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Area plays an important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. [8]
In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is T = b h / 2 , {\displaystyle T=bh/2,} where b is the length of the base of the triangle, and h is the height or altitude of the triangle.
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
Some lines in the pencil through A. In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a plane, or the set of circles that pass through two given points in a plane.
A – adele ring or algebraic numbers. a.a.s. – asymptotically almost surely. AC – Axiom of Choice, [1] or set of absolutely continuous functions. a.c. – absolutely continuous.
see discrete geometry Combinatorial group theory the theory of free groups and the presentation of a group. It is closely related to geometric group theory and is applied in geometric topology. Combinatorial mathematics an area primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite ...
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A rhombus therefore has all of the properties of a parallelogram: for example, opposite sides are parallel; adjacent angles are supplementary; the two diagonals bisect one another; any line through the midpoint bisects the area; and the sum of the squares of the sides equals the sum of the squares of the diagonals (the parallelogram law).