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The lune of Hippocrates was the first curved figure to have its exact area calculated mathematically.. Greek mathematicians understood the determination of an area of a figure as the process of geometrically constructing a square having the same area (squaring), thus the name quadrature for this process.
A complete quadrangle (at left) and a complete quadrilateral (at right).. In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting the six pairs of points.
Signs of trigonometric functions in each quadrant. In the above graphic, the words in quotation marks are a mnemonic for remembering which three trigonometric functions (sine, cosine, tangent and their reciprocals) are positive in each quadrant.
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
Configurations (4 3 6 2) (a complete quadrangle, at left) and (6 2 4 3) (a complete quadrilateral, at right).. In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.
If (P,B,I) is a generalized quadrangle with parameters (s,t), then (B,P,I −1), with I −1 the inverse incidence relation, is also a generalized quadrangle. This is the dual generalized quadrangle. Its parameters are (t,s). Even if s = t, the dual structure need not be isomorphic with the original structure.
To see the complete quadrangle applied to obtaining the midpoint, consider the following passage from J. W. Young: If two arbitrary lines AQ, AS are drawn through A and lines BS, BQ are drawn through B parallel to AQ, AS respectively, the lines AQ, SB meet, by definition, in a point R at infinity, while AS, QB meet by definition in a point P at ...
The Mandelbrot set, one of the most famous examples of mathematical visualization. Mathematical phenomena can be understood and explored via visualization. Classically, this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century).
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