In fluid dynamics, an "eddy" refers to a localized, swirling flow of fluid that occurs in various types of fluids, be they gases or liquids. Edies develop when the flow of the fluid is disturbed by obstacles, changes in flow velocity, or other discontinuities, leading to a rotational motion of fluid particles.
The Great Red Spot is a massive, persistent storm located in the atmosphere of Jupiter. It has been observed for more than 350 years and is characterized by its reddish color and enormous size, with a diameter that can be as much as 1.3 times that of Earth. The storm is situated in Jupiter's southern hemisphere and is part of a complex system of atmospheric dynamics. The Great Red Spot is a high-pressure area producing wind speeds of around 432 km/h (approximately 268 mph).
The term "Lambda2" could refer to several different concepts depending on the context in which it's used, and one common usage is related to statistical methods, particularly in the context of analytics and modeling. 1. **Lambda2 in Statistics**: In the field of statistics, particularly in relation to regression analysis or model evaluation, Lambda (λ) often denotes a penalty parameter used in techniques like Ridge regression or Lasso regression.
A landspout is a type of tornado that typically forms in a convective environment, often associated with non-supercell thunderstorms. Unlike typical tornadoes that develop from supercell storms, landspouts can form under weaker storm conditions and are usually less intense. Landspouts are characterized by a narrow, rope-like appearance and can form quickly, sometimes with little warning, as a result of localized wind shear and updrafts within a developing storm.
A post-tropical cyclone is a storm system that has lost its tropical characteristics, typically due to cooler sea surface temperatures or interaction with land. While it may still retain some features of a tropical system, such as a well-defined circulation, it no longer meets the criteria to be classified as a tropical storm or hurricane. Post-tropical cyclones can take on a variety of forms, including extratropical cyclones, which are characterized by fronts and a temperature gradient.
A smoke ring is a vortex of smoke that forms in a circular shape. It is created when a puff of smoke is expelled from a source, such as the mouth, a smoke ring machine, or a cigar, and the motion of the smoke creates a toroidal (doughnut-shaped) formation. The smoke ring is characterized by its circular motion, which is a result of differences in pressure and velocity within the smoke itself.
The Taylor-Green vortex is a classic flow field used in fluid dynamics, particularly in the study of turbulence. It represents an example of a vortical flow that is mathematically derived and often serves as a benchmark for testing computational fluid dynamics (CFD) techniques and turbulence models. ### Characteristics of Taylor-Green Vortex: 1. **Velocity Field**: The Taylor-Green vortex has a periodic velocity field that can be described in two or three dimensions.
The angular velocity tensor is a mathematical representation of the angular velocity of a rigid body or a system of particles in three-dimensional space. Unlike the scalar angular velocity, which describes the rate of rotation around a single axis, the angular velocity tensor conveys how an object rotates about multiple axes simultaneously. ### Definitions and Components 1.
Declination is an astronomical term referring to the angular measurement of a celestial object's position above or below the celestial equator. It is similar to latitude on Earth. Declination is measured in degrees (°), with positive values indicating the object is north of the celestial equator and negative values indicating it is south. For example: - An object with a declination of +30° is located 30 degrees north of the celestial equator.
The Exterior Angle Theorem is a fundamental principle in triangle geometry that relates the measures of an exterior angle of a triangle to the measures of its remote interior angles. The theorem states that: In any triangle, the measure of an exterior angle is equal to the sum of the measures of the two opposite (or remote) interior angles. To illustrate, consider triangle ABC where angle C is an exterior angle formed by extending side AC.
Hyperbolic orthogonality is a concept that arises in the context of hyperbolic geometry, a non-Euclidean geometry characterized by its unique properties in relation to distances and angles. In Euclidean geometry, orthogonality refers to the notion of two lines being perpendicular to each other, typically in two or three-dimensional spaces. In hyperbolic geometry, the definitions and implications of angles and orthogonality differ from those in Euclidean geometry.
Magnetic declination, also known as magnetic variation, is the angle between magnetic north (the direction a compass points) and true north (the geographic north pole) at a given location on the Earth's surface. This angle is measured in degrees east or west from true north. Because the Earth's magnetic field is not uniform, magnetic declination varies depending on where you are located. It can change over time due to shifts in the Earth’s magnetic field.
In astronomy, the term "position angle" typically refers to the angular measurement of the orientation of an astronomical object, particularly in the context of binary stars, planets, or other celestial bodies. The position angle is measured in degrees from a reference direction, usually north, moving clockwise. Here are a few key points about position angle: 1. **Reference Direction**: The reference direction for measuring position angle is typically defined as the direction toward the North celestial pole.
A sliding T bevel, also known as a sliding bevel gauge or angle bevel, is a hand tool used primarily in woodworking and construction for transferring and setting angles. It consists of two main components: a handle and a blade. The blade is typically made of metal or wood and can pivot relative to the handle, allowing the user to set it to a specific angle.
The term "subtended angle" refers to the angle formed by two lines or segments that extend from a specific point to the endpoints of a line segment or arc. More commonly, it is used in geometry to describe the angle at a particular point (the vertex) which "sees" a given arc or segment.
Bisection is a mathematical method used to find roots of a continuous function. It is a type of bracketing method, which means it narrows down the search for a root within a certain interval. The key idea behind the bisection method is to divide an interval in half and, based on the signs of the function at the endpoints, determine which half contains the root.
In geometry, a **cross section** refers to the intersection of a solid object with a plane. When a three-dimensional object is cut by a plane, the shape formed by this intersection is known as the cross section. The specific shape of the cross section depends on the orientation and position of the cutting plane relative to the object.
In set theory, an **ineffable cardinal** is a type of large cardinal that is defined based on properties related to certain filters and combinatorial principles. Specifically, a cardinal \( \kappa \) is called ineffable if it satisfies the following conditions: 1. **Uncountability**: \( \kappa \) is an uncountable cardinal.
In set theory, projection is a concept related to relations and the Cartesian product of sets. Given a set \( S \) and a relation \( R \subseteq S_1 \times S_2 \), a projection is a function that retrieves one part of the Cartesian product from the relation.
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).

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 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