitting is more accessible, and people have been exploring math with knitting forever.
If you ask 10 game dev friends to play your game's prototype/alpha, 5 Won't even download it, 3 of those who download it will boot it once and say "looks great, I'll try it this weekend" and never do. 2 will give you feedback, only 1 of those will give you useful feedback. Cheer up, It has nothing to do with how good your game is, it's just math.
There is no such thing as "#lawful#access". Encryption is #math. There is no math that the "good guys" can do but which cannot be done by the "bad guys".
Anyone who suggests different is #lying, to #spy on you.
One common feature of various anti-science ideologies is that their adherents lack a sense of scale. #FlatEarthers don’t understand distance, #creationists don’t understand time, #climate change #denialists don’t understand levels of emissions or rate of temperature change, #antivaxers don’t understand population morbidity and mortality. Probably other types of looniness with which I’m less familiar have the same underlying problem.
In a way I sympathize with this, because the numbers are so far outside normal human experience. But learn the #math and suddenly everything makes a lot more sense. We’re not talking about anything particularly advanced. Just grasp that intution breaks down when measuring something very large or very small.
Fun random fact: the sample rate of Audio CD format is 44100Hz. The Nyquist frequency for audible sound is roughly double the upper limit of human hearing, which is 20kHz.
So why is the CDDA sample rate more than 40kHz, but only a little bit more?
The prime factorization of 44100 is 2^2•3^2•5^2•7^2, which gives a LOT of options for computationally cheap downsampling and playback speed reduction. 😁