John Horton Conway

John Horton Conway (1937–2020) was a renowned British mathematician known for his work in various areas of mathematics, including combinatorial game theory, number theory, and coding theory. He is perhaps best known for inventing the "Game of Life," a cellular automaton that simulates the evolution of cellular patterns based on simple rules. The Game of Life has fascinated mathematicians and computer scientists alike, serving as an example of how complex behaviors can arise from simple rules.

The term "kisrhombille" refers to a specific geometric structure or a type of polyhedron in the family of Archimedean solids. The kisrhombille, also known as the "kisarhombille" or "kisarhombic dodecahedron," is comprised of hexagons and triangles.

A kisrhombille is a type of geometric structure that consists of a tessellation using rhombuses, specifically created by subdividing space with rhombus-like shapes. When referring to "4-5 kisrhombille," it appears to denote a specific arrangement or configuration of these kisrhombille tiles, typically categorized by the angles or relationships among the rhombuses involved.

The ATLAS of Finite Groups is a comprehensive reference work that provides detailed information on the finite simple groups and their characteristics. Published in 1986 by Daniel G. Higman, John Conway, and Robert W. Curtis, the ATLAS is significant in the field of group theory, particularly in the classification of finite groups.

The Alexander polynomial is an important invariant in the field of knot theory, which studies the properties of knots and links in three-dimensional space. It provides a way to distinguish between different knots and links. ### Definition For a given knot or link, the Alexander polynomial is constructed using a presentation of the knot or link's fundamental group. Specifically, it is derived from the first homology group of the knot complement, which can be computed using a Seifert surface.

The "Angel problem," also known as the "angel's problem," is a combinatorial game theory problem that involves two players: an angel and a demon. The game is played on an infinite grid or a finite board, where players take turns making moves. The angel can move any number of spaces in one direction (horizontally or vertically), while the demon can move one space in any direction.

**Architectonic tessellation** and **catoptric tessellation** are terms related to specific types of geometric patterns or arrangements, though they might not be widely recognized in all fields of study. Let's break these down: 1. **Architectonic Tessellation**: - This refers to a type of tessellation that is inspired by architectural forms and structures. It often involves the arrangement of shapes that can suggest elements of architecture, such as walls, roofs, or other building components.

Conway's 99-graph problem is a well-known problem in the field of graph theory proposed by the mathematician John Horton Conway. The problem asks whether it is possible to find a connected graph on 99 vertices in which every vertex has an even degree. In graph theory, a fundamental result is that a graph can only be Eulerian (i.e., it contains an Eulerian circuit that visits every edge exactly once) if every vertex has an even degree.

Conway's Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state without further input from human players. The game simulates the life and death of cells on an infinite grid based on a simple set of rules.

Conway's Soldiers is a mathematical game or problem proposed by mathematician John Horton Conway. The game involves a grid (often conceptualized as an infinite checkerboard) where a player can place "soldiers" on the squares of the board. The rules for the placement of soldiers are as follows: 1. Soldiers can be placed only in the rows numbered 0 (the bottom row) and 1, as well as additional rows above these (e.g.

Conway algebra refers to a mathematical framework developed by the British mathematician John Horton Conway. It is closely associated with the structure known as the "Conway group," which is part of a broader study of symmetries in higher-dimensional spaces. One of the most notable aspects of Conway's work is his exploration of algebraic systems that connect to geometrical and combinatorial structures.

The Conway base 13 function is a part of a broader family of base-n functions introduced by mathematician John Horton Conway. The most widely recognized version of the function is often referred to in the context of a notation for representing numbers in sequences or functions. In Conway's system, numbers are represented as tuples, and the behavior of the functions can be somewhat complex because they define values in a non-standard numeral system that allows for certain properties, such as self-similarity and recursive relationships.

Conway chained arrow notation is a notation developed by mathematician John Horton Conway to express very large numbers. It is a way to define numbers that grow extremely quickly, far beyond what can be expressed using conventional notation like exponentiation or even iterative exponentiation. The notation uses a series of arrows to signify operations that extend far beyond exponentiation.

The Conway Circle Theorem, developed by mathematician John Horton Conway, is a result in geometry related to circle packing and the configuration of circles tangent to each other. Specifically, it deals with the arrangement of tangent circles and their radii.

The Conway criterion is a mathematical concept used to determine whether a set of integers can be represented as sums of quadratic residues. It is particularly relevant in number theory and has applications in problems related to quadratic forms and modular arithmetic.

