A foot-pound (often abbreviated as ft-lb or ft⋅lb) is a unit of energy or work in the imperial system of measurement. It is defined as the amount of energy transferred when a force of one pound-force (lbf) acts through a distance of one foot in the direction of the force.

A square foot is a unit of area measurement commonly used in the United States and Canada. It represents a square that is one foot long on each side. To put it mathematically, one square foot is equal to 1 foot x 1 foot, which equals 1 square foot or \( 1 \, \text{ft}^2 \).

A survey township is a term used primarily in the context of land surveying and property management in the United States, particularly in the context of the Public Land Survey System (PLSS). The PLSS is a method used to divide and describe land in the United States, particularly in areas that were not originally part of the original thirteen colonies.

Cicero is a traditional unit of measurement in typography, primarily used in the context of typesetting. It refers to a unit that is equal to 12 points in the modern typographic point system. The term "cicero" historically originated from the size of the body of type used in European printing, particularly for typefaces that were designed for the Latin alphabet. In practical terms, a cicero is generally considered to be equivalent to approximately 4.5 millimeters or 0.

Katal is a unit of measurement used in chemistry to quantify the amount of a substance that can catalyze a specific reaction. Specifically, one katal is defined as the amount of catalyst that will convert one mole of substrate per second under specified conditions. The term is often used in the context of enzyme kinetics, where enzymes act as biological catalysts to speed up biochemical reactions.

The poise is a unit of dynamic viscosity in the centimeter-gram-second (CGS) system of units. It is used to measure a fluid's resistance to flow. One poise is defined as the viscosity of a fluid that exerts a shear stress of one dyne per square centimeter when subjected to a shear rate of one reciprocal second.

Mathematical typefaces refer to specific styles and designs of fonts and symbols that are used for typesetting mathematical notation. These typefaces are designed to meet the unique requirements of mathematical expressions, which often include a wide variety of symbols, characters, and formatting styles that are not typically found in standard text typography.

A heterogeneous random walk in one dimension is a type of stochastic process that describes a particle moving along a line where the step sizes and/or probabilities of moving left or right can vary based on certain conditions or locations. This contrasts with a homogeneous random walk, where each step is taken with the same probability and magnitude. In a one-dimensional heterogeneous random walk, several key features may characterize the movement: 1. **Variable Step Sizes**: The distance the walker takes in each step may vary.

Abuse of notation refers to the intentional use of a symbol or notation in a way that may not strictly adhere to its formal definition but is commonly understood within a specific context or mathematical community. This practice can facilitate communication and streamline expressions, although it may introduce ambiguity or confusion if the context is not clearly established.

Point process notation is a mathematical framework used to describe random processes where events occur at particular points in time or space. Point processes are often employed in various fields, including probability theory, statistics, spatial analysis, and telecommunications, among others. They provide a way to model and analyze the occurrence of events that are discrete and often random.

Mathematical cognition researchers study how individuals understand, learn, and reason about mathematical concepts and operations. This interdisciplinary field combines insights from psychology, cognitive science, education, neuroscience, and mathematics to investigate various aspects of mathematical thinking and performance. Key areas of focus in mathematical cognition research include: 1. **Development of Mathematical Skills**: Understanding how children and adults acquire mathematical abilities, from basic counting to advanced problem solving.

Musical notation is a system used to visually represent music through the use of symbols and signs. This allows musicians to read and interpret musical compositions, indicating elements such as pitch, rhythm, dynamics, and articulations. The primary components of musical notation include: 1. **Staff**: A set of horizontal lines and spaces used to indicate different pitches. The most common staff has five lines.

In calculus, differentiation is a process that measures how a function changes as its input changes. There are several common notations used to denote differentiation: 1. **Leibniz Notation**: This is one of the most commonly used notations.

The Schläfli symbol is a notation that describes regular polytopes and tessellations in geometry. It represents the shapes based on their vertices, edges, and faces. The symbol typically consists of a sequence of numbers that denote the following: 1. In the case of polygons (2D shapes), the Schläfli symbol is written as `{n}`, where \(n\) is the number of sides (or vertices) of the polygon.

A software calculator is a computer program or application designed to perform mathematical calculations. It can mimic the functions of a traditional physical calculator but often includes additional features and capabilities. Software calculators can range from simple applications that perform basic arithmetic (addition, subtraction, multiplication, division) to more complex tools that can handle advanced mathematics, scientific calculations, statistical analysis, and graphical plotting. ### Types of Software Calculators: 1. **Basic Calculators**: Perform simple arithmetic operations.

The Polymath Project is an initiative aimed at solving mathematical problems through collaborative efforts, primarily using the internet and online platforms. It began in 2009 when mathematician Timothy Gowers initiated a blog post inviting mathematicians and enthusiasts to collectively tackle a specific mathematical problem, known as the "density of prime numbers in progressions.

"Articles containing proofs" typically refers to scholarly or academic articles that present formal proof for theorems or propositions in various fields, such as mathematics, computer science, logic, and statistics. These articles usually include a detailed explanation of the problem being addressed, the methodology used, and step-by-step reasoning leading to the conclusion.

Computer-assisted proofs are proofs in mathematics or formal logic that involve the use of computers to aid in the verification of the proof itself or to help find the proof. These proofs typically combine traditional mathematical reasoning with computational methods to handle large computations or complex combinatorial arguments that would be impractical or impossible to work through by hand. Key aspects of computer-assisted proofs include: 1. **Verification**: A computer can verify steps in a proof that are computationally intense.