A cashless society is an economic environment in which financial transactions are conducted through digital means rather than with physical cash. This can include methods such as credit and debit cards, mobile payment apps, digital wallets, and online banking. In a cashless society, the use of cash is minimal or non-existent, and transactions are primarily facilitated by electronic systems. **Key Features of a Cashless Society:** 1.

"Digitality" is a term that often refers to the condition or state of being digital, typically encompassing the ways in which digital technologies influence society, culture, and individuals. It captures the essence of living in a world increasingly mediated by digital technologies, including the internet, social media, and various digital platforms. Key aspects of digitality include: 1. **Interconnectivity**: The ability to connect and communicate through digital means, leading to global networks of interaction.

Huang's Law is an informal principle in the field of software engineering, particularly concerning the development of software systems and projects. Conceptually, it is often summarized by the phrase: **"You can have it good, fast, or cheap. Choose two."** This means that when trying to achieve a goal in software development, there are typically three competing constraints: quality (or goodness), speed (the pace of delivery), and cost (or budget).

Brahmagupta's problem is a famous problem in the field of mathematics, particularly in number theory. It originates from Indian mathematician Brahmagupta, who lived in the 7th century. The problem involves finding integer solutions to a specific type of quadratic equation. More specifically, Brahmagupta's problem can be framed as a question about representing numbers as sums of two squares.

The Rössler attractor is a chaotic attractor named after the German physicist Otto Rössler, who introduced it in 1976. It is a system of three non-linear ordinary differential equations that model certain dynamical systems, and it is notable for its relatively simple structure compared to other chaotic systems like the Lorenz attractor. The equations that define the Rössler attractor are: 1. \(\frac{dx}{dt} = -y - z\) 2.

Software version histories refer to the systematic tracking and documentation of changes made to software over time. This practice is crucial for maintaining, updating, and improving software applications. Version history usually includes details about each version of the software, such as: 1. **Version Number**: A unique identifier for each release, typically following a versioning scheme (like Semantic Versioning) that indicates major, minor, and patch updates.

Arithmetic problems of solid geometry involve calculations and analyses related to three-dimensional shapes and structures. These problems can include a variety of topics, such as the calculation of volumes, surface areas, and dimensions of solids. Here are some common types of arithmetic problems within solid geometry: 1. **Volume Calculations**: - Finding the volume of common solids such as cubes, rectangular prisms, cylinders, cones, spheres, and pyramids using their respective formulas.

Archimedes's cattle problem is a famous and complex problem in ancient mathematics, particularly in the field of number theory. It involves counting the number of cattle owned by the Sun god, based on a series of conditions and ratios relating to their colors. The problem describes: 1. A herd of cattle owned by the Sun god, which includes white, black, yellow, and dark brown cattle.

"Software wars" generally refers to the competitive landscape and conflicts among software companies, technologies, or platforms in various sectors of the tech industry. This term can apply to several contexts: 1. **Operating Systems**: The competition between major operating systems like Microsoft Windows, macOS, and various distributions of Linux can be described as software wars, as each system strives for market dominance and user preference. 2. **Application Software**: Various applications compete for user attention and market share.

Birch's theorem, also known as the Birch and Swinnerton-Dyer conjecture, is a famous conjecture in number theory related to elliptic curves. It posits a deep relationship between the number of rational points on an elliptic curve and the behavior of an associated L-function.

As of the 20th century, this can be described well as "the phenomena described by Maxwell's equations".

Back through its history however, that was not at all clear. This highlights how big of an achievement Maxwell's equations are.

Brauer's theorem on forms, often referred to simply as Brauer's theorem, deals with the classification of central simple algebras and their associated algebraic forms, especially over fields. In more technical terms, it establishes a correspondence between two important concepts in algebra: 1. **Central simple algebras** over a field \( k \): These are finite-dimensional algebras that are simple (having no nontrivial two-sided ideals) and have center exactly \( k \).

The Chakravala method is an ancient Indian algorithm used for solving quadratic equations, particularly those of the form \(x^2 - Dy^2 = N\), where \(D\) is a non-square positive integer, and \(N\) is an integer. This method is notably associated with the work of Indian mathematician Bhaskara II in the 12th century, although it has roots in earlier Indian mathematics.

The Ramanujan–Nagell equation is a famous equation in number theory given by: \[ 2^n = x^2 + 7 \] where \(n\) is a non-negative integer and \(x\) is an integer. The equation states that \(2^n\) can be expressed as the sum of a perfect square \(x^2\) and the integer 7. The equation is considered particularly interesting because it leads to a list of specific solutions.

The "coin problem" often refers to various mathematical problems and puzzles involving coins, which can take different forms depending on the context. Here are a few versions of what might be considered a "coin problem": 1. **Coin Change Problem**: This is a classic problem in combinatorial mathematics and computer science. Given a set of coin denominations and a total amount of money, the goal is to determine the number of ways to make the total amount using the coins.

The Beck–Fiala theorem is a result in the field of combinatorial geometry, specifically concerning the covering of points by convex sets.

The discrepancy of hypergraphs is a concept in combinatorial mathematics that deals with how evenly one can color or distribute a set of points (or elements) among different subsets (or hyperedges) of a hypergraph. More formally, it is concerned with the maximum imbalance that can arise when assigning colors, typically two colors, to the vertices of the hypergraph with respect to the hyperedges.