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The Official Table of Drops, formerly issued by the British Home Office, is a manual which is used to calculate the appropriate length of rope for long drop hangings. Following a series of failed hangings, including those of John Babbacombe Lee , a committee chaired by Henry Bruce, 1st Baron Aberdare was formed in 1886 to discover and report on ...
The ropelength of a knotted curve is defined as the ratio () = / (), where is the length of and () is the knot thickness of . Ropelength can be turned into a knot invariant by defining the ropelength of a knot K {\displaystyle K} to be the minimum ropelength over all curves that realize K {\displaystyle K} .
[1] This diagram gives a visual analogue using a square: regardless of the size of the square, the added perimeter is the sum of the four blue arcs, a circle with the same radius as the offset. More formally, let c be the Earth's circumference, r its radius, Δc the added string length and Δr the added radius.
The longest measured length listed in the Rhind Mathematical Papyrus is a circumference of about a Roman mile with a diameter of 9 khet. Despite many popular claims, there is no surviving evidence that the 3-4-5 triangle, and by implication the Pythagoras' theorem, was used in Ancient Egypt to lay out right angles, such as for the pyramids. [1]
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So, the desired area A is A 1 + (A 2 − A 3 + A 4) · 2. The area(s) required to be computed are between two quadratic curves, and will necessarily be an integral or difference of integrals. The primary parameters of the problem are , the tether length defined to be 160yds, and , the radius
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A cable in this usage cable is a thick rope or by transference a chain cable. [1] The OED gives quotations from c. 1400 onwards. A cable's length (often "cable length" or just "cable") is simply the standard length in which cables came, which by 1555 had settled to around 100 fathoms (600 ft; 180 m) or 1 ⁄ 10 nautical mile (0.19 km; 0.12 mi). [1]