Mathematics
- bigthink.com How many times must you fold a paper to reach the Moon?
Each time you fold a piece of paper, you double the paper's thickness. It doesn't take all that long to even reach the Moon.
- How the Fibonacci sequence can convert between Miles and Kilometers
It's an approximation but still... It's an interesting quick read.
- The Astonishing Behavior of Recursive Sequenceswww.quantamagazine.org The Astonishing Behavior of Recursive Sequences | Quanta Magazine
Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians.
- Full Berkeley Lectures on Group Theory
cross-posted from: https://slrpnk.net/post/3863820
> Institution: Berkeley > Lecturer: Richard E Borcherds > University Course Code: Math 250A > Subject: #math #grouptheory > Description: This is an experimental online course on mathematical group theory, corresponding to about the first third of the Berkeley course 250A (introductory graduate algebra). The level is for first year graduate students or advanced undergraduates. The topics covered are roughly the parts of group theory that a mathematician not specializing in groups might find useful.
More at !opencourselectures@slrpnk.net
- www.quantamagazine.org A Brief History of Tricky Mathematical Tiling | Quanta Magazine
The discovery earlier this year of the “hat” tile marked the culmination of hundreds of years of work into tiles and their symmetries.
- The Strange Numbers That Birthed Modern Algebrawww.quantamagazine.org The Strange Numbers That Birthed Modern Algebra | Quanta Magazine
The 19th-century discovery of numbers called “quaternions” gave mathematicians a way to describe rotations in space, forever changing physics and math.
- Y'all are dark magicians
Sometimes I'll feel like "yeah, I know some math, I can do integrals!", then watch some YouTube video from Micheal Penn about why there's no three dimensional complex numbers, and suddenly it's dark magic. I understand absolutely n o t h i n g. it's impressive, inspiring, depressing, overwhelming, all at the same time. There's no fancy words. It's all mundane words like set, algebra, etc. but they're strung together in arcane ways. it's more overwhelming because you understand the individual words but they're a whole other language when together.
- www.johndcook.com Every factorial is a power
For every n, there is a base b such that n! = b^n. The relation between n and b(n) is surprisingly close to linear.
- Who else loves the brilliant app
I hate paying for the app and I wish kahn academy had something like it.
Anyone else love this app. It's definitely helping me with looking at basic math in a new way. It's fun and I'll keep going.
What courses are you or have you taken?
Should we make a community?
Have another resource like brilliant? I know Khan Academy, but they are very much deep dives.
I'd really love to create a free resource like this app.
- Unicode 15 includes glyphs for a beautiful base-20 number system invented by Inuit school children in the 90swww.scientificamerican.com A Number System Invented by Inuit Schoolchildren Will Make Its Silicon Valley Debut
Math is called the “universal language,” but a unique dialect is being reborn
- www.nytimes.com Elusive ‘Einstein’ Solves a Longstanding Math Problem
And it all began with a hobbyist “messing about and experimenting with shapes.”
- johncarlosbaez.wordpress.com The Circle of Fifths
The circle of fifths is a beautiful thing, fundamental to music theory. Sound is vibrations in air. Start with some note on the piano. Then play another note that vibrates 3/2 times as fast. Do thi…
- www.nature.com Mathematician who solved prime-number riddle claims new breakthrough
After shocking the mathematics community with a major result in 2013, Yitang Zhang now says he has solved an analogue of the celebrated Riemann hypothesis.
- explained-from-first-principles.com Number theory explained from first principles
A lot of modern cryptography builds on insights from number theory, which has been studied for centuries.
- The Amazing Math Inside the Rubik’s Cubewww.popularmechanics.com To Solve the Rubik’s Cube, You Have to Understand the Amazing Math Inside
Want to solve the puzzle? Then you have to know the numbers.
- How Isaac Newton Discovered the Binomial Power Serieswww.quantamagazine.org How Isaac Newton Discovered the Binomial Power Series | Quanta Magazine
Rethinking questions and chasing patterns led Newton to find the connection between curves and infinite sums.
- Mathematicians Crack a Simple but Stubborn Class of Equationswww.quantamagazine.org Ancient Equations Offer New Look at Number Groups | Quanta Magazine
Ever since Archimedes, mathematicians have been fascinated by equations that involve a difference between squares. Now two mathematicians have proven how often these equations have solutions, concluding a decades-old quest.
- blogs.mathworks.com The Enigma Qube, Merging an Enigma Machine and a Rubik’s Cube
An Enigma Machine combined with a Rubik's Cube makes an encryption device with unprecedented power.ContentsRubik's CubeEnigma MachineEnigma QubeKeyboardRotorsPlugboardPowerRubik's CubeI have made several posts recently about various cubes, including the Rubik's Cube. Enigma MachineIn 2015, MathWorks...
- acko.net How to Fold a Julia Fractal
A tale of numbers that like to turn: a different look at complex numbers and the strange things they do.
- Why does it seem difficult to understand math?
In general, particularly when approaching the more complex areas.
- Easy Puzzle #1
Let f be a function. We are told that f^2 (f composed with itself) has a unique fixed point. How many fixed points could f have?
- Father-Son Team Solves Geometry Problem With Infinite Foldswww.quantamagazine.org Father-Son Team Solves Geometry Problem With Infinite Folds | Quanta Magazine
The result could help researchers answer a larger question about flattening objects from the fourth dimension to the third dimension.
- getpocket.com Mathematicians Discover the Perfect Way to Multiply
By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit.
