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Ana Tamez History of Math Mathematical Instruments from The Ana Tamez History of Math Mathematical Instruments From the early beginnings of Greek mathematics and the study of astronomy, tools have been designed with the intention of helping those who wish to map out the planets and stars or wanted to navigate to different places or just perform the simple calculations. One of the earliest instruments created for the use of mapping was called the astrolabe which was used by astronomers to have a better prediction of the position of planets, the moon, and the Sun. With many great mathematicians proving theorems and creating new ways to understand the relationship between numbers, others were inspired and challenged to invent instruments to facilitate in such calculations and help better understand numerical relationships. One of the most important utensils used by mathematicians for a large period of time, and is still used to this day, was the slide rule. The history of slide rules is quite extensive because, like many other tools, in order to achieve a well working multi function instrument, it required different designs and the addition of parts. John Napier was the one who inspired the creation of slide rules with his conception of logarithms as a means of working with complicated numbers through the addition and subtraction of logarithms. It was English mathematician Edmund Gunter who created the first simple logarithmic scale. The rule was marked with scales and with the use of dividers one could use it to multiply or divide two numbers by either adding or subtracting the length between the marks. Although Gunter did create a simple log scale, William Oughtred is credited as the inventor of slide rules. Oughtred took two of these scales and place them together to allow for easier readings of the lengths without the use of dividers. From there, other mathematicians added on to Oughtred’s design; Isaac Newton added a cursor which allowed for more accurate readings and Peter Roget created a log log scale that was used to solve for roots and powers of numbers. A French officer by the name Amédée Mannheim combined the four scales, powers, roots, multiplication, and division, to create a basis for the modern slide rule. Other inventors such as Henry Coggeshall used the basics of the slide rule to create a timber and carpenter’s rule used for measuring and construction. Despite the fact that many were beginning to implement the use of slide rules for important calculations and measurements, the life of the slide rule began to diminish with the invention of the computers and scientific calculators. The very first slide rules were manufactured out of hard wood with the cursor made of glass of metal. Keuffel and Esser, a company in the United States manufactured their own more complex rules with scales of various colors, which included the reciprocal scale, and a much more precise way of reading the computations. Shortly after, a Japanese firm began fabricating their own rules made of bamboo which had a greater durability than the hardwood rules. Soon after the introduction of these bamboo slide rules in Northern Europe, rules were crafted out of plastic with acrylic cursors which later were produced in America with printed scales and was more resistant to accidental breakage. This later became the design of the modern slide rule. Since the creation of slide rules, each rule has had it’s own differently labeled scales. The typical scales that one might find on a standard slide rule are A and B, which are used for squares and square roots of numbers, C and D, which are the basic logarithm scales used for multiplication and division, CI and DI, are the reciprocals of C, D, and K which can determine the cube roots and the cubic numbers. Some of the more complex slide rules have the trigonometric scales to find sine, cosine, and tangent, as well as and the exponential and logarithmic scales. Using a slide rule is not complicated. The basic slide rule which can perform multiplication, division, square, and square roots, is composed of three bars. The outer bars, which are fixed and do not move, are two bars and are the body of the rule, that contain the scales A and D. The third bar is at the center and it is the sliding bar with the scales B and C. Along with the bars, the rule may contain braces to keep the rule sturdy as well as be equipped with a cursor that indicates the values and a hairline for accurate reading. The way this works is, for example if one wants to find the answer to a simple multiplication problem, say 2x2, this can be done using the C and D scale. The center bar would be slid so that the number 1 on the C scale lines up with the number 2 on the D scale. Then from the C and D scale one can read off the numbers and determine that 2x2 is 4. D is 2, C is 1 2 x 2 = 4 Using a virtual slide rule I am showing 2 x 2 = 4. The opposite can be done for division and your divided would be on the D scale and divisor in the C scale. As for the squares and square roots, all four scales are in use. For example, to find 32, look at 3 from the A scale and read off what it lines up with on the D scale. D is 3, A is 9 32 = 9 Using a virtual slide rule I am showing 32 = 9. The slide rule has been used extensively in the years leading up to technological advancements. Engineers would use slide rules to construct and design various buildings and even use this simple tool in the aid of calculations during space missions. Even though the slide rule was used not only to for calculations, but to show the relationship between numbers, it became a valuable tool for several centuries until it was ultimately replaced by technological computers and calculators. The slide rule was a more practical way of doing calculations and not making technical errors as one might do when entering numbers on a calculator or a computer. The determination of William Oughtred to solidify John Napier’s logarithm creations and show that there is a relationship between numbers, allowed for the invention of the slide rule. It was originally meant as a simplistic way of making complex calculations and not having to write it by hand, but as the popularity of the rule began to increase and spread to different parts of the world, each place found a way to use the design of the rule to use it in their own calculations, whether it be with gauging how much of one thing was in a container or using it for the construction of buildings. Though it is still used as a functional way of computation, most people keep it as a relic. Citations: https://en.wikipedia.org/wiki/Slide_rule#History http://www.oughtred.org/history.shtml http://www.hpmuseum.org/srinst.htm https://www.math.utah.edu/~pa/sliderules/ http://mysite.du.edu/~jcalvert/tech/slidrul.htm http://web.mit.edu/2.972/www/reports/slide_rule/slide_rule.html http://www.npr.org/sections/ed/2014/10/22/356937347/the-slide-rule-a-computing-device-that- put-a-man-on-the-moon http://www.nzeldes.com/HOC/Gunter.htm http://www.antiquark.com/sliderule/sim/virtual-slide-rule.html http://sliderulemuseum.com/SR_Course.htm .
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