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Famous Theorems: more detail

The World's Most Famous Math Problem: The Proof of Fermat's Last Theorem and Other Mathematical Mysteries by Marilyn vos Savant, 1993-10-15
Famous Geometrical Theorems And Problems: With Their History (1900) by William Whitehead Rupert, 2010-09-10
Evidence Obtained That Space Between Stars Not Transparent / New Method Measures Speed of Electrons in Dense Solids / Activity of Pituitary Gland Basis of Test for Pregnancy / Famous Old Theorem Solved After Lapse of 300 Years (Science News Letter, Volume 20, Number 545, September 19, 1931)
Geometry growing;: Early and later proofs of famous theorems by William Richard Ransom, 1961
THE WORLD'S MOST FAMOUS MATH PROBLEM THE PROOF OF FERMAT'S LAST THEOREM ETC. by Marilyn Vos Savant, 1993-01-01
THE WORLD'S MOST FAMOUS MATH PROBLEM. [The Proof of Fermat's Last Theorem & Othe by Marilyn Vos Savant, 1993-01-01
Famous Problems of Elementary Geometry / From Determinant to Sensor / Introduction to Combinatory Analysis / Fermat's Last Theorem by F., W.F. Sheppard, P.A. Macmahon, & L.J. Mordell Klein, 1962
Famous Problems, Other Monographs: Famous Problems of Elementary Geometry (Klein); From Determinant to Tensor (Sheppard); Introduction to Cominatory Analysis (Macmahon); Three Lectures on Fermat's Last Theorem (Mordell) by Sheppard, Macmahon, And Mordell Klein, 1962

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Mathematicians
Famous mathematicians and biographies. Everything you wanted to know about mathematicians. Biographies, information, famous theorems and women mathematicians. An alphabetized index of the famous mathematicians.
http://math.about.com/cs/mathematicians

Extractions: zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Homework Help Mathematics Mathematicians Home Essentials Grade By Grade Goals Math Formulas ... Math Tutors zau(256,152,145,'gob','http://z.about.com/5/ad/go.htm?gs='+gs,''); Math Help and Tutorials Math Formulas Math Lesson Plans Math Tutors ... Help zau(256,138,125,'el','http://z.about.com/0/ip/417/0.htm','');w(xb+xb); Subscribe to the About Mathematics newsletter. Search Mathematics Everything you wanted to know about mathematicians. Biographies, information, famous theorems and women mathematicians. Alphabetical Recent 135 of the Most Popular Mathematician Biographies Pictures, biographies, birthplace locations and famous findings and writings. 17th and 18th Century Mathematicians The lives and the works of the mathmaticians for the 17th and 18th century. Chronological Index of Mathematicians Mathematicians dating back as far as 1680 BC! An alphabetized index of the famous mathematicians. Chronology of Mathematicians Mathematicians by category: 650BC - 1960. Math through the ages of the Greek, Dark Ages, Renaissance to the 20th century. Current Mathematicians A growing list of mathematicians, biographies and the work they have done or are currently doing.
Gödel's Theorems And Truth
Essays by Author. Essays by Subject. Essays by Date. Summary. Famed mathematician Kurt Gödel proved two extraordinary theorems. His two famous theorems changed mathematics, logic, and even the way we
http://www.rae.org/godel.html