The Conway groups are a series of finite groups that arise in the study of symmetry and group theory, particularly associated with the mathematical work of John Horton Conway.

The Conway group \( Co_1 \) is one of the five Conway groups, which are a class of sporadic simple groups named after mathematician John Horton Conway. Specifically, \( Co_1 \) is the largest of these groups and is denoted as the first of the Conway groups.

The Conway group \( Co_2 \) is one of the sporadic simple groups in group theory, which is a branch of abstract algebra. Specifically, it is one of the 26 sporadic groups that do not fit into any of the infinite families of simple groups.

The Conway group \( Co_3 \) is one of the sporadic simple groups in group theory, which are finite groups that do not fit into the standard classifications of groups like cyclic, abelian, or simple groups derived from groups of matrices or other well-known constructions.

The Conway knot is a specific type of knot in the field of knot theory, which is a branch of topology. It is named after mathematician John Horton Conway, who introduced it in 1967. The Conway knot is notable for being a non-trivial knot, which means it cannot be untangled into a simple loop without cutting the rope or string.

Conway notation is a system used in knot theory to represent knots and links. It was introduced by mathematician John Horton Conway in the 1960s. The notation provides a way to describe the structure of a knot through a sequence of symbols that represent crossings and their order. In Conway notation, the basic idea is to represent a knot using a sequence of letters and numbers that correspond to the crossings that occur when the knot is drawn on a plane.

Conway polyhedron notation (CPN) is a system devised by mathematician and crystallographer Sir Roger Penrose to succinctly describe the three-dimensional shapes (polyhedra) that can be formed by truncating the vertices of a polyhedron. It utilizes a series of letters and symbols to represent the faces, edges, and vertices of these geometric figures, serving as a shorthand that can capture the essential structure of a polyhedron in a compact form.

The Conway polynomial, often denoted as \( C_n(x) \), is a specific polynomial that arises in the context of finite fields, particularly in relation to the construction of finite fields and the study of irreducible polynomials over finite fields.

The Conway puzzle often refers to the game "Conway's Game of Life," which is a cellular automaton devised by mathematician John Horton Conway in 1970. It is not a puzzle in the traditional sense but rather a mathematical simulation involving a grid of cells that can live, die, or multiply based on a set of rules. In the Game of Life, each cell in an infinite grid can be in one of two states: "alive" or "dead.

The Conway sphere is a geometric concept associated with the work of mathematician John Horton Conway, particularly in the field of topology and mathematics related to polyhedra and polynomial equations. Specifically, it often refers to a specific model or representation used in the analysis of certain problems in topology. In some contexts, the Conway sphere can be seen as a way to visualize and represent mappings or transformations within a three-dimensional space, often focusing on how certain properties change under specific constraints.

Conway triangle notation is a method introduced by mathematician John Horton Conway for representing ordinal numbers, particularly transfinite ordinals, in a compact and structured way. This notation is an extension of his earlier work with `surreal numbers` and the `Conway chained notation` for ordinals. In Conway triangle notation, ordinals are represented within a triangular array, where each entry corresponds to a specific ordinal.

The Doomsday rule is a mental algorithm devised by mathematician John Horton Conway to determine the day of the week for any given date. The method works based on the concept of "Doomsday," which refers to a specific day of the week that certain dates within a year always fall on.

The Free Will Theorem is a concept arising from the intersection of quantum physics and philosophy, formulated by physicists John Conway and Simon Kochen in 2006. The theorem explores the implications of quantum mechanics on the notion of free will and determinism.

Hackenbush is a combinatorial game that involves two players who take turns removing edges from a graph. The game is typically played on a connected graph with vertices and edges, where edges are colored, often in two colors representing the two players, or one color for a player and another for the graph itself. Here’s how the game works: 1. **Initial Setup**: The game starts with a graph drawn on paper with vertices connected by edges.

Holyhedron is a term that refers to a fictional polyhedron, often related to discussions in spirituality, philosophy, or alternative belief systems. It's not a standard geometric term and doesn't have a widely recognized definition in mathematics. Nonetheless, it may be used in specific contexts, such as art, literature, or certain metaphysical practices, to symbolize harmony, balance, or a connection to the divine.

The notation "II25,1" is not immediately recognizable as it does not correspond to a commonly known concept or term in popular subjects like mathematics, science, literature, or coding. However, if we break it down: - "II" could stand for the Roman numeral for 2, or it might denote a set of items, categories, or sections.

