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The summary from www.geeksforgeeks.org/tree-traversals-inorder-preorder-and-postorder/ is a winner:
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4 5In principle one could talk about tree traversal of unordered trees as a number of possible traversals without a fixed order. But we won't consider that under this section, only deterministic ordered tree traversals.
50,000,000x Magnification by AlphaPhoenix (2022)
Source. Testing and Circuit for a Condenser microphone by RSD Academy (2018)
Source. Not very numerical, but shows a simple working breadboard circuit and an oscilloscope. He whistles with his mouth to get a pretty pure frequency.
That type of microphone requires a bias voltage. The circuit is in Ciro's ASCII art circuit diagram notation:
DC_9---R_10k--+--MICROPHONE--+--G
| |
+-------V------+Soundwaves on an oscilloscope by Animated Science (2015)
Source. Dude speaking to microphone. Some analysis of how different sounds look like. No circuit diagram.There's a billion simple looking expressions which are not known to be transcendental numbers or not. It's cute simple to state but hard to prove at its best.
Open as of 2020:
Bibliography:
- www.quantamagazine.org/recounting-the-history-of-maths-transcendental-numbers-20230627/ How Math Achieved Transcendence by David S. Richeson (2023).
- 2024 www.uktech.news/foodtech/alternative-meat-research-centre-20240829A research centre examining the implementation of alternatives to meat, backed by £38m, will be launched by the University of Leeds.
- 2024 techcrunch.com/2024/08/04/even-after-1-6b-in-vc-money-the-lab-grown-meat-industry-is-facing-massive-issues/ "Even after $1.6B in VC money, the lab-grown meat industry is facing 'massive' issues"
- www.reuters.com/markets/commodities/hoxton-farms-raises-22-million-cultivated-animal-fat-2022-10-20/ Hoxton Farms, cultured animal fat
This is not a truly "fundamental" constant of nature like say the speed of light or the Planck constant.
Rather, it is just a definition of our Kelvin temperature scale, linking average microscopic energy to our macroscopic temperature scale.
The way to think about that link is, at 1 Kelvin, each particle has average energy:per degree of freedom.
For an ideal monatomic gas, say helium, there are 3 degrees of freedom. so each helium atom has average energy:
Another conclusion is that this defines temperature as being proportional to the total energy. E.g. if we had 1 helium atom at 2 K then we would have about energy, 3 K and so on.
This energy is of course just an average: some particles have more, and others less, following the Maxwell-Boltzmann distribution.
chemistry.stackexchange.com/questions/7696/how-do-i-distinguish-between-internal-energy-and-enthalpy/7700#7700 has a good insight:
To summarize, internal energy and enthalpy are used to estimate the thermodynamic potential of the system. There are other such estimates, like the Gibbs free energy G. Which one you choose is determined by the conditions and how easy it is to determine pressure and volume changes.
OK, can someone please just stop the philosophy and give numerical predictions of how entropy helps you predict the future?
The Unexpected Side of Entropy by Daan Frenkel
. Source. 2021.- www.quantamagazine.org/what-is-entropy-a-measure-of-just-how-little-we-really-know-20241213/ What Is Entropy? A Measure of Just How Little We Really Know. on Quanta Magazine attempts to make the point that entropy is observer dependant. TODO details on that.
TODO can anything interesting and deep be said about "why phase transition happens?" physics.stackexchange.com/questions/29128/what-causes-a-phase-transition on Physics Stack Exchange
Refrigerator - How Does It Work? by Curiosity Show
. Source. For scales from absolute 0 like Kelvin, is proportional to the total kinetic energy of the material.
Pinned article: 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!
Intro to OurBigBook
. Source. 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - 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 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. 
- Infinitely deep tables of contents:
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