Extractions: Essays by Date Summary Famed mathematician Kurt Gödel proved two extraordinary theorems. Accepted by all mathematicians, they have revolutionized mathematics, showing that mathematical truth is more than logic and computation. Does Gödel's work imply that someone or something transcends the universe? Truth and Provability Kurt Gödel has been called the most important logician since Aristotle.(1) Such praise is evidence of how seriously Gödel's ideas are taken by mathematicians. His two famous theorems changed mathematics, logic, and even the way we look at our universe. This article explains what Gödel proved and why it matters to Christians. But first we must set the stage. A very simple formal system cannot support number theory but such a system is easily proven to be self-consistent. All we have to do is to show that it can't make a silly proof such as A=Non-A, which would be like saying 2=17. To handle number theory a complex formal system is needed. But as systems get more complex, they are harder to prove consistent. One result is that we don't know if our number theories are sound or if there are contradictions hidden in them. Gödel worked with such problems. He especially studied undecidable statements. An undecidable statement is one which can neither be proven true nor false in a formal system. Gödel proved that any formal system deep enough to support number theory has at least one undecidable statement.(2) Even if we know that the statement is true, the system cannot prove it. This means the system is incomplete. For this reason, Gödel's first proof is called "the incompleteness theorem".
Famous Theorems In Plane Geometry By Cabri
We knows these conics by names found in Apollonius (BC 247?205?).Ellipse Hyperbola Parabola famous theorems in Plane Geometry.
http://www.f.waseda.jp/takezawa/mathenglish/geometry.htm
Math Forum: Famous Problems In The History Of Mathematics
History of mathematics presented through famous problems, with some exercises and their solutions. Done in conjunction with the Math Forum, the home of Ask Dr. Math. Famous Paradoxes In the history of mathematical thought, several paradoxes have challenged the notion One of the most famous theorems in mathematics, the Pythagorean theorem has
http://mathforum.com/~isaac/mathhist.html

Extractions: A Math Forum Project Mathematics has been vital to the development of civilization; from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. As a result, the history of mathematics has become an important study; hundreds of books, papers, and web pages have addressed the subject in a variety of different ways. The purpose of this site is to present a small portion of the history of mathematics through an investigation of some of the great problems that have inspired mathematicians throughout the ages. Included are problems that are suitable for middle school and high school math students, with links to solutions, as well as links to mathematicians' biographies and other math history sites. WARNING: Some of the links on the page in this site lead to other math history sites. In particular, whenever a mathematician's name is highlighted, you can follow it to link to his biography in the MacTutor archives. The Bridges of Konigsberg - This problem inspired the great Swiss mathematician Leonard Euler to create graph theory, which led to the development of topology. The Value of Pi - Throughout the history of civilization various mathematicians have been concerned with discovering the value of and different expressions for the ratio of the circumference of a circle to its diameter.
Math Forum: Famous Problems In The History Of Mathematics
A Proof of the Pythagorean Theorem One of the most famous theoremsin mathematics, the Pythagorean theorem has many proofs. Presented
http://mathforum.org/isaac/mathhist.html

Extractions: A Math Forum Project Mathematics has been vital to the development of civilization; from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. As a result, the history of mathematics has become an important study; hundreds of books, papers, and web pages have addressed the subject in a variety of different ways. The purpose of this site is to present a small portion of the history of mathematics through an investigation of some of the great problems that have inspired mathematicians throughout the ages. Included are problems that are suitable for middle school and high school math students, with links to solutions, as well as links to mathematicians' biographies and other math history sites. WARNING: Some of the links on the page in this site lead to other math history sites. In particular, whenever a mathematician's name is highlighted, you can follow it to link to his biography in the MacTutor archives. The Bridges of Konigsberg - This problem inspired the great Swiss mathematician Leonard Euler to create graph theory, which led to the development of topology. The Value of Pi - Throughout the history of civilization various mathematicians have been concerned with discovering the value of and different expressions for the ratio of the circumference of a circle to its diameter.
Society For Philosophy And Technology - Volume 2, Numbers 3-4
paper I discuss whether Gödel's incompleteness theorems have any implications for studies in completeness and consistency that Gödel is worried about in his famous theorems
http://scholar.lib.vt.edu/ejournals/SPT/v2n3n4/sullins.html

Extractions: Editor: Davis Baird bairdd@gwm.sc.edu Spring-Summer 1997 Volume 2 Numbers 3-4 DLA Ejournal Home SPT Home Table of Contents for this issue Search SPT and other ejournals John P. Sullins III, San Jose State University It is not my purpose to rehash these argument in terms of Cognitive Science. Rather my project here is to look at the two incompleteness theorems and apply them to the field of AL. This seems to be a reasonable project as AL has often been compared and contrasted to AI ( Sober, 1992 Keeley, 1994 ); and since there is clearly an overlap between the two studies, criticisms of one might apply to the other. We must also keep in mind that not all criticisms of AI can be automatically applied to AL; the two fields of study may be similar but they are not the same ( Keeley, 1994 Wang, 1987, pg. 197 ). In fact there is an interesting argument posed by Rudy Rucker where he shows that it is possible to construct a Lucas style argument using the incompleteness theorems which actually suggests the possibility of creating machine minds ( Rucker, 1983, pp. 315-317
Famous Theories
last theorem http//wwwgroups.dcs.st-and.ac.uk/~history/HistTopics/Fermat s_last_theorem.htmlA presentation of one of the most famous theorems ever solved.
http://www.hypography.com/topics/famoustheories.cfm

