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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 mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. 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.
Decades later, his friend Leon Battista Alberti wrote De pictura (1435/1436), a treatise on proper methods of showing distance in painting based on Euclidean geometry. Alberti was also trained in the science of optics through the school of Padua and under the influence of Biagio Pelacani da Parma who studied Alhazen's Optics .
In the Greek deductive geometry exemplified by Euclid's Elements, distances were not represented as numbers but line segments of the same length, which were considered "equal". The notion of distance is inherent in the compass tool used to draw a circle, whose points all have the same distance from a common center point. The connection from the ...
Karl Menger was a young geometry professor at the University of Vienna and Arthur Cayley was a British mathematician who specialized in algebraic geometry. Menger extended Cayley's algebraic results to propose a new axiom of metric spaces using the concepts of distance geometry up to congruence equivalence, known as the Cayley–Menger determinant.
Distance geometry; Elliptic geometry; Enumerative geometry; Epipolar geometry; ... Modern geometry History of analytic geometry. History of the Cartesian coordinate ...
The same sense of distance is used in Euclidean geometry to define distance from a point to a line, distance from a point to a plane, or, more generally, perpendicular distance between affine subspaces. Even more generally, this idea can be used to define the distance between two subsets of a metric space.
Aristarchus's 3rd century BCE calculations on the relative sizes of, from left, the Sun, Earth and Moon, from a 10th-century CE Greek copy. On the Sizes and Distances (of the Sun and Moon) (Ancient Greek: Περὶ μεγεθῶν καὶ ἀποστημάτων [ἡλίου καὶ σελήνης], romanized: Perì megethôn kaì apostēmátōn [hēlíou kaì selḗnēs]) is widely accepted ...