Parallelogram law, the Glossary
In mathematics, the simplest form of the parallelogram law (also called the parallelogram identity) belongs to elementary geometry.[1]
Table of Contents
24 relations: Alexander Bogomolny, Angle, Complex number, Dot product, Euclidean geometry, Euler's quadrilateral theorem, Geometry, Inner product space, Law of cosines, Line segment, List of trigonometric identities, Lp space, Mathematics, Midpoint, Norm (mathematics), Normed vector space, Parallelogram, Polarization identity, Ptolemy's inequality, Pythagorean theorem, Quadrilateral, Real coordinate space, Real number, Rectangle.
- Theorems about quadrilaterals
Alexander Bogomolny
Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet-born Israeli-American mathematician.
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Angle
In Euclidean 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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Complex number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^.
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Dot product
In mathematics, the dot product or scalar productThe term scalar product means literally "product with a scalar as a result".
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Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.
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Euler's quadrilateral theorem
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. Parallelogram law and Euler's quadrilateral theorem are Euclidean geometry and theorems about quadrilaterals.
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Geometry
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
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Inner product space
In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product.
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Law of cosines
In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
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Line segment
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.
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List of trigonometric identities
In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.
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Lp space
In mathematics, the spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
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Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
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Midpoint
In geometry, the midpoint is the middle point of a line segment.
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Norm (mathematics)
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin.
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Normed vector space
In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined.
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Parallelogram
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
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Polarization identity
In linear algebra, a branch of mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space.
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Ptolemy's inequality
In Euclidean geometry, Ptolemy's inequality relates the six distances determined by four points in the plane or in a higher-dimensional space.
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Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
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Quadrilateral
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices).
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Real coordinate space
In mathematics, the real coordinate space or real coordinate n-space, of dimension, denoted or, is the set of all ordered n-tuples of real numbers, that is the set of all sequences of real numbers, also known as coordinate vectors.
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Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
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Rectangle
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.
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See also
Theorems about quadrilaterals
- Anne's theorem
- Bretschneider's formula
- British flag theorem
- Euler's quadrilateral theorem
- Finsler–Hadwiger theorem
- Parallelogram law
- Petr–Douglas–Neumann theorem
- Thébault's theorem
- Theorem of the gnomon
- Van Aubel's theorem
- Varignon's theorem
References
[1] https://en.wikipedia.org/wiki/Parallelogram_law
Also known as Parallelogram equality, Parallelogram equation, Parallelogram identity, Parallelogram rule.