Extractions: Ads_kid=0;Ads_bid=0;Ads_xl=0;Ads_yl=0;Ads_xp='';Ads_yp='';Ads_opt=0;Ads_wrd='';Ads_prf='';Ads_par='';Ads_cnturl='';Ads_sec=0;Ads_channels='Pop'; Ads_kid=0;Ads_bid=0;Ads_xl=468;Ads_yl=60;Ads_xp='';Ads_yp='';Ads_opt=0;Ads_wrd='';Ads_prf='';Ads_par='';Ads_cnturl='';Ads_sec=0;Ads_channels='Full'; Hypography Science sites Amazon.com Hypographies From a theory of incompleteness to how to pack spheres in a box: this week we feature ten of the most famous theories in modern history. Created by Tormod Guldvog Take Kepler's Conjecture, for example. It simply states that there is an ultimate way to pack spheres into a box. It has taken centuries of experiments and calculations to show that there are in fact an endless number of ways to do it - and scientists have yet to prove that there is one way which is better than the others.
Hypography Science Search: Theory,equation,formula
URL http//www.hypography.com/info.cfm?id=18035 10KB - 16 May 2004 2. Fermat slast theorem A presentation of one of the most famous theorems ever solved.
http://www.hypography.com/searchresults.cfm?query_string=theory,equation,formula
Mathematics - Reference Library
Applied Mathematics. Mechanics Numerical analysis Optimization Probability Statistics Financial mathematics. famous theorems and Conjectures.
http://www.campusprogram.com/reference/en/wikipedia/m/ma/mathematics.html

Extractions: Main Page See live article Alphabetical index Mathematics is commonly defined as the study of patterns of structure, change , and space ; more informally, one might say it is the study of 'figures and numbers'. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation ; other views are described in Philosophy of mathematics The specific structures that are investigated by mathematicians often have their origin in the natural sciences , most commonly in physics , but mathematicians also define and investigate structures for reasons purely internal to mathematics, because the structures may provide, for instance, a unifying generalization for several subfields, or a helpful tool for common calculations. Finally, many mathematicians study the areas they do for purely aesthetic reasons, viewing mathematics as an art form rather than as a practical or applied science Mathematics is often abbreviated to math in North America and maths in other English-speaking countries.
GODEL'S THEOREMS AND TRUTH
GODEL'S THEOREMS AND TRUTH. By Daniel Graves, MSL. Summary. Famed mathematician Kurt Godel proved two extraordinary theorems. His two famous theorems changed mathematics, logic, and even the way
http://www.evanwiggs.com/articles/GODEL.html

Extractions: GODEL'S THEOREMS AND TRUTH By Daniel Graves, MSL Summary Famed mathematician Kurt Godel proved two extraordinary theorems. Accepted by all mathematicians, they have revolutionized mathematics, showing that mathematical truth is more than logic and computation. Does Godel's work imply that someone or something transcends the universe? Truth and Provability Kurt Godel has been called the most important logician since Aristotle.(1) Such praise is evidence of how seriously Godel's ideas are taken by mathematicians. His two famous theorems changed mathematics, logic, and even the way we look at our universe. This article explains what Godel proved and why it matters to Christians. But first we must set the stage. A very simple formal system cannot support number theory but such a system is easily proven to be self-consistent. All we have to do is to show that it can't make a silly proof such as A=Non-A, which would be like saying 2=17. To handle number theory a complex formal system is needed. But as systems get more complex, they are harder to prove consistent. One result is that we don't know if our number theories are sound or if there are contradictions hidden in them. Godel worked with such problems. He especially studied undecidable statements. An undecidable statement is one which can neither be proven true nor false in a formal system. Godel proved that any formal system deep enough to support number theory has at least one undecidable statement.(2) Even if we know that the statement is true, the system cannot prove it. This means the system is incomplete. For this reason, Godel's first proof is called "the incompleteness theorem".
WTHS Mathematics Links
Calculus, Biographers, Math Help Desk, famous theorems, Test Prep Central, Mathematicians, Pure Biographers, Math Help Desk, famous theorems, Test Prep Central, Mathematicians, Pure
http://www.wtps.org/links/math.htm
Theorem - Wikipedia, The Free Encyclopedia
Of course, the distinction between theorems and lemmas is rather arbitrary, since one mathematics for a list of famous theorems and conjectures. Gödel's incompleteness theorem
http://en.wikipedia.org/wiki/Theorem

