Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions from these.Although many of Euclid's results had been stated earlier, Euclid was …

Non Euclid geometry is a part of non Euclid mathematics. It discusses the hyperbolic and spherical figures. It is also known as hyperbolic geometry. The figures of non-Euclidean geometry do not satisfy Euclid's parallel postulate. It is the main reason for the existence of non-Euclidean geometry. In this article, we are going to discuss non ...

In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points.It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance.These names come from the ancient Greek mathematicians Euclid and Pythagoras, …

Alternatively, one can define a conic section purely in terms of plane geometry: it is the locus of all points P whose distance to a fixed point F (called the focus) is a constant multiple (called the eccentricity e) of the distance from P to a fixed line L (called the directrix).For 0 < e < 1 we obtain an ellipse, for e = 1 a parabola, and for e > 1 a hyperbola.

Given parallel straight lines l and m in Euclidean space, the following properties are equivalent: . Every point on line m is located at exactly the same (minimum) distance from line l (equidistant lines).; Line m is in the same plane as line l but does not intersect l (recall that lines extend to infinity in either direction).; When lines m and l are both intersected by a third straight line ...

The Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry ...

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History. Differential equations first came into existence with the invention of calculus by Newton and Leibniz.In Chapter 2 of his 1671 work Methodus fluxionum et Serierum Infinitarum, Isaac Newton listed three kinds of differential equations: = = (,) + = In all these cases, y is an unknown function of x (or of x 1 and x 2), and f is a given function. He solves these examples and others …

Euclid (/ ˈ juː k l ɪ d /; Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new ...

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.. The fundamental objects of study in algebraic geometry are algebraic varieties, which are …