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By Clint Brookhart

Pass determine. is an interesting and numerous selection of maths-related anecdotes, puzzles and formulation. It exhibits readers all of the attention-grabbing issues they could determine utilizing simple algebra.'

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2n. To find the number of ancestors for four generations, n = 4, so: n ͚ϭ2 ϭ2 i iϭ1 1 ϩ 22 ϩ 23 ϩ 24 ϭ 2 ϩ 4 ϩ 8 ϩ 16 ϭ 30 Computing the sum of the terms in this geometric series for large numbers (n) can be laborious. Fortunately, the following formula is much easier: n ͚2 ϭ a i 1 iϭ1 rn Ϫ 1 rϪ1 In this formula, a 1 is the first term in the series (2), and r is the common ratio of the terms (also 2). Each term is twice the term before. Now let’s use the formula to check our answer. Do you really have thirty direct ancestors in the previous four generations?

Beginning with a variation of the Pythagorean theorem, we have S2 ϭ L2 ϩ h2 ∆S ϭ S Ϫ L or: L ϭ S Ϫ ∆S Then, substituting for L in the original equation, we get S2 ϭ (S Ϫ ∆S)2 ϩ h2 or: S2 ϭ S2 Ϫ 2S∆S ϩ ∆S2 ϩ h2 2S∆S ϭ ∆S2 ϩ h2 To simplify, we assume that ∆S2 is close to zero. Therefore, we can derive this formula for slope correction: ∆S ϭ h2 2S This is a much simpler way to approximate corrections and can be used on most slopes that are not extremely steep. The following table compares the accuracy of using the approximation formula in calculating slope corrections to using the Pythagorean theorem.

50 Not bad for twenty days’ work! Something for Everyone Looking for a Date? Carbon Dating and the Shroud of Turin Carbon dating is a method for determining the age of prehistoric organic material by measuring its radioactivity. The technique was developed by an American chemist, Dr. Willard F. Libby (1908 –1980), in the late 1940s. All living things absorb carbon 14 from carbon dioxide in the atmosphere. After an animal or plant dies, the amount of carbon 14 present begins to break down by releasing particles at a uniform rate.

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