Descartes' theorem, also known as the "kissing circles theorem," relates to the geometric properties of circles. Specifically, it provides a relationship between the curvatures (or bending) of four mutually tangent circles. In this context, the curvature of a circle is defined as the reciprocal of its radius (i.e., \( k = \frac{1}{r} \)).
The Wilkinson matrix is a specific type of structured matrix used in numerical analysis, particularly in the study of matrix algorithms and eigenvalue problems. It is named after the mathematician and computer scientist James H. Wilkinson. The Wilkinson matrix is notable for its properties, especially its sensitivity to perturbations, which makes it useful for testing numerical algorithms for stability and accuracy.
Root Mean Square (RMS) is a statistical measure used to quantify the magnitude of a varying quantity. It is especially useful in contexts where alternating values are present, such as in electrical engineering, signal processing, and physics. The RMS value provides a way to express the average of a set of values, where all values are taken into account without regard to their sign (positive or negative).
Sensemaking is a cognitive process through which individuals and groups interpret and understand complex, ambiguous, or uncertain situations. It involves gathering information, interpreting data, and creating meaning from experiences. Sensemaking is particularly important in environments where information is incomplete or rapidly changing, such as in organizational decision-making, crisis management, or during transformative shifts in social or technological contexts.
The quasi-arithmetic mean is a generalization of the arithmetic mean, and it is defined using a function that transforms the values before averaging them.
The term "Riesz mean" refers to a concept in mathematical analysis, specifically in the study of summability and convergence of series or functions. It is named after the Hungarian mathematician Frigyes Riesz. The Riesz mean is a way to assign a value to a divergent series or to improve the convergence properties of a series. It can be viewed as a generalization of the concept of taking limits.
A demand oracle is a concept typically used in the field of economics and decision-making, particularly in the context of auctions, markets, or mechanisms where the value of items or services is determined by the demand from participants. In a more technical or theoretical sense, a demand oracle can be thought of as an entity or a function that provides information about the demand for a particular good or service at various price points or conditions.
Triton is the largest moon of Neptune and the seventh-largest moon in the solar system. It was discovered on October 10, 1846, by British astronomer William Lassell just 17 days after the discovery of Neptune itself. Triton is particularly interesting for several reasons: 1. **Retrograde Orbit**: Triton has a unique retrograde orbit, meaning it orbits Neptune in the opposite direction to the planet's rotation.
"Radix" can refer to different concepts depending on the context in which it is used: 1. **Mathematics**: In mathematics, "radix" refers to the base of a number system. For instance, the decimal system (base 10) has a radix of 10, while binary (base 2) has a radix of 2. The radix indicates how many unique digits, including zero, are available to represent numbers.
The Bild Lilli doll is a fashion doll that originated in Germany in the late 1950s. Created by the German cartoonist Reinhard Beuthin, the doll was initially inspired by a comic strip character named Lilli, who was featured in a comic series that debuted in 1952. The Lilli doll was designed as a gift for adults rather than children and was marketed towards young women as a fashion and lifestyle accessory.
Liquids are one of the four fundamental states of matter, the others being solids, gases, and plasma. They have distinct characteristics that distinguish them from other states: 1. **Definite Volume**: Liquids have a definite volume, meaning they occupy a fixed amount of space. This is in contrast to gases, which can expand to fill any container. 2. **Indefinite Shape**: Unlike solids, which have a fixed shape, liquids take the shape of their container.
Integrity Toys is a company known for producing high-quality fashion dolls and collectibles. Founded in 1995, the company gained prominence for its detailed craftsmanship and artistic designs, particularly its fashion dolls that cater to adult collectors. Integrity Toys is renowned for its lines such as the Fashion Royalty series, which features stylish dolls with a focus on high fashion, as well as other collections like Poppy Parker, Nu. Face, and the Beetlejuice series, among others.
Arrow types are a concept in programming, particularly in functional programming and type theory. They can be thought of as a way to generalize functions and represent computations. An arrow is often used to describe computations that have an input-output relation but can also include additional structure, such as the ability to combine or sequence computations.
The 179th meridian west is a line of longitude that is located 179 degrees west of the Prime Meridian, which is defined as 0 degrees longitude. It is one of the meridians in the geographic coordinate system and is part of the International Date Line (IDL). The 179th meridian west closely follows the 180th meridian but deviates slightly in places to accommodate political and geographic considerations.
DNA sequencing is a laboratory technique used to determine the precise order of nucleotides in a DNA molecule. Nucleotides are the building blocks of DNA and consist of four types: adenine (A), thymine (T), cytosine (C), and guanine (G). The sequence of these nucleotides encodes genetic information and plays a crucial role in various biological functions.
HaeIII is a restriction enzyme, also known as a restriction endonuclease, which is derived from the bacterium *Haemophilus aphrophilus*. It recognizes and cleaves specific sequences of DNA, typically at the sequence "GG|CC" (where the vertical bar indicates the cut point). Restriction enzymes like HaeIII are crucial tools in molecular biology and biotechnology for various applications, including DNA cloning, genetic engineering, and analysis of DNA fragments.
Elfatih Eltahir is a prominent Sudanese-American hydrologist and climate scientist known for his research on hydroclimatology, water resources, and the impacts of climate change on water systems. He is a faculty member at the Massachusetts Institute of Technology (MIT), where he conducts research and teaches in areas related to hydrology and climate.
Russian cryptographers are individuals from Russia who specialize in the study and practice of cryptography, which is the science of securing communication and information by transforming it into a secure format. This field encompasses a variety of techniques and methodologies for encoding messages, ensuring confidentiality, integrity, authentication, and non-repudiation. Historically, Russia has a prominent role in the development of cryptographic techniques and cryptographic theory, especially during the Cold War era, when secure communication was vital for national security.
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





