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This file is licensed under the United Kingdom Open Government Licence v3.0.: You are free to: copy, publish, distribute and transmit the Information; adapt the Information; ...
Archimedes introduced the salinon in his Book of Lemmas by applying Book II, Proposition 10 of Euclid's Elements.Archimedes noted that "the area of the figure bounded by the circumferences of all the semicircles [is] equal to the area of the circle on CF as diameter."
The rise (height) of a round arch is limited to 1 ⁄ 2 of its span, [7] so it looks more "grounded" than a parabolic arch [3] or a pointed arch. [7] Whenever a higher semicircular arch was required (for example, for a narrow arch to match the height of a nearby broad one), either stilting or horseshoe shape were used, thus creating a stilted arch and horseshoe arch respectively. [8]
For a semicircle with a diameter of a + b, the length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths a and b, and then connecting their common endpoint to the semicircle with a segment perpendicular to the diameter ...
An arbelos (grey region) Arbelos sculpture in Kaatsheuvel, Netherlands In geometry, an arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others (connected), all on the same side of a straight line (the baseline) that contains their diameters.
The area A of any triangle is the product of its inradius (the radius of its inscribed circle) and its semiperimeter: A = r s . {\displaystyle A=rs.} The area of a triangle can also be calculated from its semiperimeter and side lengths a, b, c using Heron's formula :
The moment of inertia for a semicircle, best expressed in cylindrical coordinates, is = (,,). Solving the integral, one finds that the moment of inertia of a semicircle is I = m s 2 {\displaystyle I=ms^{2}} , exactly the same for a hoop of the same radius.
A set of sides that can form a cyclic quadrilateral can be arranged in any of three distinct sequences each of which can form a cyclic quadrilateral of the same area in the same circumcircle (the areas being the same according to Brahmagupta's area formula). Any two of these cyclic quadrilaterals have one diagonal length in common. [17]: p. 84
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