The concept of a graph minor is a fundamental notion in graph theory, particularly in the study of graph structure and graph algorithms. A graph \( H \) is said to be a **minor** of another graph \( G \) if \( H \) can be formed from \( G \) by performing a series of operations that includes: 1. **Edge Deletion**: Removing edges from the graph. 2. **Vertex Deletion**: Removing vertices and incident edges from the graph.

The Alexander horned sphere is a classic example in topology, specifically in the study of knot theory and manifold theory. It is constructed by taking a sphere and creating a complex embedding that demonstrates non-standard behavior in three-dimensional space. The construction of the Alexander horned sphere involves a series of increasingly complicated iterations that result in a space that is homeomorphic to the standard 2-sphere but is not nicely embedded in three-dimensional Euclidean space.

The Borromean rings are a set of three interlinked rings that are arranged in such a way that no two rings are directly linked together; instead, all three are interlinked with one another as a complete set. The key property of the Borromean rings is that if any one of the rings is removed, the remaining two rings will be unlinked, meaning they will not be entangled with each other.

Hermann Brunn is not widely recognized in popular culture or historical context, so it's likely that you might be referring to a specific individual or a relatively obscure topic.

A Dehn twist is a fundamental concept in the field of topology, particularly in the study of surfaces and 3-manifolds. It is a type of homeomorphism that can be used to analyze the properties of surfaces and their mappings.

The Double Suspension Theorem is a concept in algebraic topology, particularly related to the behavior of suspensions in homotopy theory. The theorem provides a relationship between the suspension of a space and the suspension of built spaces from that space.

The JTS Topology Suite (Java Topology Suite) is an open-source library designed for performing geometric operations on planar geometries. It is implemented in Java and follows the principles of the OGC (Open Geospatial Consortium) Simple Features Specification, which standardizes the representation and manipulation of spatial data.

The Geometry Center was a research and educational institution based in Minneapolis, Minnesota, that focused on the visualization of mathematical concepts, particularly in geometry and topology. Established in the late 1980s, the center aimed to promote the understanding of mathematical ideas through various means, including computer graphics, animations, and interactive software. It served as a hub for mathematicians, educators, and artists to collaborate on projects that highlighted the beauty and intricacies of geometry.

Interactive geometry software allows users to create and manipulate geometric constructions and models. These applications are commonly used in education for teaching geometry concepts, as well as by professionals in fields such as architecture and engineering. Here is a list of some popular interactive geometry software: 1. **GeoGebra** - A dynamic mathematics software that combines geometry, algebra, spreadsheets, graphing, statistics, and calculus.

A spherical octahedron is a polyhedral shape that can be inscribed within a sphere. It consists of eight equilateral triangular faces, twelve edges, and six vertices. The concept of great circles arises from spherical geometry, where a great circle is the largest possible circle that can be drawn on a sphere. Great circles are the spherical equivalent of straight lines in plane geometry.

The Adams hemisphere-in-a-square projection is a map projection used for representing the spherical surface of the Earth on a flat surface, specifically designed to preserve the relationships and proportions of areas. This projection is characterized by its ability to contain a hemisphere within a square boundary, which makes it useful for visualizations that require compact representation of large areas. In the Adams projection, the hemisphere is represented in such a way that the edges of the square remain straight, while the curvature of the Earth is taken into account.

The Baily–Borel compactification is a method used in the field of algebraic geometry and arithmetic geometry to compactify certain types of locally symmetric spaces, particularly those associated with Hermitian symmetric domains. It is named after the mathematicians William Baily and Armand Borel, who introduced the concept. ### Context and Motivation In many situations, particularly in number theory and the theory of modular forms, one deals with spaces that are not compact.

In topology, a **signature** often refers to the collection of topological invariants that characterize a particular topological space. More formally, it is a way to uniquely classify or describe a topological space up to homeomorphism (a continuous deformation of the space).

A **surface bundle** is a specific type of fiber bundle in the field of topology and differential geometry. In general, a fiber bundle consists of three main components: a total space \(E\), a base space \(B\), and a fiber \(F\) that is associated with each point in the base space.

Direct Linear Transformation (DLT) is a mathematical approach commonly used in computer vision and photogrammetry for establishing a correspondence between two sets of points. Specifically, it is used to compute a transformation matrix that maps points from one coordinate space to another in a linear manner. DLT is particularly useful for tasks such as camera calibration, image rectification, and 3D reconstruction.

3D pose estimation refers to the process of determining the spatial configuration of an object or a person in three-dimensional space. This typically involves estimating the 3D coordinates of key points (joints or landmarks) on the object or body being analyzed, which can then be used to understand its orientation, position, and movement.

Triangulation in computer vision refers to the method of determining the position of a point in 3D space by using the geometric principles derived from two or more observations of that point from different camera viewpoints. It is a fundamental technique used in various applications such as 3D reconstruction, camera calibration, and depth estimation. ### How Triangulation Works 1. **Multiple Camera Views**: Triangulation typically uses two or more cameras capturing images of the same scene from different angles.

In computer vision, the **fundamental matrix** is a key concept used in the context of stereo vision and 3D reconstruction. It is a \(3 \times 3\) matrix that captures the intrinsic geometric relationships between two views (images) of the same scene taken from different viewpoints. ### Key Points about the Fundamental Matrix: 1. **Epipolar Geometry**: The fundamental matrix encapsulates the epipolar geometry between two camera views.

The Laguerre formula, commonly referred to in the context of numerical methods, is associated with the Laguerre's method for finding roots of polynomial equations.

The Bevan Point is a concept in the field of economics and public policy, particularly in relation to healthcare. It is named after Aneurin Bevan, the British politician who was the Minister of Health and a key architect of the National Health Service (NHS) in the UK. The term typically refers to the principles or ideals associated with Bevan's vision for a fair and equitable healthcare system.