"The First Moderns" is a term that typically refers to a group of individuals, artists, or thinkers who are considered to be pioneers or early representatives of modern thought or modernism, particularly in the context of art, literature, and philosophy. This term can pertain to various movements across different disciplines. One prominent use of the term is in art history, where "The First Moderns" may describe artists who broke from traditional forms and conventions, paving the way for modern and contemporary art.

Yuktibhāṣā is an Indian philosophical text written in the 14th century by the mathematician and philosopher Madhava of Sangamagrama. It is one of the earliest works to present a systematic exposition of mathematical and astronomical ideas in the context of the Indian mathematical tradition. The text is notable for its argumentation and exposition in a dialogue form, focusing on various mathematical concepts, particularly related to infinitesimal calculus, trigonometry, and approximations of functions.

"Zenzizenzizenzic" is a term from the 16th century that refers to the eighth power of a number. The term is derived from a kind of playful construction of the word "zenzizenzic," which itself referred to the fourth power, and was built upon the earlier concept of "zenzic," which referred to the square (or second power).

A primitive notion, also known as a primitive concept or primitive term, is a basic concept or idea that is not defined in terms of other concepts within a particular framework or system. Instead, it serves as a foundational building block for developing more complex concepts and theories. Primitive notions are often used in various fields, including mathematics, logic, and philosophy. In formal systems, primitive notions are the terms or concepts that are taken to be self-evident or basic and are accepted without further definition.

Gelfond's constant, denoted as \( G \), is a transcendental number defined as: \[ G = 2^{\sqrt{2}} \] It is named after the Russian mathematician Aleksandr Gelfond, who, along with Theodor Schneider, proved that \( G \) is transcendental in 1934. A transcendental number is a number that is not a root of any non-zero polynomial equation with rational coefficients.

The square root of 5 is approximately 2.236.

The square root of 3 is approximately 1.732.

Vertex configuration typically refers to how the vertices (corners or points) of a geometric object are arranged or categorized, particularly in the context of polyhedra or other polygonal shapes. In mathematics and computer graphics, the term could also relate to the organization or representation of vertex data in graphical contexts, such as in 3D modeling.

Active and passive transformations are concepts primarily used in the context of data processing, particularly in ETL (Extract, Transform, Load) processes within data warehousing. ### Active Transformation: Active transformations change the number of records that pass through the transformation. They can add, modify, or delete records, which fundamentally alters the data flow. Examples include: - **Filter**: Removes records that do not meet certain criteria.

The term "complete set of invariants" typically refers to a collection of quantities or properties associated with a mathematical object that remain unchanged (invariant) under certain transformations or operations. Invariants are crucial in fields such as algebra, geometry, topology, and physics, as they help classify and understand the underlying structure of objects.

A lemniscate is a figure-eight-shaped curve that is a type of algebraic curve. The most famous version is the lemniscate of Bernoulli, which can be described mathematically by the equation: \[ \left( x^2 + y^2 \right)^2 = a^2 (x^2 - y^2) \] where \( a \) is a constant that defines the size of the curve.

In statistics and mathematics, variables can be classified as continuous or discrete based on the nature of their values. ### Continuous Variables - **Definition**: A continuous variable can take an infinite number of values within a given range. These values can be or approximated to any real number, including fractions and decimals. - **Examples**: - Height (e.g., 170.5 cm) - Weight (e.g., 65.8 kg) - Time (e.

The Jacobian is a mathematical concept primarily used in multivariable calculus and differential geometry. It describes how a function changes as its input changes, particularly in the context of functions that map vectors from one space to another.

In mathematics, the term "modulo" refers to a mathematical operation that finds the remainder when one integer is divided by another. This operation is commonly denoted using the symbol "mod". For example, the expression \( a \mod b \) means "the remainder when \( a \) is divided by \( b \)".

The Gurzadyan theorem, proposed by the Armenian mathematician A. G. Gurzadyan, deals with a specific aspect of the geometry of circles. It states that if you have a circle and you consider its inscribed and circumscribed polygons, certain properties hold regarding their areas and relationships. One of the most notable implications of Gurzadyan's work is related to the properties of cyclic quadrilaterals and their area expressions.

The term "Representation Theorem" can refer to several concepts across various fields of mathematics, including functional analysis, probability theory, and economics. Here are a few notable examples: 1. **Representation Theorem in Functional Analysis**: In the context of functional analysis, one important representation theorem is the Riesz Representation Theorem. This theorem states that every continuous linear functional on a Hilbert space can be expressed as an inner product with a fixed element of the space.