The Neovius surface refers to a specific type of mathematical surface that has properties useful in the study of differential geometry and topology. It is named after the Finnish mathematician A.F. Neovius, who studied the surface and its properties. The Neovius surface is typically characterized by its complex structure, including features like cusps and self-intersections, making it interesting from the perspectives of both geometry and mathematical physics.
Supergeometry is a branch of mathematics that extends the concepts of geometry to include both geometric structures and "supersymmetrical" objects, which involve odd or "fermionic" dimensions. It arises from the study of supersymmetry in theoretical physics, where it plays a crucial role in string theory and quantum field theory. In conventional geometry, one typically works with spaces that are defined by traditional notions of points and curves in even-dimensional Euclidean spaces.
Synthetic Differential Geometry (SDG) is a branch of mathematics that provides a framework for differential geometry using a synthetic or categorical approach, rather than relying on traditional set-theoretic and analytical foundations. This approach is particularly notable for its use of "infinitesimals," which are small quantities that can be treated algebraically in a way that is similar to how they are used in non-standard analysis.
The term "tangential angle" can refer to different concepts depending on the context, but it generally relates to the angle formed by a tangent line to a curve or surface. Here are a couple of specific interpretations: 1. **In Geometry**: The tangential angle can refer to the angle between a tangent line (a line that just touches a curve at a single point) and the horizontal axis (or another reference line).
The Disc theorem is a concept in complex analysis and deals with the behavior of holomorphic functions. Specifically, it is related to the area of function theory. While there are various formulations and different contexts in which the term "Disc theorem" might be used, one specific interpretation often referenced involves properties related to holomorphic functions defined on the unit disk in the complex plane.
The Generalized Stokes' Theorem is a fundamental result in differential geometry and vector calculus that extends the classical Stokes' theorem, relating integrals of differential forms over manifolds to their behavior on the boundaries of those manifolds. It serves as a powerful tool in various fields such as physics, engineering, and mathematics, particularly in the study of differential forms, topology, and manifold theory.
The Kervaire invariant is a concept in algebraic topology, specifically in the study of bordism theory and the classification of high-dimensional manifolds. It is named after the mathematician Michel Kervaire, who introduced it in the context of differentiable manifolds. More formally, the Kervaire invariant is a specific invariant associated with a smooth manifold, particularly focusing on the topology of the manifold's tangent bundle.
In the context of differential geometry and complex analysis, a **complex geodesic** typically refers to a generalization of the concept of a geodesic in the realm of complex manifolds or complex spaces. The classical notion of a geodesic is a curve that is locally a distance minimizer between points in a given space. In Riemannian geometry, geodesics are trajectories that exhibit extremal properties (typically, minimizing lengths) in a curved space.
Static spacetime is a concept in general relativity that refers to a type of spacetime geometry that is both time-independent (static) and has a specific symmetry. More formally, a static spacetime is one where the gravitational field does not change over time and exhibits certain symmetries, particularly time translation symmetry and spatial symmetry. Key characteristics of static spacetimes include: 1. **Time Independence**: The metric tensor, which describes the geometry of spacetime, does not vary with time.
Serge Rudaz is a philosopher, filmmaker, and writer known for his contributions to discussions on philosophy, ethics, and the intersection of these fields with cinematic narratives. His work often explores the impact of media on societal values and individual perception.
As of my last knowledge update in October 2021, Thomas Timusk is a prominent physicist known for his contributions to the field of condensed matter physics. He has worked on topics such as superconductivity, magnetism, and other critical phenomena in materials. His research has often focused on the use of experimental techniques to study the properties of materials at low temperatures.
W. G. Unruh is a prominent theoretical physicist known for his work in several areas of physics, including general relativity, quantum field theory, and cosmology. One of his most significant contributions is the formulation of what is now known as the Unruh effect. This phenomenon predicts that an observer accelerating through a vacuum will observe thermal radiation (akin to blackbody radiation), even though an inertial observer in that same vacuum would perceive it as empty space.
Russell W. Porter was an American astronomer and a significant figure in the field of optics and telescope design, particularly known for his pioneering work in amateur astronomy. He is best known for his contributions to the design and construction of high-quality telescopes, particularly the "Porter Garden Telescope," which served as a model for many amateur telescopes in the 20th century.
Vladilen Minin is not a widely recognized figure, concept, or term within the public domain as of my last knowledge update in October 2023. It's possible that he could be a private individual, a local figure, or a recent development that hasn’t gained broad recognition.
Vladimir Shiltsev is a prominent physicist and researcher known for his work in the field of particle physics, particularly in relation to accelerator science and technology. He has been involved with major projects, including work at Fermilab, where he has contributed to the development and improvement of particle accelerators and experiments in high-energy physics. Shiltsev's contributions often focus on challenges in the fields of beam dynamics, accelerator design, and applications of particle accelerators in various scientific disciplines.
Neil Turok is a South African theoretical physicist known for his work in cosmology and theoretical physics. He is particularly recognized for his contributions to understanding the early universe and the nature of the Big Bang. Turok has been involved in research related to the cyclic universe model, which proposes that the universe undergoes endless cycles of expansion and contraction. He has also done significant work in mathematical physics and has been an advocate for scientific education in Africa.
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 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. - 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





