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Grade is usually expressed as a percentage - converted to the angle α by taking the inverse tangent of the standard mathematical slope, which is rise / run or the grade / 100. If one looks at red numbers on the chart specifying grade, one can see the quirkiness of using the grade to specify slope; the numbers go from 0 for flat, to 100% at 45 ...
Naismith's rule helps with the planning of a walking or hiking expedition by calculating how long it will take to travel the intended route, including any extra time taken when walking uphill. This rule of thumb was devised by William W. Naismith, a Scottish mountaineer, in 1892. [1] [3] [4] A modern version can be formulated as follows:
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[2] [3] Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics , most notably in Euclid 's Elements . [ 4 ] Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions ), until the 16th and 17th centuries, when ...
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If the result of step 4 does not equal the result of step 5, then the original answer is wrong. If the two results match, then the original answer may be right, though it is not guaranteed to be. Example Assume the calculation 6,338 × 79, manually done, yielded a result of 500,702: Sum the digits of 6,338: (6 + 3 = 9, so count that as 0) + 3 ...
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