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Distance geometry is the branch of mathematics concerned with characterizing and studying sets of points based only on given values of the distances between pairs of points. [1] [2] [3] More abstractly, it is the study of semimetric spaces and the isometric transformations between them. In this view, it can be considered as a subject within ...
Resolving sets for graphs were introduced independently by Slater (1975) and Harary & Melter (1976), while the concept of a resolving set and that of metric dimension were defined much earlier in the more general context of metric spaces by Blumenthal in his monograph Theory and Applications of Distance Geometry. Graphs are special examples of ...
Robin Hartshorne (1938–) – geometry, algebraic geometry; Phillip Griffiths (1938–) – algebraic geometry, differential geometry; Enrico Bombieri (1940–) – algebraic geometry; Robert Williams (1942–) Peter McMullen (1942–) Richard S. Hamilton (1943–2024) – differential geometry, Ricci flow, Poincaré conjecture; Mikhail Gromov ...
The distance is measured by a function called a metric or distance function. [1] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance.
Distance from the Earth to the Moon: S: Distance from the Earth to the Sun: ℓ: Radius of the Moon: s: Radius of the Sun: t: Radius of the Earth: D: Distance from the center of Earth to the vertex of Earth's shadow cone d: Radius of the Earth's shadow at the location of the Moon n: Ratio, d/ℓ (a directly observable quantity during a lunar ...
Many of these problems are easily solvable provided that other geometric transformations are allowed; for example, neusis construction can be used to solve the former two problems. In terms of algebra , a length is constructible if and only if it represents a constructible number , and an angle is constructible if and only if its cosine is a ...
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past.Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales.
Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century. [1]