Jump wire by Ciro Santilli 40 Updated 2025-07-16
Notably used to connect:
You can buy large sets of them in combitation of male/male, male/female, female/female. Male/male is perhaps the most important
Video 1.
Making Jumper Wires by PCBurn! (2018)
Source.
Pin header by Ciro Santilli 40 Updated 2025-07-16
These often come pre-soldered on devboards, e.g. and allow for easy access to GPIO pins. E.g. they're present on the Raspberry Pi 2.
Why would someone ever sell a devboard without them pre-soldered!
Figure 2.
Underside of a Raspberry Pi 2
. Source. At the top of this image we can clearly see how the usually pre-soldered pin header connectors go through the PCB and are soldered on both sides.
Jumper (computing) by Ciro Santilli 40 Updated 2025-07-16
Allows you to connect two adjacent pins of a pin header. Sometimes used as a hardware configuration interface!
Spin structure is a concept from topology and theoretical physics that arises in the context of manifold theory, particularly in relation to spin manifolds. In mathematics, a spin structure is typically defined on a manifold that enables the definition of spinors, which are mathematical objects that generalize the notion of complex numbers and vectors.
Light-emitting diode by Ciro Santilli 40 Updated 2025-07-16
Video 1.
How LEDs work by VirtualBrain
. Source. 2021. Good 3d schematics clearly explaining part of the LED electronic package.
Boltzmann constant by Ciro Santilli 40 Updated 2025-07-16
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.
This is why the units of the Boltzmann constant are Joules per Kelvin.
For an ideal monatomic gas, say helium, there are 3 degrees of freedom. so each helium atom has average energy:
If we have 2 atoms at 1 K, they will have average energy , and so on.
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.
Two-dimensional Yang–Mills theory is a gauge theory that generalizes the concept of Yang–Mills theories to two spatial dimensions. In general, Yang–Mills theories are constructed from a gauge field that transforms under a symmetry group (the gauge group), and they play a crucial role in modern theoretical physics, particularly in quantum field theory and the Standard Model of particle physics.

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!
We have two killer features:
  1. 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-calculus
    Articles 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
  2. 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.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . 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.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant 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