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Before calculators were cheap and plentiful, people would use mathematical tables —lists of numbers showing the results of calculation with varying arguments— to simplify and drastically speed up computation. Tables of logarithms and trigonometric functions were common in math and science textbooks. Specialized tables were published for applications such as astronomy, celestial navigation and statistics. ==A simple example== To compute the sine function of 75 degrees, 9 minutes, 50 seconds〔The longitude of Philadelphia City Hall〕 using a table of trigonometric functions such as the Bernegger table from 1619 illustrated here, one might simply round up to 75 degrees, 10 minutes and then find the 10 minute entry on the 75 degree page, shown above-right, which is 0.9666746. However, this answer is only accurate to four decimal places. If one wanted greater accuracy, one could interpolate linearly as follows: From the Bernegger table: :sin (75° 10′) = 0.9666746 :sin (75° 9′) = 0.9666001 The difference between these values is 0.0000745. Since there are 60 seconds in a minute of arc, we multiply the difference by 50/60 to get a correction of (50/60) *0.0000745 ≈ 0.0000621; and then add that correction to sin (75° 9′) to get : :sin (75° 9′ 50″) ≈ sin (75° 9′) + 0.0000621 = 0.9666001 + 0.0000621 = 0.9666622 A modern calculator gives sin (75° 9′ 50″) = 0.96666219991, so our interpolated answer is accurate to the 7-digit precision of the Bernegger table. For tables with greater precision (more digits per value), higher order interpolation may be needed to get full accuracy.〔Abramowitz and Stegun Handbook of Mathematical Functions, Introduction §4〕 In the era before electronic computers, interpolating table data in this manner was the only practical way to get high accuracy values of mathematical functions needed for applications such as navigation, astronomy and surveying. To understand the importance of accuracy in applications like navigation note that at sea level one minute of arc along the Earth's equator or a meridian (indeed, any great circle) equals approximately one nautical mile (). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Mathematical table」の詳細全文を読む スポンサード リンク
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