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where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
Now let x = cos 20°. Note that cos 60° = cos π / 3 = 1 / 2 . Then by the triple-angle formula, cos π / 3 = 4x 3 − 3x and so 4x 3 − 3x = 1 / 2 . Thus 8x 3 − 6x − 1 = 0. Define p(t) to be the polynomial p(t) = 8t 3 − 6t − 1. Since x = cos 20° is a root of p(t), the minimal polynomial for cos 20° is ...
The formula is a special case of the Euler–Boole summation formula for alternating series, providing yet another example of a convergence acceleration technique that can be applied to the Leibniz series. In 1992, Jonathan Borwein and Mark Limber used the first thousand Euler numbers to calculate π to 5,263 decimal places with the Leibniz ...
Tungsten carbide hole saw with arbor A 52 mm (2.0 in) hole saw with pilot bit A 115 mm (4.5 in) diamond hole saw. A hole saw (also styled holesaw), also known as a hole cutter, [1] is a saw blade of annular (ring) shape, whose annular kerf creates a hole in the workpiece without having to cut up the core material.
The National Park Service is cautioning spectators to heed warnings and safety precautions after the latest eruption of Hawaii's Kilauea volcano, one of the most active in the world. Kilauea began ...
In March, residents of the southern city of Taxco lynched a woman they accused of murdering an 8-year-old girl. Two men also suspected by locals of involvement were attacked but survived, the BBC ...
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