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Index Trapezoid

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. [1]

61 relations: American English, Angle, Arithmetic mean, Aryabhata, Aryabhatiya, Astronomer, Bhāskara I, Brahmagupta's formula, Bretschneider's formula, Calculus, Canadian English, Collinearity, Convex polygon, Crossed ladders problem, Cyclic quadrilateral, Degree (angle), Diagonal, Encyclopedia of Mathematics, Euclid, Euclid's Elements, Euclidean geometry, Ex-tangential quadrilateral, Harmonic mean, Heron's formula, Inca architecture, Indian astronomy, Indian mathematics, Integral, Isosceles trapezoid, Lambert quadrilateral, Mathematician, Metropolitan Museum of Art, Midpoint, Morphology (biology), New York City, Oxford English Dictionary, Parallel (geometry), Parallelogram, Perpendicular, Planar lamina, Point reflection, Polite number, Proclus, Quadrilateral, Ratio, Rectangle, Reflection symmetry, Rhombus, Right angle, Rotational symmetry, ..., Saccheri quadrilateral, Semiperimeter, Similarity (geometry), Special case, Square, Tangential quadrilateral, Tangential trapezoid, Taxonomy (biology), Trapezoidal rule, Triangle, Wedge (geometry). Expand index (11 more) »

American English

American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States.

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In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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Arithmetic mean

In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.

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Aryabhata (IAST) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.

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Aryabhatiya (IAST) or Aryabhatiyam, a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata.

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An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside the scope of Earth.

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Bhāskara I

Bhāskara (c. 600 – c. 680) (commonly called Bhaskara I to avoid confusion with the 12th century mathematician Bhāskara II) was a 7th-century mathematician, who was the first to write numbers in the Hindu decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work.

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Brahmagupta's formula

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.

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Bretschneider's formula

In geometry, Bretschneider's formula is the following expression for the area of a general quadrilateral: Here,,,, are the sides of the quadrilateral, is the semiperimeter, and and are two opposite angles.

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Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

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Canadian English

Canadian English (CanE, CE, en-CA) is the set of varieties of the English language native to Canada.

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In geometry, collinearity of a set of points is the property of their lying on a single line.

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Convex polygon

A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon.

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Crossed ladders problem

The crossed ladders problem is a puzzle of unknown origin that has appeared in various publications and regularly reappears in Web pages and Usenet discussions.

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Cyclic quadrilateral

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.

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Degree (angle)

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.

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In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.

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Encyclopedia of Mathematics

The Encyclopedia of Mathematics (also EOM and formerly Encyclopaedia of Mathematics) is a large reference work in mathematics.

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Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

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Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

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Ex-tangential quadrilateral

In Euclidean geometry, an ex-tangential quadrilateral is a convex quadrilateral where the extensions of all four sides are tangent to a circle outside the quadrilateral.

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Harmonic mean

In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means.

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Heron's formula

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulae for the area of a triangle, such as half the base times the height or half the norm of a cross product of two sides.

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Inca architecture

Incan architecture is the most significant pre-Columbian architecture in South America.

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Indian astronomy

Indian astronomy has a long history stretching from pre-historic to modern times.

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Indian mathematics

Indian mathematics emerged in the Indian subcontinent from 1200 BC until the end of the 18th century.

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In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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Isosceles trapezoid

In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.

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Lambert quadrilateral

In geometry, a Lambert quadrilateral, named after Johann Heinrich Lambert, is a quadrilateral in which three of its angles are right angles.

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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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Metropolitan Museum of Art

The Metropolitan Museum of Art of New York, colloquially "the Met", is the largest art museum in the United States.

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In geometry, the midpoint is the middle point of a line segment.

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Morphology (biology)

Morphology is a branch of biology dealing with the study of the form and structure of organisms and their specific structural features.

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New York City

The City of New York, often called New York City (NYC) or simply New York, is the most populous city in the United States.

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Oxford English Dictionary

The Oxford English Dictionary (OED) is the main historical dictionary of the English language, published by the Oxford University Press.

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Parallel (geometry)

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

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In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.

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In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

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Planar lamina

In mathematics, a planar lamina is a closed set in a plane of mass m and surface density \rho\ (x,y) such that: The center of mass of the lamina is at the point where M_y moment of the entire lamina about the x-axis and M_x moment of the entire lamina about the y-axis.

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Point reflection

In geometry, a point reflection or inversion in a point (or inversion through a point, or central inversion) is a type of isometry of Euclidean space.

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Polite number

In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers.

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Proclus Lycaeus (8 February 412 – 17 April 485 AD), called the Successor (Greek Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers (see Damascius).

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In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners.

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In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.

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In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.

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Reflection symmetry

Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, is symmetry with respect to reflection.

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In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length.

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Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.

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Rotational symmetry

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.

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Saccheri quadrilateral

A Saccheri quadrilateral (also known as a Khayyam–Saccheri quadrilateral) is a quadrilateral with two equal sides perpendicular to the base.

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In geometry, the semiperimeter of a polygon is half its perimeter.

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Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.

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Special case

In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of.

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In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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Tangential quadrilateral

In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides are all tangent to a single circle within the quadrilateral.

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Tangential trapezoid

In Euclidean geometry, a tangential trapezoid, also called a circumscribed trapezoid, is a trapezoid whose four sides are all tangent to a circle within the trapezoid: the incircle or inscribed circle.

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Taxonomy (biology)

Taxonomy is the science of defining and naming groups of biological organisms on the basis of shared characteristics.

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Trapezoidal rule

In mathematics, and more specifically in numerical analysis, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) is a technique for approximating the definite integral The trapezoidal rule works by approximating the region under the graph of the function f(x) as a trapezoid and calculating its area.

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A triangle is a polygon with three edges and three vertices.

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Wedge (geometry)

In solid geometry, a wedge is a polyhedron defined by two triangles and three trapezoid faces.

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[1] https://en.wikipedia.org/wiki/Trapezoid

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