Extractions: A theorem is a statement which can be proven true within some logical framework. Proving theorems is a central activity of mathematics . Note that 'theorem' is distinct from ' theory A theorem generally has a set-up - a number of conditions , which may be listed in the theorem or described beforehand. Then it has a conclusion - a mathematical statement which is true under the given set up. The proof, though necessary to the statement's classification as a theorem is not considered part of the theorem. In general mathematics a statement must be interesting or important in some way to be called a theorem. Less important statements are called: lemma : a statement that forms part of the proof of a larger theorem. Of course, the distinction between theorems and lemmas is rather arbitrary, since one mathematician's major result is another's minor claim. Gauss' Lemma and Zorn's Lemma , for example, are interesting enough per se for some authors to stop at the nominal lemma without going on to use that result in any "major" theorem. corollary : a statement which follows immediately or very simply from a theorem. A proposition
Introduction To Arithmetic: Number Theory; Prime Numbers, Fermat Theorem, Goldba
An Infinity Of Primes Mersenne Numbers Largest Prime Numbers famous theorems DiophantineEquations Solving Diophantine Equations Fermat s Last Theorem History
http://www.geocities.com/mathfair2002/school/arit/arithm3.htm

Extractions: History of the Theorem Proof Of The Theorem Number theory is the branch of mathematics concerned with studying the properties and relations of integers. Many of these problems are concerned with the properties of prime numbers. Number theory also includes the study of irrational numbers, transcendental numbers, Diophantine equations, and continued fractions. There are a number of branches of number theory, including algebraic number theory, analytic number theory, geometric number theory, and probabilistic number theory. Algebraic number theory is the study of numbers that are the roots of polynomial equations with integer coefficients, and includes the study of Gaussian integers. One of the most famous problems in number theory is Goldbach's conjecture, proposed in 1742 by Christian Goldbach (1690-1764), the Prussian-born number theorist and analyst, in a letter to Leonhard Euler. Goldbach's conjecture states that any even number greater than or equal to 6 can be expressed as the sum of two odd prime numbers (for example, 6 = 3 + 3, 8 = 5 + 3, 48 = 29 + 19). Although there is every reason to believe that this conjecture is true, and computers have been used to verify it for some very large numbers, it has never been proved. Goldbach's conjecture is a good example of the way in which a problem in number theory can be stated very simply yet be very difficult to solve.
Goedels Theorem
Pseudoaxiomatic definitions. Pseudo-philosophers The set of self-appointedphilosophers who abuse famous theorems to prove hobby horses are real.
http://c2.com/cgi/wiki?GoedelsTheorem
The Pythagorean Theorem
In this session, you will look at a few proofs and several applications ofone of the most famous theorems in mathematics the Pythagorean theorem.
http://www.learner.org/channel/courses/learningmath/geometry/session6/

Extractions: In this session, you will look at a few proofs and several applications of one of the most famous theorems in mathematics: the Pythagorean theorem. Proof is an essential part of mathematics, and what separates it from other sciences. Mathematicians start from assumptions and definitions, then follow logical steps to draw conclusions. If the assumptions are correct and the steps are indeed logical, then the result can be trusted and used to prove further results. When a result has been proved, it becomes a theorem. For information on required and/or optional materials for this session, see Note 1
AllRefer Encyclopedia - Theorem (Mathematics) - Encyclopedia
There are many famous theorems in mathematics, often known by the name of theirdiscoverer, eg, the Pythagorean Theorem, concerning right triangles.
http://reference.allrefer.com/encyclopedia/T/theorem.html

