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@cirosantilli/_file/numpy/numpy/fft_plot.py by 
Ciro Santilli 35 Updated 2024-12-15 +Created 2024-07-04
Ciro Santilli 35 Updated 2024-12-15 +Created 2024-07-04The output was also uploaded to: commons.wikimedia.org/wiki/File:DFT_2sin(t)_%2B_sin(4t).svg and added to en.wikipedia.org/w/index.php?title=Discrete_Fourier_transform&oldid=1176616763 only to be later removed of course: Deletionism on Wikipedia.
DFT of with 25 points
. Source code at: numpy/fft_plot.py.wiki.bbchallenge.org/wiki/Antihydra:
- news.ycombinator.com/item?id=40864949 BB(6), The 6th Busy Beaver Number, is harder than a Collatz-like math problem
- www.reddit.com/r/math/comments/1dubva0/finding_the_6th_busy_beaver_number_%CF%836_aka_bb6_is/ "Finding the 6th busy beaver number (Σ(6), AKA BB(6)) is at least as hard as a hard Collatz-like math problem called Antihydra":
- www.reddit.com/r/compsci/comments/1duc62e/finding_the_6th_busy_beaver_number_%CF%836_aka_bb6_is/
The good:
- a bit of Students must be allowed to progress as fast as they want. Though not fully as once you're in your stuck for 6 weeks in their rythm. Though there are research projects going on too which helps.
- Peer tutoring-like: they seem to pick undergraduate students to serve as supervisors
The bad: everything else. Closed source learning materials + a university-like selection program. Such a waste of efforts that could benefit way more people with more open resources.
meta.mathoverflow.net/questions/4889/request-to-keep-an-eye-out-for-promys-admissions-problems asking to remove PROMYS problems from MathOverflow. And it seems to have been mostly accepted. Newbs. Any maths problem should be allowed to be askeable online. There are no fundamentally new problems, copyright takedown is just silly.
The Abstraction and Reasoning Challenge by Ciro Santilli 35 Updated 2024-12-15 +Created 2024-07-04
Ciro Santilli 35 Updated 2024-12-15 +Created 2024-07-04
Standing wave caused by wave interference of two waves
. Source. Staring from a triangle wave, this explains why we always get the same musical notes:See also: solving partial differential equations with the Fourier series.
- www.math.hmc.edu/~ajb/PCMI/lecture7.pdf "7.5.1. Musical instruments" is very good. Also mentions that in the piano it is more like an initial speed is applied, and it is not the same as plucking
- music.stackexchange.com/questions/135635/confusion-about-overtones-and-a-slow-motion-video-of-a-plucked-string
- music.stackexchange.com/questions/60833/what-determines-the-relative-volumes-of-the-harmonics-when-plucking-a-guitar-str
TODO: do higher overtones decay faster in time than the base ones?
- www.physicsforums.com/threads/why-do-harmonics-decay-faster-than-the-fundamental.955731/ But presumaby yes, damping force is proportional to speed, and higher harmonics have higher speeds going up and down
Wave equation on string with one vibrating side by Ciro Santilli 35 Updated 2024-12-15 +Created 2024-07-04
Ciro Santilli 35 Updated 2024-12-15 +Created 2024-07-04You know things are bad when the extracurricular activities are what studnets should actually be doing full time instead!
_%2B_sin(4t).svg){kind=link}
The FASCINATING 200-Year History of Benzene by Chemistorian
. Source. Interesting history. Notably how things were only finally well settled by X-ray crystallography.Discovering them was not so easy because they don't form chemical compounds. So they exist only as gases. And Helium disperses off into space.
Argon was the first to be found by density considerations because it is so abundant on Earth's atmosphere (~1%): Argon is abundant on Earth's atmosphere because it comes from the decay of Potassium-40.
Then basically all of the others were discovered by spectral lines. Helium notably was first found on the Sun like that, and only later on Earth! Thus its name. Pretty cool.
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivative - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - Internal cross file references done right:
- Infinitely deep tables of contents:
Figure 6. Dynamic article tree with infinitely deep table of contents.Live URL: ourbigbook.com/cirosantilli/chordateDescendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact