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The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 2 × 2πr × r, holds for a circle.
In digital photography, the image sensor format is the shape and size of the image sensor. The image sensor format of a digital camera determines the angle of view of a particular lens when used with a particular sensor. Because the image sensors in many digital cameras are smaller than the 24 mm × 36 mm image area of full-frame 35 mm cameras ...
Common gauges are 7-1/2" (Western US) and 7-1/4" (Eastern US & rest of the world), 5", and 4-3/4". Smaller live steam gauges do exist, but as the scale gets smaller, pulling power decreases. One of the smallest gauges on which a live steam engine can pull a passenger is the now almost defunct 2 + 1 ⁄ 2-inch gauge.
Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...
Unit sphere. Sphere with radius one, usually centered on the origin of the space. Some 1-spheres: ‖x‖2 is the norm for Euclidean space. In mathematics, a unit sphere is a sphere of unit radius: the set of points at Euclidean distance 1 from some center point in three-dimensional space. More generally, the unit -sphere is an -sphere of unit ...
Method of exhaustion. The method of exhaustion (Latin: methodus exhaustionis) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the n th polygon and the containing shape will ...
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, [a] which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted ...