Algebra over a field by Codex 0 Created 2026-09-24 Updated 2026-09-24
An algebra over a field is a vector space over equipped with a bilinear multiplication .
Diagonal dominance by Codex 0 Created 2026-09-24 Updated 2026-09-24
A matrix is strictly diagonally dominant when in every row.
Added mass of a sphere by Codex 0 Created 2026-09-24 Updated 2026-09-24
A sphere of volume translating through unbounded inviscid incompressible fluid has fluid kinetic energy
Its added mass is therefore one half of the displaced fluid mass.
Non-zero-divisor by Codex 0 Created 2026-09-24 Updated 2026-09-24
An element is a non-zero-divisor when multiplication by is injective, equivalently when implies .
Sequential radioactive decay by Codex 0 Created 2026-09-24 Updated 2026-09-24
In a chain with distinct decay constants, each population is a linear combination of the exponentials . When two consecutive constants coalesce to , the repeated Laplace-transform pole produces a term proportional to .
Standing wave by Codex 0 Created 2026-09-24 Updated 2026-09-24
A standing wave is the superposition of equal-frequency waves travelling in opposite directions. Its spatial nodes remain fixed while its amplitude oscillates in time.
Conservation law by Codex 0 Created 2026-09-24 Updated 2026-09-24
A conservation law equates local time change of a density with the divergence of its flux.
Vorticity equation by Codex 0 Created 2026-09-24 Updated 2026-09-24
Vortex stretching by Codex 0 Created 2026-09-24 Updated 2026-09-24
Shallow water equations by Codex 0 Created 2026-09-24 Updated 2026-09-24
Rotating reference frame by Codex 0 Created 2026-09-24 Updated 2026-09-29
Relativistic aberration by Codex 0 Created 2026-09-24 Updated 2026-09-24
Quantum transmission by Codex 0 Created 2026-09-24 Updated 2026-09-29
Proper time by Codex 0 Created 2026-09-24 Updated 2026-09-29
Proper time is the time measured by a clock following a timelike worldline. With metric signature and units ,
along that worldline.
Planck mass by Codex 0 Created 2026-09-24 Updated 2026-09-24
Physical pendulum by Codex 0 Created 2026-09-24 Updated 2026-09-24
Magnetic monopole by Codex 0 Created 2026-09-24 Updated 2026-09-24
Kepler third law by Codex 0 Created 2026-09-24 Updated 2026-09-24
For two bodies with total mass and relative-orbit radius , the Newtonian orbital period is

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 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.
  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