Newton's theorem, often referred to as the "Newton's theorem on ovals," relates to the properties of an oval, particularly in the context of projective geometry and combinatorial geometry. The theorem essentially states that given a set of points in the plane, if these points are located on a smooth convex curve (an oval), then there exists a certain relationship concerning the tangents, secants, and other lines drawn from these points.
The Mohr–Mascheroni theorem is a result in geometry that states that it is possible to construct any length using only a compass, without the need for a straightedge. This theorem is named after the German mathematician Max Mohr and the Italian mathematician Giovanni Mascheroni, who independently proved this result. The theorem can be surprising because traditional geometric constructions often rely on both a compass and a straightedge.
Isomerism is a phenomenon in chemistry where two or more compounds have the same molecular formula but different structural arrangements of atoms. This results in distinct physical and chemical properties among the isomers. Isomers can be categorized into two main types: 1. **Structural Isomers (or Constitutional Isomers)**: These isomers differ in the connectivity of their atoms. There are several subtypes, including: - **Chain Isomerism**: Different arrangements of the carbon skeleton (e.g.
The term "progressive function" can refer to different concepts depending on the field of study. Here are a few interpretations: 1. **Mathematics:** In a mathematical context, a "progressive function" is often not a standard term. However, it might refer to a function that increases in a certain way, such as being a monotonically increasing function.
Go! Sudoku is a video game based on the classic puzzle game Sudoku. It is typically available on various gaming platforms, including consoles and handheld devices. The game presents players with a grid of numbers, where the objective is to fill in the empty cells following the standard rules of Sudoku: each row, column, and region must contain all numbers in a specific range (usually 1-9) without repetition. Go!
The Tweedie distribution is a family of probability distributions that generalizes several well-known distributions, including the normal, Poisson, gamma, and inverse Gaussian distributions. It is characterized by a parameter \(\p\) (the power parameter), which determines the specific type of distribution within the Tweedie family.
Kurt Gödel was an Austrian-American logician, mathematician, and philosopher, best known for his groundbreaking work in mathematical logic and the foundations of mathematics. He was born on April 28, 1906, in Brünn, Austria-Hungary (now Brno, Czech Republic) and died on January 14, 1978, in Princeton, New Jersey, USA.
A Shelah cardinal, named after the mathematician Saharon Shelah, is a certain kind of large cardinal in set theory, which is a branch of mathematics. Large cardinals are infinite numbers that extend the concept of cardinality beyond the standard infinite sets recognized in Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC).
Alexander S. Kechris is a prominent mathematician known for his contributions to set theory and its connections to other areas of mathematics, particularly in model theory and descriptive set theory. He has published numerous research papers and has co-authored influential texts, including works on the structure of the real line and on the foundations of set theory. Kechris is known for his rigorous approach to mathematics and has made significant contributions to the understanding of topological groups and their classifications.
Itay Neeman is a mathematician known for his work in the fields of model theory, set theory, and descriptive set theory. His research often involves topics like the interaction between logic and other areas of mathematics, including analysis and topology. He has produced a number of important results and publications in these areas.
The "Two Truths Doctrine" is a philosophical concept primarily associated with Buddhist epistemology and metaphysics. It is a framework for understanding how different levels of reality coexist and how they can be truthfully articulated. The doctrine posits that there are two kinds of truths: 1. **Conventional Truth (Samvṛti-satya)**: This refers to the everyday truths that arise within the context of ordinary experience and social conventions.
The Journal of Agricultural, Biological, and Environmental Statistics (JABES) is a peer-reviewed academic journal that focuses on statistical methods and their applications in agricultural, biological, and environmental research. It serves as a platform for the dissemination of research related to statistical techniques, methodologies, and novel applications that address challenges in these fields.
In the context of theology, a practical syllogism is a form of reasoning that links theoretical knowledge or beliefs with practical action or behavior. It typically takes the form of a syllogism, which consists of a major premise, a minor premise, and a conclusion. In theological discussions, this method often helps to illustrate how one's beliefs impact real-life decisions and moral actions.
Parametric statistics refers to a category of statistical techniques that make specific assumptions about the parameters of the population distribution from which samples are drawn. These techniques typically assume that the data follows a certain distribution, most commonly the normal distribution. Key features of parametric statistics include: 1. **Assumptions**: Parametric tests often assume that the data is normally distributed, that variances are equal across groups (homogeneity of variance), and that the observations are independent.
The Transferable Belief Model (TBM) is a theory in the field of evidence theory, particularly dealing with the representation and management of uncertain information. It was introduced by Philippe Smets in the context of artificial intelligence and decision-making. ### Overview of the Transferable Belief Model: 1. **Foundation on Belief Functions**: The TBM is based on belief functions, which provide a framework for managing uncertainty.
Ik Onkar is a fundamental concept in Sikhism, representing the oneness of God. The term is derived from the Gurmukhi script, where "Ik" means "one" and "Onkar" signifies the creative energy or essence of God. Together, "Ik Onkar" proclaims that there is only one supreme being, who is the source of all creation and is present in everything.
A double dactyl is a specific form of poetry that consists of two stanzas, each with four lines. The first two lines of each stanza are usually made up of two dactylic feet (a dactyl being a metrical foot consisting of one stressed syllable followed by two unstressed syllables). The third and fourth lines typically contain a single long syllable followed by a short one, often culminating in a playful or humorous punchline.
A testimonial is a statement or endorsement from a person or organization that reflects their experience with a product, service, or individual. Testimonials are often used in marketing and advertising to build credibility and trust, as they provide social proof and help potential customers make informed decisions. They can be written or verbal and typically highlight the benefits or positive aspects of the experience. For example, a satisfied customer might provide a testimonial praising a company's excellent customer service, quality products, or reliable performance.
As of my last knowledge update in October 2021, Anuar Dyusembaev does not appear to be a widely recognized public figure, event, or term. It's possible that he could be a private individual, a name that has gained prominence after that date, or it could refer to someone in a more localized or specific context.
Igor Dmitrievich Ado is a prominent Russian mathematician known for his significant contributions to the field of functional analysis and topology. He is particularly recognized for his work on the theory of linear operators and the study of infinite-dimensional spaces. Ado is also noteworthy for his involvement in the development of mathematical education and research in Russia.

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