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Diagonal
A diagonal is a line segment joining two non-adjacent vertices of a polygon or polyhedron; a polygon with n vertices has n(n−3)/2 diagonals, and a triangle has none.
Diagonal lemma
The diagonal lemma, also called the diagonalization or fixed-point lemma, is a mathematical logic theorem giving each arithmetic formula a sentence describing itself, key to Gödel's incompleteness theorems.
Diagonal matrix
A diagonal matrix is a square matrix in which every entry off the main diagonal is zero, so arithmetic, powers, determinants, and inverses reduce to operations on the diagonal entries.
Diagonalizable matrix
A diagonalizable matrix, or nondefective matrix, is a square matrix similar to a diagonal matrix, meaning it has n linearly independent eigenvectors and acts as simple scaling in the eigenbasis.
Diagonalization (linear algebra)
Diagonalization is a linear algebra method rewriting a square matrix A as A = PDP⁻¹, with D diagonal of eigenvalues and P's columns eigenvectors, making powers and functions of A easy to compute.
Diagonals (2002)
Diagonals (2002) is Walter Joris's two-player pencil-and-paper abstract game on a 5x10 board: drop stones along diagonal lines of sight or turn enemy stones into walls; most stones wins.
Diagonals (ludii 1803)
Diagonals (ludii 1803) is a two-player abstract placement game on an 8x8 board: players drop stones, and completing a full diagonal scores its friendly stones; most points when the board fills wins.
Diagram
Diagram: a simplified drawing representing a machine, system, process, or idea to explain how it works, from Greek diágramma. Covers types (flowchart, Venn, tree), diagram versus chart selection, and the diagram's role in art theory and art history.
Diahann Carroll
Diahann Carroll (1935–2019), American actress and singer, star of NBC's Julia (1968–71), the first TV series led by an African-American woman in a non-domestic role; Tony winner for No Strings, Oscar nominee for Claudine, and Dynasty's Dominique Deveraux.
Dial H for Hero
Dial H for Hero is a DC Comics concept, the H-Dial rotary phone that turns its user into a random superhero for one hour. Created by Dave Wood and Jim Mooney in House of Mystery #156 (1966); dialers include Robby Reed, Chris King, Vicki Grant, Hero Cruz, and Miguel Montez.
Dial M for Murder
Dial M for Murder (1954) is Alfred Hitchcock's thriller adapted by Frederick Knott from his stage play, starring Ray Milland, Grace Kelly, and Robert Cummings; shot in 3-D, released mostly flat, grossing $6.1 million.
Dial-up Internet access
Dial-up Internet access is a way of connecting to the Internet over the telephone network with a modem, dominant from the early 1990s to the early 2000s.
Dialect
Dialect: a variety of a language differing in pronunciation, grammar, and vocabulary, tied to region or social group; covers the language-versus-dialect problem, dialectology history, assessment bias, and speech technology.
Dialect continuum
Dialect continuum: a chain of adjacent dialects in which neighboring varieties are mutually intelligible while the end varieties are not, seen in West Germanic, Romance, Slavic, and Arabic speech; standards and borders cut the chain.
Dialect levelling
Dialect levelling, or supralocalisation: erosion of local dialect features through contact, mobility, and accommodation, producing homogenized regional speech, koines, and reallocation, as documented in Tyneside, Corby, the Fens, and South East England.
Dialect levelling in Britain
Dialect levelling in Britain: reduction of differences between regional English varieties through geographical diffusion and accommodation, driven by socio-geographical mobility, producing larger city-oriented dialect regions.
Dialectic (διαλεκτική)
Dialectic (διαλεκτική, dialektike): the Greek art of philosophical dialogue by question and answer, from Socrates and Plato through Aristotle, the Stoics, and Hegel's three-moment method of determinate negation, later adapted by Marx.
Dialectica interpretation
The Dialectica interpretation, also called Gödel's functional interpretation or D-interpretation, is a proof interpretation reducing Heyting arithmetic to Gödel's quantifier-free System T, published by Kurt Gödel in 1958.
Dialectical behavior therapy
Dialectical behavior therapy (DBT), a cognitive-behavioral therapy developed by Marsha Linehan in the 1980s, treats chronically suicidal people with borderline personality disorder through individual therapy, skills training, phone coaching, and consultation teams.
Dialectical materialism
Dialectical materialism (diamat): the Marxist philosophy combining materialism with a dialectical view of reality as process and contradiction; term coined after Engels by Plekhanov or Dietzgen, codified by Engels, official Soviet philosophy under Stalin.
Dialectometry
Dialectometry, or quantitative dialectology, measures distances and similarities between dialects using statistical and computational methods. Founded by Jean Séguy (dialectométrie) and developed by Hans Goebl's Salzburg school, it uses aggregate analysis, edit distance, and mapping.
Dialetheism
Dialetheism is the view that some contradictions, called dialetheias, are both true and false, developed by Graham Priest and Richard Routley in the late 1970s.
Dialifos
Dialifos (dialifor, Torak, CAS 10311-84-9) is an obsolete organophosphate insecticide and acaricide, an acetylcholinesterase inhibitor with rat oral LD50 5-71 mg/kg; its JMPR ADI was withdrawn in 1982 and it is not EU-approved.
Dialium
Dialium L. is a pantropical genus of Fabaceae trees (subfamily Dialioideae), type species D. indum, with about 37 accepted species, indehiscent edible-pulped fruits (velvet tamarind, keranji), and centers of diversity in West-Central Africa and western Malesia.
Diallel analysis
Diallel analysis is a quantitative genetics method in which inbred lines are crossed in all pairwise combinations, partitioning progeny performance into general and specific combining ability effects.
Diallyl disulfide
Diallyl disulfide (DADS) is an organosulfur compound making up 17.5 to 35.6% of garlic oil, formed when allicin breaks down and giving garlic its odor.
Diallyl sulfide
Diallyl sulfide is an organic sulfide with a strong garlic odor, formed when crushed garlic's allicin decomposes, and a standard inhibitor of the enzyme CYP2E1.
Dialog (organization)
Dialog (organization), also Dialog Society, is an invitation-only secret society founded in 2006 by Peter Thiel and Auren Hoffman, holding off-the-record elite retreats; its membership grading system and 222-person 2026 retreat roster leaked in June 2026.
Diálogos
Diálogos, subtitled Artes, Letras, Ciencias humanas, was a Mexican cultural and literary magazine directed by Ramón Xirau, published from 1964 to 1985 and affiliated with El Colegio de México.
Dialogue
Dialogue: a conversation between two or more people and a literary form, from Greek dialegeisthai, to converse. Covers Socratic dialectic, dialogical logic of Lorenzen and Lorenz, dialogue games, and dialogue systems.