Extractions: By Alphabet : Encyclopedia A-Z T Related Category: Mathematics theorem, in mathematics and logic, statement in words or symbols that can be established by means of deductive logic; it differs from an axiom in that a proof is required for its acceptance. A lemma is a theorem that is demonstrated as an intermediate step in the proof of another, more basic theorem. A corollary is a theorem that follows as a direct consequence of another theorem or an axiom. There are many famous theorems in mathematics, often known by the name of their discoverer, e.g., the Pythagorean Theorem, concerning right triangles. One of the most famous problems of number theory was the proof of Fermat's Last Theorem (see Fermat, Pierre de ); the theorem states that for an integer n greater than 2 the equation x n y n z n admits no solutions where x, y, and z are also integers.
Dirac Notation:
Proof of the Two famous theorems Regarding Hermitian Operators Let q be a HermitianOperator and let 1 and 2 be two eigenfunctions of q with respective
http://people.deas.harvard.edu/~jones/ap216/lectures/ls_2/ls2_u1/dirac_notation/

Extractions: If Q eigenket of the operator Q and a is called the associated eigenvalue A ket is often labelled by its eigenvalues, as Q > = a The completeness postulate y > may be expanded in terms of the eigenkets of Q , as y > = c > + c > + c where the c i y = c *c (with proper normalization) gives the probability that if a measurement of Q is made, the result will be a
Incompleteness Theorem
In response to this challenge Gödel developed his famous theoremsknown as the first and second incompleteness theorems. These
http://www.mtnmath.com/book/node56.html

Extractions: Next: Physics Up: Set theory Previous: Recursive functions Recursive functions are good because we can, at least in theory, compute them for any parameter in a finite number of steps. As a practical matter being recursive may be less significant. It is easy to come up with algorithms that are computable only in a theoretical sense. The number of steps to compute them in practice makes such computations impossible. Just as recursive functions are good things decidable formal systems are good things. In such a system one can decide the truth value of any statement in a finite number of mechanical steps. Hilbert first proposed that a decidable system for all mathematics be developed. and that the system be proven to be consistent by what Hilbert described as `finitary' methods.[ ]. He went on to show that it is impossible for such systems to decide their own consistency unless they are inconsistent. Note an inconsistent system can decide every proposition because every statement and its negation is deducible. When I talk about a proposition being decidable I always mean decidable in a consistent system. S he is working with a statement that says ``I am unprovable in S''(128)[ ]. Of course if this statement is provable in
ThinkQuest : Library : Math For Morons Like Us
a Greek scholar who lived way back in the 6th century BC (back when Bob Dole waslearning geometry), came up with one of the most famous theorems ever, the
http://library.thinkquest.org/20991/geo/stri.html

Extractions: Index Math Have you ever been stuck on math? If it was a question on algebra, geometry, or calculus, you might want to check out this site. It's all here from pre-algebra to calculus. You'll find tutorials, sample problems, and quizzes. There's even a question submittal section, if you're still stuck. A formula database gives quick access and explanations to all those tricky formulas. Languages: English. Visit Site 1998 ThinkQuest Internet Challenge Languages English Students J. Robert Davis High School Library, Kaysville, UT, United States John Davis High School Library, Kaysville, UT, United States Garrett Davis High School Library, Kaysville, UT, United States Coaches Jeff Davis High School Library, Kaysville, UT, United States Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy
PlanetMath: Three Theorems On Parabolas
Equivalently,. By any of many very famous theorems (Euclid book II theorem twentysomething,Cauchy-Schwarz-Bunyakovski (overkill), differential calculus, what
http://planetmath.org/encyclopedia/ThreeTheoremsOnParabolas.html

Extractions: three theorems on parabolas (Topic) In the Cartesian plane, pick a point with coordinates (subtle hint!) and construct (1) the set of segments joining with the points , and (2) the set of right-bisectors of the segments The envelope described by the lines of the set is a parabola with -axis as directrix and focal length We're lucky in that we don't need a fancy definition of envelope; considering a line to be a set of points it's just the boundary of the set Strategy fix an coordinate and find the max/minimum of possible 's in C with that . But first we'll pick an from by picking a point on the axis. The midpoint of the segment through is . Also, the slope of this

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