A gyroelongated cupola is a type of geometric shape that belongs to the family of Archimedean solids. It can be described as a convex polyhedron that combines features of two other solids: a cupola and a prism. Specifically, the gyroelongated cupola is formed by taking a cupola (which is created by connecting a base polygon to a top polygon through triangular faces) and then elongating it by joining two identical bases via a series of square faces.

The medial disdyakis triacontahedron is a geometric figure related to the disdyakis triacontahedron, which is one of the Johnson solids. A Johnson solid is a strictly convex polyhedron that has regular faces but is not uniform (meaning it does not have the same types of faces at each vertex). To break it down further: - The **disdyakis triacontahedron** itself has 32 faces: 30 triangular faces and 2 square faces.

Grid cells are specialized types of neurons found in the entorhinal cortex of the brain, particularly involved in spatial navigation and the cognitive mapping of the environment. They play a crucial role in providing a metric for spatial navigation, helping to create a coordinate system that allows for the representation of space. Key characteristics of grid cells include: 1. **Hexagonal Grid Pattern**: The firing pattern of grid cells forms a hexagonal grid.

Elwyn Berlekamp is a distinguished mathematician and computer scientist known for his work in game theory, combinatorial games, and coding theory. He is particularly recognized for his contributions to the field of combinatorial game theory, where he has developed strategies and mathematical frameworks for analyzing games like Nim and Go. Berlekamp is also notable for his involvement in developing error-correcting codes, which have significant applications in telecommunications and data storage.

The De Bruijn–Erdős theorem is an important result in incidence geometry that deals with the structure of finite geometric configurations. Specifically, the theorem addresses the relationship between points and lines in a finite projective plane.

The Steinitz Exchange Lemma is a result in combinatorial geometry and convex geometry, particularly related to the concepts of polytopes and their properties. It is named after the mathematician Ernst Steinitz. The lemma provides a foundation for understanding properties related to the exchange of vertices in polytopes and helps in establishing connections between the combinatorial and geometric structures of these shapes.

The Infantry Shoulder Cord, also known as the Infantry Blue Cord, is a distinctive piece of military insignia worn by soldiers in the United States Army who are part of the infantry branch. It is a representation of the soldier's affiliation with the infantry and is typically worn on the right shoulder of the uniform. The cord is made of blue and white braid and is worn as part of the Army uniform, particularly with the Army Service Uniform (ASU).

The Q-function, or action-value function, is a fundamental concept in reinforcement learning and is used to evaluate the quality of actions taken in a given state. It helps an agent determine the expected return (cumulative future reward) from taking a particular action in a particular state, while following a specific policy thereafter.

Combinatorics of finite geometries is a field of study that explores the properties, structures, and configurations of geometric systems that are finite in nature. It combines principles from combinatorics—the branch of mathematics concerned with counting, arrangement, and combination of objects—with geometric concepts. Here are some key aspects of the combinatorics of finite geometries: 1. **Finite Geometries**: Finite geometries are geometric structures defined over a finite number of points.

Combinatorial Geometry is a branch of mathematics that deals with the study of geometric objects and their combinatorial properties, often in a discrete setting. When we refer specifically to "Combinatorial Geometry in the Plane," we are primarily concerned with planar arrangements of points, lines, polygons, and other geometric figures, and how these arrangements relate to various combinatorial aspects.

Warwick Tucker is a mathematician and academic known for his work in mathematical analysis and numerical methods. He has contributed to the fields of differential equations, numerical simulations, and chaos theory. Notably, he is associated with the development of techniques for verifying the behavior of dynamical systems and computational methods tailored for rigorous analysis.

The Minimum Total Potential Energy Principle is a fundamental concept in variational calculus and structural mechanics. It is used to analyze the stability and equilibrium of mechanical systems. The principle states that for a system in static equilibrium, the total potential energy is at a minimum compared to any other configuration the system may take.

Sudoku Mania typically refers to a heightened interest or enthusiasm for the game of Sudoku, a popular logic-based puzzle. In this context, it may also denote specific events, tournaments, or themed productions related to Sudoku, such as apps, websites, or books that offer a variety of Sudoku puzzles.

Nikolai Smirnov (1900–1974) was a prominent Russian mathematician known for his contributions to various areas of mathematics, particularly in statistics and probability theory. He is best known for the Smirnov tests, which are statistical methods used for assessing the goodness of fit of a distribution, specifically the Kolmogorov-Smirnov test that compares a sample distribution to a reference probability distribution or compares two sample distributions.

A thermal copper pillar bump is a type of microelectronic interconnect technology used to improve heat dissipation and electrical performance in semiconductor devices, particularly in 3D packaging and flip-chip applications. Here are some key points about thermal copper pillar bumps: 1. **Structure**: A copper pillar bump typically consists of a small vertical column (the pillar) made of copper. It can be formed directly on the chip's surface or on a substrate.

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.

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 group theory, the term "component" can refer to various concepts depending on the context. However, one common usage pertains to the component of a group element in a topological or algebraic sense. 1. **Connected Components in Topological Groups**: In the context of topological groups, the component of a group element \( g \) refers to the connected component of the identity element that contains \( g \).

Bredon cohomology is a type of cohomology theory that is particularly useful in the context of spaces with group actions. It was introduced by Glen Bredon in the 1960s and is designed to study topological spaces with an additional structure of a group action, often leading to insights in equivariant topology.