Icosian refers to a type of mathematical problem or puzzle related to a specific graph known as the icosahedron. The term is often associated with the Icosian game, which involves finding a Hamiltonian cycle in the graph representing the vertices and edges of an icosahedron. In graph theory, a Hamiltonian cycle is a cycle that visits every vertex exactly once and returns to the starting vertex.

Kisrhombille, also known as the kisrhombic dodecahedron, is a type of geometric structure classified as a polyhedron. Specifically, it belongs to a family of Archimedean solids, which are highly symmetrical, convex polyhedra composed of two or more types of regular polygons.

John Horton Conway was a distinguished mathematician known for his work in various fields, including combinatorial game theory, geometry, and number theory. Several concepts, theorems, and objects in mathematics and related fields have been named after him. Here is a list of some noteworthy items named after John Horton Conway: 1. **Conway's Game of Life**: A cellular automaton devised by Conway, which simulates the evolution of patterns based on simple rules.

The Look-and-say sequence is a sequence of numbers where each term is generated from the previous term by describing its consecutive digits. The process involves "reading" the digits of the previous term and counting the number of digits in groups, then forming the next term based on that count. Here's how it works: 1. Start with an initial term, usually "1".

The term "Mathieu groupoid" might not be widely recognized in the same way as Mathieu groups, which are a family of highly symmetric groups that play an important role in various areas of mathematics, particularly in group theory, combinatorics, and algebraic geometry. Mathieu groups are finite groups that arise from the permutation of sets and are particularly known for their properties related to symmetry and error-correcting codes.

Monstrous moonshine is a term used in mathematics, specifically in the field of modular forms and algebraic geometry. It refers to a surprising and deep connection between the monster group, which is the largest of the sporadic finite simple groups, and modular functions. The term was introduced by mathematician Richard Borcherds in the context of his work on the representation theory of the monster group.

"On Numbers and Games" is a book written by mathematician John H. Conway, published in 2001. The work delves into the field of combinatorial game theory, exploring how games can be analyzed mathematically. Conway introduces concepts such as surreal numbers and various types of games, including impartial games (where the allowed moves depend only on the state of the game and not on which player's turn it is) and partisan games (where the allowed moves depend on whose turn it is).

Orbifold notation is a way of describing the local structure of certain types of spaces that appear in the study of algebraic geometry, topology, and string theory, particularly in the context of singular spaces. The term "orbifold" itself refers to a generalization of manifolds that allows for certain types of singularities.

Phutball is a tabletop game that combines elements of soccer (football) and strategy board games. It is played on a board that represents a field, typically divided into a grid, on which players move pieces that represent their soccer players. The objective is to score goals by maneuvering these pieces effectively, often using strategic planning and tactical decisions.

Sprouts is a two-player pencil-and-paper game that involves strategy and spatial reasoning. The game begins with a certain number of "dots" (or "spots") drawn on a sheet of paper, and players take turns connecting these dots with lines. Each line must be drawn under specific rules: 1. A line must connect two dots (or a dot to itself). 2. A line cannot cross any existing lines. 3. Each dot can have a maximum of three lines connected to it.

Surreal numbers are a class of numbers that extend the real numbers and include infinitesimal and infinite values. They were introduced by mathematician John Horton Conway in the early 1970s. The surreal numbers can be constructed in a specific way, involving the use of sets.

In mathematics, a "tangle" generally refers to a specific type of structure that arises in the study of low-dimensional topology, particularly in the theory of links and knots. The concept of tangles can be classified in various ways, but it is often associated with a division of 3-dimensional space into regions contoured by strands, which may represent parts of a knot or link.

Topswops is a trading card game and collectible franchise that focuses on swapping and collecting various cards, often featuring different themes such as sports, characters, or other collectibles. Players typically collect cards, trade with others, and may participate in games or competitive activities using their cards. The specific details, gameplay mechanics, and themes can vary depending on the version or series of Topswops being referenced.

"Winning Ways for Your Mathematical Plays" is a comprehensive book on combinatorial game theory written by Elwyn Berlekamp, John H. Conway, and Richard K. Guy. First published in 1982, the book explores the mathematical principles underlying various two-player games, providing insights into strategy, winning tactics, and the mathematical framework that governs these games. The authors analyze a wide range of games, from traditional board games like Nim and chess to more abstract combinatorial games.