King's graph by Wikipedia Bot 0
In graph theory, King’s graph, denoted as \( K_n \), is a specific type of graph that is related to the movement of a king piece in chess on an \( n \times n \) chessboard. Each vertex in King's graph represents a square on the chessboard, and there is an edge between two vertices if a king can move between those two squares in one move.
Knight's graph by Wikipedia Bot 0
Knight's graph is a mathematical graph representation based on the moves of a knight in chess. Specifically, the vertices of the graph represent the squares of a chessboard, and there is an edge between two vertices if a knight can move from one square to the other in a single move. In a standard 8x8 chessboard, the knight moves in an "L" shape: it can move two squares in one direction (either horizontally or vertically) and then one square in a perpendicular direction.
A mathematical chess problem refers to a type of puzzle or scenario involving chess that emphasizes logical reasoning, combinatorial analysis, or algorithmic strategies rather than the traditional gameplay aspects of chess. These problems can take various forms, such as: 1. **Chess Puzzles**: These often present a specific position on the board and require the solver to find the best move or series of moves, usually leading to checkmate in a specified number of moves.
The Mutilated Chessboard Problem is a classic problem in combinatorial mathematics and recreational mathematics. The problem is often presented as follows: Imagine a standard 8x8 chessboard, which has 64 squares. If you remove two opposite corners of the chessboard, can you cover the remaining 62 squares completely with dominoes, where each domino covers exactly two adjacent squares?
The Encyclopedia of Triangle Centers is a comprehensive resource dedicated to the study of various notable points associated with triangles, known as triangle centers. These include well-known centers such as the centroid, orthocenter, circumcenter, and incenter, among many others. The encyclopedia aims to catalog these centers, providing their mathematical properties, relationships, formulas, and sometimes historical contexts. The work typically includes both theoretical aspects and practical applications, offering insights that could be beneficial for mathematicians, educators, and students.
Inspec by Wikipedia Bot 0
Inspec is an open-source testing framework primarily used for infrastructure as code (IaC) compliance and security auditing. Developed by the company Chef, Inspec allows users to write automated tests for their applications and infrastructure, validating that they meet specific compliance and security requirements. Key features of Inspec include: 1. **Human-Readable DSL**: Inspec uses a domain-specific language (DSL) that is easy for both developers and non-developers to understand, enabling clear and concise test definitions.
MathSciNet by Wikipedia Bot 0
MathSciNet is an online database and review service that provides access to a vast collection of mathematical literature. It is produced by the American Mathematical Society (AMS) and is widely used by researchers, mathematicians, and students in the field of mathematics. Key features of MathSciNet include: 1. **Bibliographic Information**: It includes bibliographic data for over three million articles, books, and other mathematical documents.
David Goodall (1914–2018) was an Australian botanist known for his extensive work in the field of plant science, particularly in the study of the ecology and conservation of Australian flora. He had an illustrious career, contributing significantly to our understanding of plant species, their habitats, and their interactions within ecosystems. Goodall was also recognized for his advocacy for environmental issues and for promoting science education.
Erik Rauch by Wikipedia Bot 0
As of my last update in October 2023, Erik Rauch does not appear to be a widely recognized figure in popular culture, politics, science, or other notable fields. It's possible that Erik Rauch could refer to a local or lesser-known individual, a fictional character, or a name that emerged after my last update.
G. David Tilman by Wikipedia Bot 0
G. David Tilman is an American ecologist known for his research in population, community, and ecosystem ecology. He is particularly recognized for his work on biodiversity and its effects on ecosystem functioning. Tilman has explored how plant diversity influences productivity, stability, and nutrient cycling in ecosystems. He has contributed to our understanding of ecological interactions and the importance of preserving biodiversity for ecosystem health and resilience. His research has implications for agriculture, conservation, and environmental management.
Graeme Ruxton by Wikipedia Bot 0
Graeme Ruxton is a biologist known for his work in ecology and evolution. He is particularly recognized for his research on animal behavior, the dynamics of predator-prey interactions, and the principles of evolutionary ecology. Ruxton's contributions often focus on modeling and understanding various biological phenomena through mathematical and theoretical approaches. He has published numerous academic papers and is involved in educational activities, often emphasizing the importance of ecological principles in understanding biological systems.
Lee R. Dice by Wikipedia Bot 0
Lee R. Dice is known primarily for his contributions to the field of biology, particularly in relation to population genetics and evolutionary biology. His work often focused on the mathematical modeling of biological processes and the study of how genetic variations occur within populations. Dice is also recognized for his development of techniques in the study of genetic variability and his research on the role of genetic drift in evolution.
Richard Levins by Wikipedia Bot 0
Richard Levins is an influential American ecologist, mathematician, and theorist known for his work in the fields of population biology, theoretical ecology, and the philosophy of science. He is best recognized for his contributions to the understanding of model building in ecology and the use of mathematical models to analyze biological systems.
Robert H. MacArthur (1930-1972) was an influential American ecologist known for his pioneering work in the field of ecology and biogeography. He is perhaps best recognized for his contributions to the development of the theory of island biogeography, which he co-developed with Edward O. Wilson. This theory explains the ecological and evolutionary dynamics of island species, suggesting that the number of species on an island is determined by the balance between immigration and extinction rates.
Economic theorems are fundamental propositions or principles in economics that are derived from a set of assumptions and are supported by logical reasoning or empirical evidence. These theorems provide insights into how economic agents behave, how markets function, and how various economic phenomena are interrelated.
Mathematical economists are economists who use mathematical methods and techniques to analyze economic theories and models. Their work often involves the formulation of economic problems in mathematical terms, which allows for precise definitions, derivations, and predictions. Mathematical economists may focus on various areas of economics, including microeconomics, macroeconomics, game theory, econometrics, and optimization. Key characteristics of mathematical economists include: 1. **Mathematical Modeling**: They develop models to represent economic phenomena.
The Almost Ideal Demand System (AIDS) is a model used in economics to analyze consumer demand for goods and services. It was introduced by economists Angus Deaton and John Muellbauer in 1980. The AIDS model is particularly valued for its flexibility and ability to approximate a wide range of demand systems while maintaining desirable properties such as adding up, homogeneity, and symmetry.
The Averch–Johnson effect is an economic phenomenon observed in the context of regulated utilities, particularly in industries like electricity or gas. It describes the tendency for regulated firms to over-invest in capital relative to what would be considered efficient or optimal. This effect arises when regulatory frameworks allow firms to earn a return on their invested capital.

Pinned article: ourbigbook/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