{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HistoryofMaths

# HistoryofMaths - The History of Mathematics...

This preview shows pages 1–10. Sign up to view the full content.

The History of Mathematics http://www-groups.dcs.st-and.ac.uk/~history/BiogIndex.html http://www.math.wichita.edu/~richardson/timeline.html http://www-groups.dcs.st-and.ac.uk/~history/Indexes/HistoryTopics.html

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
x 2 + 10 x = 39 x 2 + 10 x + 4· 25 / 4 = 39+25 (x+5) 2 = 64 x + 5 = 8 x = 3 al-Khwarizm i  Iraq  (c a. 780-850) Completing a Square Solving a Quadratic Equation
In Ko nig s be rg , G e rm any, a rive r ran thro ug h the  c ity s uc h  that in its  c e ntre  was  an is land, and afte r pas s ing  the   is land, the  rive r bro ke  into  two  parts . S e ve n bridg e s  we re   built s o  that the  pe o ple  o f the  c ity c o uld g e t fro m  o ne  part  to  ano the r.  The  pe o ple  wo nde re d whe the r o r no t o ne  c o uld walk  aro und the  c ity in a way that wo uld invo lve  c ro s s ing  e ac h  bridg e  e xac tly o nc e The Bridges of Konigsberg Topology Leonhard Euler Switzerland 1707 - 1783

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The city
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 Chung-Chi - 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
François Viète (1540-1603) France - determined that: John Wallis (1616-1703) English - showed that: While Euler (1707-1783) Switzerland derived his famous formula: Today Pi is known to more than 10 billion decimal places. The Search for Pi

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Ancient Babylonia The Sumerians had developed an abstract form of writing  based on cuneiform (i.e. wedge-shaped) 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  positional system with a base of 60 rather than the system  with base 10 in widespread use today.  Laura T
The Four Colour Conjecture  was first stated just over  150 years ago, and finally  proved conclusively in 1976.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}