A tetradic number is a concept from number theory that refers to a specific type of number. A number \( n \) is considered a tetradic number if it can be expressed as the sum of two squares in two different ways.
The Toy Theorem is a concept from mathematical logic, specifically in the context of set theory and model theory. However, it isn't widely recognized as a fundamental theorem like Gödel's Incompleteness Theorems or the Zermelo-Fraenkel axioms of set theory.
1965 Nobel Prize in Physics laureate by
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
The Uniqueness Theorem is an important concept in various fields of mathematics, particularly in calculus, complex analysis, and differential equations. The specific details can vary depending on the context in which it is applied.
Univariate analysis refers to the examination of a single variable in a dataset. The term "univariate" comes from "uni," meaning one, and "variate," which refers to a variable. This type of analysis is fundamental in statistics and is often the first step in exploring data. Key aspects of univariate analysis include: 1. **Descriptive Statistics**: This involves summarizing and describing the main features of a dataset.
"Up to" can have multiple meanings depending on the context in which it is used. Here are a few common interpretations: 1. **Limit or Capacity**: "Up to" can indicate a maximum limit or capacity. For example, "This elevator can hold up to 10 people" means it cannot hold more than 10 people. 2. **Activity or Responsibility**: It can also refer to being responsible for or engaged in something.
Inequalities are mathematical statements that express the relationship between two expressions that are not necessarily equal to each other. They are used to show that one quantity is greater than, less than, greater than or equal to, or less than or equal to another quantity. The basic symbols used in inequalities include: 1. **Greater than**: \(>\) - Example: \(5 > 3\) (5 is greater than 3) 2.
Probability theorems are fundamental concepts and principles in the field of probability theory, which is the branch of mathematics that deals with the analysis of random phenomena. These theorems help in the understanding, formulation, and calculation of the likelihood of various events occurring.
A compass, in the context of drawing and drafting, is a tool used to create arcs, circles, and angles. It consists of two arms: one with a pointed end (the pivot point) and the other with a pencil or drawing implement attached. By fixing the pointed end at a specific point on paper and rotating the pencil end around that pivot, users can draw accurate circles or portions of circles. Compasses are commonly used in mathematics, geometry, engineering, and various artistic applications.
The Approximate Max-Flow Min-Cut Theorem is a concept in network flow theory, particularly relevant in the context of optimization problems involving flow networks. The theorem relates to the maximum flow that can be sent from a source node to a sink node in a directed graph, and the minimum cut that separates the source from the sink in that graph.
Buchdahl's theorem is a result in general relativity concerning the maximum mass of a spherical, isotropic, perfect fluid star in equilibrium. Specifically, the theorem states that the maximum ratio of a star's mass \( M \) to its radius \( R \) is constrained by: \[ \frac{M}{R} \leq \frac{4}{9} \] when measured in geometrized units (where \( G = c = 1 \)).
Chasles' theorem, in the context of kinematics and rigid body motion, states that any rigid body displacement can be described as a combination of a rotation about an axis and a translation along a vector. This theorem is particularly useful in the analysis of the motion of rigid bodies because it provides a systematic way to break down complex movements into simpler components.
The term "Existence Theorem" is commonly used in various fields of mathematics, particularly in analysis, topology, and differential equations. In general, an existence theorem provides conditions under which a certain mathematical object (such as a solution to an equation or a particular structure) actually exists.
The mathematics of apportionment deals with the methods and principles used to allocate seats, resources, or representation among various parties or groups based on certain criteria. It is commonly applied in political elections, allocation of resources, and distribution of goods, ensuring a fair representation or division according to specific rules and mathematical formulas. ### Key Concepts: 1. **Apportionment Methods**: Various mathematical methods exist for apportioning seats or resources.
The Ohsawa–Takegoshi L² extension theorem is a significant result in complex analysis, particularly in the theory of several complex variables. It provides conditions under which holomorphic functions defined on a submanifold can be extended to a larger domain while retaining certain properties, such as being in the L² space. More precisely, the theorem addresses the problem of extending holomorphic functions that are square-integrable on certain subvarieties of complex manifolds.
Calculators are electronic or mechanical devices designed to perform mathematical calculations, ranging from basic arithmetic (addition, subtraction, multiplication, and division) to more complex operations such as trigonometry, logarithms, and calculus. There are several types of calculators, including: 1. **Basic Calculators**: Simple devices that handle basic arithmetic operations. 2. **Scientific Calculators**: These calculators can perform more advanced functions, including trigonometric calculations, exponentiation, and statistical operations.
Stochastic Portfolio Theory (SPT) is a mathematical framework used to analyze portfolio allocations and their performance in a probabilistic context. It combines elements of probability theory, stochastic processes, and financial modeling to understand how portfolios behave over time under uncertainty. The key aspects of SPT include: 1. **Stochastic Processes**: SPT treats asset prices and portfolio returns as stochastic processes, meaning they evolve randomly over time according to certain probabilistic rules.
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!
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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.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. - 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