Who invented the trapezoidal rule?
342329
Well, I think I found something; it says that the rule is part of the Newton-Cotes formulas (Isaac Newton and Roger Cotes).\n\nThis is the page where I found the info:\nhttp://www.absoluteastronomy.com/ref/trapezium_rule
730807
René Descartes is regarded as having invented analytic or coordinate geometry in 1637.  I can't find any information on who invented simultaneous equations.  However, the reason for this is clearly because they are much more ancient than Cartesian geometry.  The Indian mathematician Baudhayana was solving simultaneous equations as early as 800 BCE!  It is true that simultaneous equations have a relationship with coordinate geometry, because a system of equations is solved by a point that is the intersection of the curves represented by the equations.  However, this aspect of simultaneous equations is not fundamental to solving them.
406822
It it considered that the first proposal of using symboll "pi"  as the ratio of the circumference of a circle to its diameter was firstly appeared in the works of William Jones. But he was  a Welsh mathematician, not Swiss.\n\nFrom section "History of the notation" of first attached wiki article:\nThe symbol "π" for Archimedes' constant was first introduced in 1706 by William Jones when he published A New Introduction to Mathematics, although the same symbol had been used earlier to indicate the circumference of a circle. The notation became standard after it was adopted by Leonhard Euler.
472081
Gottfried Wilhelm von LEIBNIZ\n(1646-1716)  . \n\n \n Leibniz, sometimes called the last universal genius, invented at least two things that are essential for the modern world: calculus, and the binary system. \nModern physics, math, engineering would be unthinkable without the former: the fundamental method of dealing with infinitesimal numbers. Leibniz developed it around 1673. In 1679, he perfected the notation for integration and differentiation that everyone is still using today. \n\nThe bit and the binary system he invented around 1679, and published in 1701. This became the basis of virtually all modern computers. \n\nLeibniz' final years were overshadowed by a priority fight with the powerful president of the Royal Society, Isaac Newton, who claimed he had invented calculus before Leibniz (without publishing it), and who made friends sign texts he wrote to support this claim.
53619
Lagrange is considered the father of calculus.
523203
a trapazoid has 2 parallel sides and two non parallel sides.\n\nArea=( 1/2 sum of the parallel sides) * height\n\nremember the height must be the perpendicular height.\ni.e the height perpendicular to the parallel sides
399239
The first reference to this triangle occurs in Indian mathematician Pingala's book on Sanskrit poetics that may be as early as 450 BC as Meru-prastaara, the "staircase of Mount Meru". The commentators of this book were also aware that the shallow diagonals of the triangle sum to the Fibonacci numbers. It was also known to Chinese mathematicians. It is said that the triangle was called "Yang Hui's triangle" by the Chinese. Later, the Persian mathematician Karaji and the Persian astronomer-poet Omar Khayyám; thus the triangle is referred to as the "Khayyam triangle" in Iran. Several theorems related to the triangle were known, including the binomial theorem. In fact we can be fairly sure that Khayyam used a method of finding nth roots based on the binomial expansion, and therefore on the binomial coefficients. Finally, in Italy, it is referred to as "Tartaglia's triangle", named for the Italian algebraist Niccolo Fontana Tartaglia who lived a century before Pascal; Tartaglia is credited with the general formula for solving cubic polynomials.\n\nIn modern times, Pascal's triangle takes its name from the Traité du triangle arithmétique (1655) by Blaise Pascal. In that work, Pascal collected several results then known about the triangle, and employed them to solve problems in probability theory. The "arithmetical" triangle was later called after Pascal by Pierre Raymond de Montmort (1708) and Abraham de Moivre (1730).
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ARYABHATA [Aryabhata] , c.476-550, Hindu mathematician and astronomer. He is one of the first known to have used algebra; his writings include rules of arithmetic and of plane and spherical trigonometry, and solutions of quadratic equationsr.
