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Unformatted text preview: The History of Mathematics http://wwwgroups.dcs.stand.ac.uk/~history/BiogIndex.html http://www.math.wichita.edu/~richardson/timeline.html http://wwwgroups.dcs.stand.ac.uk/~history/Indexes/HistoryTopics.html x 2 + 10 x = 39 x 2 + 10 x + 4 25 / 4 = 39+25 (x+5) 2 = 64 x + 5 = 8 x = 3 a lKhwa rizm i Ira q (c a . 780850) Completing a Square Solving a Quadratic Equation In Ko nig s b e rg , G e rm a ny, a rive r ra n thro ug h the c ity s uc h tha t in its c e ntre wa s a n is la nd, a nd a fte r pa s s ing the is la nd, the rive r b ro ke into two pa rts . S e ve n b ridg e s we re b uilt s o tha t the pe o ple o f the c ity c o uld g e t fro m o ne pa rt to a no the r. The pe o ple wo nde re d whe the r o r no t o ne c o uld wa lk a ro und the c ity in a wa y tha t wo uld invo lve c ro s s ing e a c h b ridg e e xa c tly o nc e The Bridges of Konigsberg Topology Leonhard Euler Switzerland 1707  1783 T h e c i t y Theorem: There are infinitely many prime numbers. Proof: Suppose the opposite, that is, that there are a finite number of prime numbers. Call them p 1 , p 2 , p 3 , p 4 ,.... ,p n . Now consider the number (p 1 *p 2 *p 3 *...*p n )+1 Every prime number, when divided into this number, leaves a remainder of one. So this number has no prime factors (remember, by assumption, it's not prime itself). This is a contradiction. Thus there must, in fact, be infinitely many primes. Infinite Prime Numbers Euclid Greece 325 265BC The Search for Pi Person/People Year Value Babylonians ~2000 B.C. 3 1/8 Egyptians ~2000 B.C. (16/9)^2= 3.1605 Archimedes Italy ~300 B.C. proves 3 10/71<Pi<3 1/7 uses 211875/67441=3.14163 Ptolemy Greece ~200 A.D. 377/120=3.14166. .. Tsu ChungChi  China ~500 A.D. proves 3.1415926<Pi<3.1415929 Aryabhatta Indian ~500 3.1416 Fibonacci Italy 1220 3.141818 Ludolph van Ceulen  German 1596 Calculates Pi to 35 decimal places Machin England 1706 100 decimal places CDC 6600 1967 500,000 decimal places Franois Vite (15401603) France  determined that: John Wallis (16161703) English  showed that: While Euler (17071783) Switzerland derived his famous formula: Today Pi is known to more than 10 billion decimal places. The Search for Pi Ancient Babylonia The Sumerians had developed an abstract form of writing based on cuneiform (i.e. wedgeshaped) symbols. Their symbols were written on wet clay tablets which were baked in the hot sun and many thousands of these tablets have survived to this day. It was the use of a stylus on a clay medium that led to the use of cuneiform symbols since curved lines could not be drawn. The later Babylonians adopted the same style of cuneiform writing on clay tablets. The Babylonians had an advanced number system, in some ways more advanced than our present systems. It was a ways more advanced than our present systems....
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This note was uploaded on 11/11/2011 for the course MATH 112 taught by Professor Jarvis during the Winter '08 term at BYU.
 Winter '08
 JARVIS
 Math

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