Parametric design is a design methodology that utilizes algorithms and parameters to generate and manipulate geometries, structures, and forms. Instead of defining a design by fixed dimensions and shapes, parametric design focuses on a set of rules and parameters that can be altered to create variations or adapt the design based on specific requirements. Key features of parametric design include: 1. **Parameters and Variables**: Designers set parameters that can be adjusted to influence the design.
Michael D. Morley is a legal scholar and professor known for his expertise in administrative law, election law, and constitutional law in the United States. He has contributed significantly to the discourse on issues related to election administration and has published various articles and papers in the field.
The conjunction fallacy is a logical fallacy that occurs when people incorrectly believe that specific conditions are more probable than a single general one. This fallacy was famously illustrated in a study by psychologists Daniel Kahneman and Amos Tversky. In their experiments, participants were presented with a description of a person and then asked to evaluate the likelihood of different statements about that person.
Sundance Bilson-Thompson is an artist and researcher known for his work in the field of speculative design and art, often focusing on themes related to climate change, Indigenous perspectives, and future scenarios. He utilizes various media, including digital technology and installations, to explore the intersection of culture, technology, and the environment. Bilson-Thompson's work is notable for blending traditional knowledge with contemporary practices, and he often engages with Indigenous narratives to address modern challenges.
The Erasmus Smith's Professor of Mathematics is a prestigious academic position at Trinity College Dublin, the University of Dublin, Ireland. Established in 1752 through a bequest from Erasmus Smith, a wealthy merchant and philanthropist, the role is typically filled by a leading mathematician and involves both teaching and research responsibilities. The position is known for its contributions to mathematical sciences and its influence on mathematical education in Ireland.
In the context of mathematics, particularly in topology and related fields, a "maximal arc" typically refers to a segment or a subset of a space that cannot be extended further while maintaining certain properties—often related to continuity or connectedness. The term is often associated with the study of curves or paths in metric spaces or topological spaces.
A Schlegel diagram is a geometric representation of a polytope, which is a high-dimensional generalization of polygons and polyhedra. Specifically, it is a way to visualize a higher-dimensional object in lower dimensions, typically projecting a convex polytope into three-dimensional space. Essentially, a Schlegel diagram allows us to see the structure of a polytope by looking at a "shadow" of it, emphasizing its vertices and faces.
A translation plane is a concept used primarily in the field of geometry, particularly in projective geometry. It refers to a specific type of geometric structure characterized by the properties of translation. However, the term may have varied meanings depending on the context in which it's used. Here are two interpretations: 1. **In Projective Geometry**: A translation plane is a two-dimensional projective plane where the points can be translated (shifted) along a certain direction.
Methods of proof are techniques used in mathematics and logic to demonstrate the validity of mathematical statements, theorems, or propositions. There are several fundamental methods of proof, each with its own approach. Here are some of the most common methods: 1. **Direct Proof**: This method involves directly showing that a statement is true by using definitions, axioms, and previously established theorems. You start from known truths and use logical reasoning to arrive at the statement you want to prove.
Metalanguage is a language or set of terms used to describe, analyze, or discuss another language. This concept can apply in various fields, including linguistics, philosophy, and computer science. Here are some key points about metalanguage: 1. **Descriptive Function**: Metalanguage serves as a tool for talking about the elements, structure, and functions of a particular language (often referred to as the "object language").
The cross-ratio is a concept from projective geometry often used in various mathematical fields, including geometry and complex analysis.
The Fubini–Study metric is a Riemannian metric defined on complex projective space, specifically on the projective Hilbert space \( \mathbb{CP}^n \). It is often used in the context of quantum mechanics and quantum information theory as it provides a way to measure distances and angles between quantum states represented as rays in complex projective space.