Information AboutSlide Rule |
| CATEGORIES ABOUT SLIDE RULE | |
| mathematical tools | |
| mechanical calculators | |
| theory of computation | |
| logarithms | |
| english inventions | |
| 1620 introductions | |
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Despite their similar appearance, a slide rule serves a purpose different from that of a standard Ruler : a ruler measures physical distances and aids in drawing straight lines, while a slide rule performs mathematical operations by using distances on nonlinearly-divided scales. BASIC CONCEPTS In its most basic form, the slide rule uses two Logarithmic scales to allow rapid multiplication and division of numbers, common operations that can be time-consuming and error-prone when done on paper. More complex slide rules allow other calculations, such as square roots, exponentials, logarithms, and trigonometric functions. In general, mathematical calculations are performed by aligning a mark on the sliding central strip with a mark on one of the fixed strips, and then observing the relative positions of other marks on the strips. Numbers aligned with the marks give the approximate value of the product, quotient, or other calculated result. The user determines the location of the decimal point in the result, based on mental estimation. Scientific Notation is used to track the decimal point in more formal calculations. Addition and subtraction steps in a calculation are done mentally or on paper, not on the slide rule. Even the most basic student slide rules have more than two scales. Most consist of three linear strips of the same length, aligned in parallel and interlocked so that the central strip can be moved lengthwise relative to the other two. The outer two strips are fixed so that their relative positions do not change. Some slide rules ("duplex" models) have scales on both sides of the rule and slide strip, others on one side of the outer strips and both sides of the slide strip, still others on one side only ("simplex" rules). A sliding cursor with a vertical alignment line is used to find corresponding points on scales that are not adjacent to each other or, in duplex models, are on the other side of the rule. The cursor can also record an intermediate result on any of the scales. OPERATION Multiplication The figure below shows a simplified slide rule. It consists of two scales that can move with respect to each other. A numeral is printed on each scale at a distance from the "index" (the left side number 1) equal to its Base-10 Logarithm () times the length of the scale. Tick marks between each numeral are similarly placed according to logarithmic distance. A logarithm transforms the operations of multiplication and division to addition and subtraction according to the rules and . Sliding the top scale rightward by a distance of aligns each number , at position on the top scale, with the number at position on the bottom scale. Since , reading this position on the bottom scale gives , the product of and . The illustration below shows the slides arranged for multiplication of 2 with any other number. The index on the upper scale is aligned with the 2 on the lower scale. This shifts the entire upper scale rightward by The numbers on the upper scale line up with the multiplication-by-2 result on the lower scale. For example, the 3.5 on the upper scale is aligned with the product 7 on the lower scale, the 4 with the 8, and so on: Operations may go "off the scale." For example the diagram above shows that the slide rule has not positioned the 7 on the upper scale above any number on the lower scale, so it does not give any answer for . In such cases, the user may slide the upper scale to the left, effectively multiplying by 0.2 instead of by 2, as in the illustration below: Here the user of the slide rule must remember to adjust the decimal point appropriately to correct the final answer. We wanted to find , but instead we calculated . So the true answer is not 1.4 but 14. Division The illustration below demonstrates the computation of 5.5/2. The 2 on the top scale is placed over the 5.5 on the bottom scale. The 1 on the top scale lies above the quotient, 2.75. Other operations In addition to the logarithmic scales, some slide rules have other mathematical Function s encoded on other auxiliary scales. The most popular were Trigonometric , usually Sine and Tangent , Common Logarithm (log10) (for taking the log of a value on a multiplier scale), Natural Logarithm (ln) and Exponential (''ex'') scales. Some rules include a Pythagorean scale, to figure sides of triangles, and a scale to figure circles. Others feature scales for calculating Hyperbolic Functions . On linear rules, the scales and their labeling are highly standardized, with variation usually occurring only in terms of which scales are included and in what order:
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