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PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass.
In France examples such as the Baptistry of St. Jean at Poitiers created in the 6th through 7th century CE defined Merovingian architecture. The form became even more abstracted in this period, replacing sculptures with geometric engravings and mosaics, and using small alternating curved and triangular pediments above windows on churches such ...
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.
Semicircular arch (Pianella bridge, Corse-du-Sud, 15th century) In architecture, a semicircular arch is an arch with an intrados (inner surface) shaped like a semicircle. [1] [2] This type of arch was adopted and very widely used by the Romans, thus becoming permanently associated with Roman architecture.
The basic shape of the modern tiara is a semi-circle, usually made of silver, gold or platinum and richly decorated with precious stones, pearls or cameos. Tiaras were extremely popular during the late 19th century and were worn at events where the dress code was white tie .
The phases of the moon make spherical lunes perceived as the intersection of a semicircle and semi-ellipse. The visibly lighted portion of the Moon visible from the Earth is a spherical lune. The first of the two intersecting great circles is the terminator between the sunlit half of the Moon and the dark half. The second great circle is a ...
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The inner circle is observed to slip with respect to its track. The paradox is that the smaller inner circle moves 2πR, the circumference of the larger outer circle with radius R, rather than its own circumference. If the inner circle were rolled separately, it would move 2πr, its own circumference with radius r. The inner circle is not ...