312542
Ancient. This is the "Law of Superposition. See\n \nhttp://en.wikipedia.org/wiki/Law_of_superposition
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The first measurement of the equator was done by Eratosthenes of Samos--centuries ago.  He computed it as being roughly 25,000 miles, which is really quite accurate.\n\nEratosthenes was a hotshot at geometry.  He knew that on the spring equinox, the sun cast no shadow at noon in (as I recall it) Syene, Egypt (? on the spelling); in Samos, the shadow at the same time cast a shadow that made an angle of about 6 degrees with the top of the stick.  Using the known distance between the two places, the already accepted fact that the earth was spherical, and a little geometry, he figured out the equitoral diameter, and did a very fine job of it as well.\n\nHe later recomputed the figure, by the way, getting 18,000 miles.  Columbus repeated the calculation, long afterward, and got 19,400.  The Portuguese (the premier mapmakers of Columbus' day) had computed it as about 24,800 or so... They knew the world was round--and bigger than ol' Christopher Columbus thought...  An aside, but a fun one...
82598
alfred wegener\njust learned this myself (:
1070816
Charles F. Prentice is regarded as the Father of Optometry. He was the originator of the method now used to specify the power of prisms in ophthalmic lenses, now known simply as Prentice's Rule. The first model to demonstrate static and dynamic refraction of the eye was also produced by Prentice. He is credited with producing an astigmatic eye model and optical principles which relate to sphero-cylindrical lens prescriptions. Prentice led the movement in the early part of the 20th century for legalizing the profession of optometry. \n\n-----------------------\n\nSo now we come to the second most used formula in optical theory -- Prentice's rule. This formula gives us an approximation of the amount of prism present at any given point on a lens based on the dioptric power of the lens and the distance that the point is from the optical center of the lens. \n\nPrentice's rule is: \n\nP = (distance from optical center in cm)(power of the lens in diopters)\nThere are several versions of this formula. Since we use it for measurements that we take in the lab, and since we usually use mm in the lab instead of cm, there is another form of the formula that I prefer for you to use. This form of the formula does not require you to remember to convert the measurement to cm. \n\n    dD \nP = ------- \n   10\nwhere: \n    P = the amount of prism present at a particular point, \n    d = the distance of that point from the optical center, in mm, \n    D = the dioptric power of the lens.
1124961
To calculate perimeter of trapezoid you need to know the dimension of each side of trapeziod..\nthen.. sum of sides give you perimeter.
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"Cartesian coordinates come from his last name, Descarte."\n\nActually, you are only half right. The Cartesian plane comes from Descarte's Latin name, Cartesius, which is what he used when publishing his proofs. \n\nOnto the question at hand, I'm not even sure what you are asking. What did Rene Descartes use the first letters of? Grammatical abnormalities notwithstanding, this question is very vague. What exactly do you mean?
1134789
most people will tell you Abner Doubleday, but he didnt.  Alexander Cartwright had a hand in compiling and publishing an early list of rules in 1845 to meet the demands of the already popular sport.  So Cartwright invented the organized rules.  Abner Doubleday even said he made no such claim.  It could have also been John Newbery.  Who knows.
93252
It's easy\n\nYou can use the formula A=(b1+b2)h/2 wherein 1 and 2 are subscripts.\nA=area of trapezoid\nb1=1st base or top base\nb2=2nd base or bottom base\nh=height or altitude. Altitude is the line segment from b1 that is perpendicular to b2.
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The use of grid lines on maps (latitude and longitude) was first suggested by the Greek astronomer Hipparcus about 300 years before Christ. He was the first who devised a method for fixing the location of places on earth by observation of the the sun, moon and stars. He worked out the mathematics of spherical trigonometry, which allowed the results of these observations to be plotted on an earth which he knew already to be a sphere.\n\nLatitude can be found easily by measuring the height of the sun at noon. The measurement of longitude is not so simple as you need an accurate clock.