Subject:
All Disciplines Arts & Humanities Biology & Life Sciences Business & Economics Chemistry & Materials Science Computer Science & Mathematics Engineering Environmental & Earth Sciences Medicine & Pharmacology Physical Sciences Public Health & Healthcare Social Sciences
Sort:
Hottest Latest Alphabetical (A-Z) Alphabetical (Z-A)
Type:
All Topic Review Biography
Topic Review
Complement (Set Theory)
In set theory, the complement of a set A, often denoted by Ac (or A′), is the set of elements not in A. When all sets in the universe, i.e. all sets under consideration, are considered to be members of a given set U, the absolute complement of A is the set of elements in U that are not in A. The relative complement of A with respect to a set B, also termed the set difference of B and A, written [math]\displaystyle{ B \setminus A, }[/math] is the set of elements in B that are not in A.
  • 12.2K
  • 28 Nov 2022
Topic Review
Fresh Fruit Supply Chain Optimization
The fresh fruit chain has been recognized as a very important and strategic part of the economic development of many countries. The planning framework for production and distribution is highly complex as a result. Mathematical models have been developed over the decades to deal with this complexity. This review focuses on the recent progress in mathematically based decision making to account for uncertainties in the fresh fruit supply chain
  • 4.3K
  • 27 Jul 2021
Topic Review
Two-Dimensional Space
Two-dimensional space (also known as 2D space, 2-space, or bi-dimensional space) is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point). The set [math]\displaystyle{ \mathbb{R}^2 }[/math] of pairs of real numbers with appropriate structure often serves as the canonical example of a two-dimensional Euclidean space. For a generalization of the concept, see dimension. Two-dimensional space can be seen as a projection of the physical universe onto a plane. Usually, it is thought of as a Euclidean space and the two dimensions are called length and width.
  • 3.7K
  • 28 Nov 2022
Topic Review
Incircle and Excircles of a Triangle
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides. The center of the incircle, called the incenter, can be found as the intersection of the three internal angle bisectors. The center of an excircle is the intersection of the internal bisector of one angle (at vertex [math]\displaystyle{ A }[/math], for example) and the external bisectors of the other two. The center of this excircle is called the excenter relative to the vertex [math]\displaystyle{ A }[/math], or the excenter of [math]\displaystyle{ A }[/math]. Because the internal bisector of an angle is perpendicular to its external bisector, it follows that the center of the incircle together with the three excircle centers form an orthocentric system.:p. 182 All regular polygons have incircles tangent to all sides, but not all polygons do; those that do are tangential polygons. 
  • 2.2K
  • 11 Nov 2022
Topic Review
Areas of Mathematics
Mathematics encompasses a growing variety and depth of subjects over its history, and comprehension of it requires a system to categorize and organize these various subjects into more general areas of mathematics. A number of different classification schemes have arisen, and though they share some similarities, there are differences due in part to the different purposes they serve. A traditional division of mathematics is into pure mathematics; mathematics studied for its intrinsic interest, and applied mathematics; the mathematics that can be directly applied to real-world problems. This division is not always clear and many subjects have been developed as pure mathematics to find unexpected applications later on. Broad divisions, such as discrete mathematics, computational mathematics and so on have emerged more recently. An ideal system of classification permits adding new areas into the organization of previous knowledge, and fitting surprising discoveries and unexpected interactions into the outline. For example, the Langlands program has found unexpected connections between areas previously thought unconnected, at least Galois groups, Riemann surfaces and number theory.
  • 2.2K
  • 29 Sep 2022
Biography
James Harris Simons
James Harris "Jim" Simons (/ˈsaɪmənz/; born April 25, 1938) is an American mathematician, billionaire hedge fund manager, and philanthropist. He is known as a quantitative investor and in 1982 founded Renaissance Technologies, a private hedge fund based in New York City . Although Simons retired from the fund in 2009, he remains its non-executive chairman and adviser.[1] He is also known for
  • 2.0K
  • 15 Nov 2022
Topic Review
μ-Recursive Function
In mathematical logic and computer science, the general recursive functions (often shortened to recursive functions) or μ-recursive functions are a class of partial functions from natural numbers to natural numbers that are "computable" in an intuitive sense. In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines(this is one of the theorems that supports the Church–Turing thesis). The μ-recursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that of the primitive recursive functions. However, not every μ-recursive function is a primitive recursive function—the most famous example is the Ackermann function. Other equivalent classes of functions are the λ-recursive functions and the functions that can be computed by Markov algorithms. The subset of all total recursive functions with values in {0,1} is known in computational complexity theory as the complexity class R.
  • 1.8K
  • 01 Dec 2022
Topic Review
Sine
In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse). For an angle [math]\displaystyle{ x }[/math], the sine function is denoted simply as [math]\displaystyle{ \sin x }[/math]. More generally, the definition of sine (and other trigonometric functions) can be extended to any real value in terms of the length of a certain line segment in a unit circle. More modern definitions express the sine as an infinite series, or as the solution of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. The sine function is commonly used to model periodic phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations throughout the year. The function sine can be traced to the jyā and koṭi-jyā functions used in Gupta period Indian astronomy (Aryabhatiya, Surya Siddhanta), via translation from Sanskrit to Arabic, and then from Arabic to Latin. The word "sine" (Latin "sinus") comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, jya-ardha.
  • 1.7K
  • 11 Oct 2022
Topic Review Peer Reviewed
Mechanics and Mathematics in Ancient Greece
This entry presents an overview on how mechanics in Greece was linked to geometry. In ancient Greece, mechanics was about lifting heavy bodies, and mathematics almost coincided with geometry. Mathematics interconnected with mechanics at least from the 5th century BCE and became dominant in the Hellenistic period. The contributions by thinkers such as Aristotle, Euclid, and Archytas on fundamental problems such as that of the lever are sketched. This entry can be the starting point for a deeper investigation on the connections of the two disciplines through the ages until our present day.
  • 1.6K
  • 13 Apr 2022
Topic Review
Euler–Mascheroni Constant
The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma (γ). It is defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by [math]\displaystyle{ \log: }[/math] Here, [math]\displaystyle{ \lfloor x\rfloor }[/math] represents the floor function. The numerical value of the Euler–Mascheroni constant, to 50 decimal places, is: 0.57721566490153286060651209008240243104215933593992... 
  • 1.6K
  • 02 Dec 2022
  • Page
  • of
  • 8
Featured Entry Collections
>>

Featured Books

>>
Encyclopedia of Social Sciences
Encyclopedia of COVID-19
Encyclopedia of Fungi
Encyclopedia of Digital Society, Industry 5.0 and Smart City
Feedback