Brahmagupta's formula may be seen as a formula in the half-lengths of the sides, but it also gives the area as a formula in the altitudes from the center to the sides, although if the quadrilateral does not contain the center, the altitude to the longest side must be taken as negative. In the case of non-cyclic quadrilaterals, Brahmagupta's formula can be extended by considering the measures of two opposite angles of the quadrilateral:. It follows from this fact that the area of a cyclic quadrilateral is the maximum possible area for any quadrilateral with the given side lengths.
This more general formula is sometimes known as Bretschneider's formula , but according to MathWorld is apparently due to Coolidge in this form, Bretschneider's expression having been. The relationship between the general and extended form of Brahmagupta's formula is similar to how the law of cosines extends the Pythagorean theorem.
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How to pronounce brahmagupta's formula? Alex US English. Daniel British. Karen Australian. Veena Indian. How to say brahmagupta's formula in sign language? Numerology Chaldean Numerology The numerical value of brahmagupta's formula in Chaldean Numerology is: 8 Pythagorean Numerology The numerical value of brahmagupta's formula in Pythagorean Numerology is: 6. In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.
This contrasts with synthetic geometry. Analytic geometry is widely used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight.
It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane two dimensions and Euclidean space three dimensions. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations.
That the algebra of the real numbers can be employed t. Distance geometry is the characterization and study of sets of points based only on given values of the distances between member pairs.
In this view, it can be considered as a subject within general topology. The modern theory began in 19th century with work by Authur Cayley, followed by more extensive developments in the 20th century by Karl Menger and others. Distance geometry problems arise whenever one needs to infer the shape of a configuration of points from the distances between them, such as in biology, sensor network, surveying, navigation, cartography, and physics.
Introduction and definitions The concepts of distance geometry will first be explained by describing two particular problems. Problem of hyperbolic navigation First problem: hyperbolic navigation Consider three ground radio. An eponym is a person real or fictitious from whom something is said to take its name. The word is back-formed from "eponymous", from the Greek "eponymos" meaning "giving name". The red and blue lines on this graph have the same slope gradient ; the red and green lines have the same y-intercept cross the y-axis at the same place.
A representation of one line segment. The notion of line or straight line was introduced by ancient mathematicians to represent straight objects i. Lines are an idealization of such objects. Until the 17th century, lines were defined as the "[…] first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width.
In geometry, a Heronian triangle is a triangle that has side lengths and area that are all integers. The term is sometimes applied more widely to triangles whose sides and area are all rational numbers, since one can rescale the sides by a common multiple to obtain a triangle that is Heronian in the above sense.
Properties Any right-angled triangle whose sidelengths are a Pythagorean triple is a Heronian triangle, as the side lengths of such a triangle are integers, and its area is also an integer, being half of the product of the two shorter sides of the triangle, at least one of which must be even. An example of a Heronian triangle which is not right-angled is the isosceles triangle with sidelengths 5, 5, and 6, whose area is This triangle is obtained by joining two copies of the right-angled triangle with sides 3, 4, and 5 along the sides of length 4.
This approach works in ge. Timeline of Indian Innovation encompasses key events in the history of technology in the subcontinent historically referred to as India and the modern Indian state. The entries in this timeline fall into the following categories: architecture, astronomy, cartography, metallurgy, logic, mathematics, metrology, mineralogy, automobile engineering, information technology, communications, space and polar technology. This timeline examines scientific and medical discoveries, products and technologies introduced by various peoples of India.
Inventions are regarded as technological firsts developed in India, and as such does not include foreign technologies which India acquired through contact. An IVC site in Mehrgarh indicates that this form of dentistry involved curing tooth related disorders with bow drills operated, perhaps, by skilled bead crafters. Joseph Louis Lagrange proved that, as long as n is not a perfect square, Pell's equation has infinitely many distinct integer solutions.
This equation was first studied extensively in India, starting with Brahmagupta, who developed the chakravala method to solve Pell's equation and other quadratic indeterminate equations in his Brahma Sphuta Siddhanta in , about a thousa. A representation of a three-dimensional Cartesian coordinate system with the x-axis pointing towards the observer.
Three-dimensional space also: 3-space or, rarely, tri-dimensional space is a geometric setting in which three values called parameters are required to determine the position of an element i. This is the informal meaning of the term dimension. In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. This serves as a three-parameter model of the physical universe that is, the spatial part, without considering time in which all known matter exists. However, this space is only one example of a large variety of spaces in three dimensions called 3-manifolds.
In this classical example, when the three values refer to measurements in different directions coordinates , any three directions can be chosen, p. For most authors, an algebraic equation is univariate, which means that it involves only one variable. On the other hand, a polynomial equation may involve several variables, in which case it is called multivariate and the term polynomial equation is usually preferred to algebraic equation.
Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression that can be found using a finite number of.
This is a list of number theory topics, by Wikipedia page. Creating a regular hexagon with a straightedge and compass Straightedge and compass construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass. The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it.
The compass is assumed to "collapse" when lifted from the page, so may not be directly used to transfer distances. This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with collapsing compass; see compass equivalence theorem. More formally, the only permissible constructions are those granted by Euclid's first three postulates.
It turns out to be the case that every point constructible using straightedge and compass may also be constructed using compass alone. The ancient Greek mathematicians first conceived straightedge and compass constructions, and. In elementary mathematics, a variable is a symbol, commonly a single letter, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown. Making algebraic computations with variables as if they were explicit numbers allows one to solve a range of problems in a single computation.
