Curie temperature by Ciro Santilli 40 Updated 2025-07-16
Figure 1.
Variation of saturation magnetisation with temperature for Nickel
. Source. This graph shows what happens when you approach the Curie temperature from below.
Ferromagnetism by Ciro Santilli 40 Updated 2025-07-16
The wiki comments: en.wikipedia.org/w/index.php?title=Ferromagnetism&oldid=965600553#Explanation
The Bohr-van Leeuwen theorem, discovered in the 1910s, showed that classical physics theories are unable to account for any form of magnetism, including ferromagnetism. Magnetism is now regarded as a purely quantum mechanical effect. Ferromagnetism arises due to two effects from quantum mechanics: spin and the Pauli exclusion principle.
Magnetic dipole by Ciro Santilli 40 Updated 2025-07-16
A tiny idealized magnet! It is a very good model if you have a small strong magnet interacting with objects that are far away, notably other magnetic dipoles or a constant magnetic field.
The cool thing about this model is that we have simple explicit formulas for the magnetic field it produces, and for how this little magnet is affected by a magnetic field or by another magnetic dipole.
This is the perfect model for electron spin, but it can also be representative of macroscopic systems in the right circumstances.
The intuition for the name is likely that "dipole" means "both poles are on the same spot".
Figure 1.
Different macroscopic magnets can be approximated by a magnetic dipole when shrunk seen from far away
. Source.
Mathematics in the United Kingdom encompasses a broad range of activities, including education, research, and applications across various fields. Here’s an overview of its key aspects: ### 1. **Education System:** - **Curriculum**: Mathematics is a core subject in the UK education system. Students usually begin learning mathematics at an early age, and it continues to be a mandatory subject through secondary education (ages 5-16).
Mathematics in the United States encompasses a wide range of topics, practices, and educational frameworks that reflect both the discipline itself and its application within various contexts. Here are some key points about mathematics in the U.S.: ### 1. **Educational Framework** - **K-12 Education**: Mathematics is a core subject in the U.S. education system, starting from elementary school through high school.
A Banach space is a complete normed vector space, meaning that it is a vector space equipped with a norm such that every Cauchy sequence in the space converges to an element within the space. Here’s a list of some important examples and types of Banach spaces: 1. **Finite-Dimensional Banach Spaces** - Any finite-dimensional normed vector space is a Banach space.
Fourier analysis is a vast and rich field in mathematics that studies the representation of functions as sums of sinusoidal components and the study of the properties of these representations.
Wenninger polyhedra are a class of convex polyhedra that were studied and categorized by mathematician Alfred Wenninger. They are particularly notable for their unique geometric properties and can be constructed from various symmetrical configurations. Wenninger's work primarily focused on polyhedra that possess a high degree of symmetry, including those that are derived from regular polyhedra and those that exhibit complex topological features.
String theory is a complex and expansive field of theoretical physics that aims to reconcile quantum mechanics and general relativity. Below is a list of important topics and concepts related to string theory: 1. **String Types**: - Open Strings - Closed Strings 2. **Dimensions**: - Extra Dimensions - Compactification - Calabi-Yau Manifolds 3.
Integration and measure theory are fundamental branches of mathematics, particularly in real analysis and functional analysis. Here’s a list of essential topics within these fields: ### Basic Concepts 1. **Sets and Functions** - Set operations (union, intersection, difference) - Functions and relations - Bounded and unbounded functions 2.
Large cardinals are certain kinds of infinite cardinal numbers that have strong and significant properties in set theory. They are used to explore the foundations of mathematics and understand the hierarchy of infinities.
Numerical analysis software encompasses a wide range of applications and programming environments used to perform numerical computations. Here’s a list of some popular numerical analysis software packages: 1. **MATLAB**: A high-level language and interactive environment for numerical computation, visualization, and programming. It includes numerous built-in functions for numerical analysis. 2. **NumPy/SciPy**: Open-source libraries for Python.
Planar symmetry groups refer to the mathematical groups that describe the symmetries present in two-dimensional shapes. These groups capture how a pattern can be transformed through rotations, translations, reflections, and glide reflections while preserving its overall structure. The main types of planar symmetry groups can be categorized into: 1. **Cyclic Groups (C_n)**: These consist of rotations about a point. For example, C_3 corresponds to a triangle where you can rotate the shape 120 degrees.

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