A typical example is the quadratic formula, which allows one to solve every quadratic equation by simply substituting the numeric values of the coefficients of the given equation for the variables that represent them. The concept of a variable is also fundamental in calculus. The term "variable" comes from the fact that, when the argument also called the "variable of the function" varies, then the value varies accordingly.
Pythagorean theoremThe sum of the areas of the two squares on the legs a and b equals the area of the square on the hypotenuse c. In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse the side opposite the right angle is equal to the sum of the squares of the other two sides.
Although it is often argued that knowledge of the theorem predates him, the theorem is named after the ancient Greek mathematician Pythagoras c. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment. The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal and large en.
Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics Rhind Mathematical Papyrus and Babylonian mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. During the Middle Ages, the study of trigonometry continued in Islamic mathematics, hence it was adopted as a separate subject in the Latin West beginning in the Renaissance with Regiomontanus. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics Isaac Newton and James Stirling and reaching its modern form with Leonhard Euler Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects.
However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra in fact, every proof must use the completeness of the real numbers, which is not an algebraic property.
This article describes the history of the theory of equations, called here "algebra", from the origins to the emergence of algebra as a separate area of mathematics. The treatise provided. A timeline of numerals and arithmetic Before BC c. Diagram for reference. Maley, F. Miller; Robbins, David P.
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Advances in Applied Mathematics. Brahmagupta's formula topic In Euclidean geometry, Brahmagupta's formula is used to find the area of any cyclic quadrilateral one that can be inscribed in a circle given the lengths of the sides. Brahmagupta topic Brahmagupta born c. However, he lived and worked there for a good part of his li Folders related to Brahmagupta: Recipients of the Shanti Swarup Bhatnagar Award Heron's formula topic A triangle with sides a, b, and c.
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Brahmagupta's interpolation formula topic Brahmagupta's interpolation formula is a second-order polynomial interpolation formula developed by the Indian mathematician and astronomer Brahmagupta — CE in the early 7th century CE. Preliminaries Given a set of tabulated values of a function f x in the table below, let it be required to compute the value of f a , x Folders related to Brahmagupta's interpolation formula: Indian mathematics Revolvy Brain revolvybrain Interpolation Revolvy Brain revolvybrain History of mathematics Revolvy Brain revolvybrain.
Cyclic quadrilateral topic Examples of cyclic quadrilaterals. The section characterizations below states what necessary and su Folders related to Cyclic quadrilateral: Quadrilaterals Revolvy Brain revolvybrain. Bretschneider's formula topic A quadrilateral. Area topic The combined area of these three shapes is approximately Indian mathematics topic Indian mathematics emerged in the Indian subcontinent from BC until the end of the 18th century. Ancient and medieval Indian mathematical works, all composed in Sanskrit, usually consisted of a section of sutras in which a set of rules or problems were stated with great economy Folders related to Indian mathematics: Recipients of the Shanti Swarup Bhatnagar Award Quadrilateral topic In Euclidean plane geometry, a quadrilateral is a polygon with four edges or sides and four vertices or corners.
Simple quadrilaterals Any quadrilateral that is not self-intersecting is a si Folders related to Quadrilateral: 4 number Revolvy Brain revolvybrain Polygons Revolvy Brain revolvybrain Quadrilaterals Revolvy Brain revolvybrain. Geometrically, these roots represent the x values at which any parabola, explicitly given as Folders related to Quadratic formula: Equations Revolvy Brain revolvybrain Elementary algebra Revolvy Brain revolvybrain Polynomials Revolvy Brain revolvybrain.
So a quadratic equation has always two roots, if complex roots are considered, and Folders related to Quadratic equation: Parabolas Revolvy Brain revolvybrain Equations Revolvy Brain revolvybrain Elementary algebra Revolvy Brain revolvybrain. List of mathematical identities topic This page lists mathematical identities, that is, identically true relations holding in mathematics.
Semiperimeter topic In geometry, the semiperimeter of a polygon is half its perimeter. Trapezoid topic In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English but as a trapezium in English outside North America. List of geometry topics topic This is a list of geometry topics, by Wikipedia page. Absolute geometry Affine geometry Algebraic geometry Analytic geometry Archimedes' use of infinitesimals Birational geometry Complex geometry Combinatorial geometry Computational geometry Conformal geometry Constructive solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic geometry Enumerative geometry Epipolar geometry Finite geometry Fractal geometry Geometry of numbers Hyperbolic geometry Incidence geometry Information geometry Integral geometry Inversive geometry Inversive ring geometry Klein geometry Lie sphere geometry Non-Euclidean geometry Numerical geometry Ordered geometry Parabolic geometry Plane geometry Projective geometry Quantum geometry Reticular geometry Riemannian geometry Ruppeiner geometr Folders related to List of geometry topics: Lists of topics Revolvy Brain revolvybrain Geometry Revolvy Brain revolvybrain Mathematics-related lists Revolvy Brain revolvybrain.
Isosceles triangle topic In geometry, an isosceles triangle is a triangle that has two sides of equal length. Every isosceles triangle has an axi Folders related to Isosceles triangle: Triangles Revolvy Brain revolvybrain Triangle geometry Revolvy Brain revolvybrain Elementary shapes Revolvy Brain revolvybrain.
Bhaskara I's sine approximation formula topic In mathematics, Bhaskara I's sine approximation formula is a rational expression in one variable for the computation of the approximate values of the trigonometric sines discovered by Bhaskara I c.