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  1. 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
  2. Famous Geometrical Theorems And Problems: With Their History (1900) by William Whitehead Rupert, 2010-09-10
  3. 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)
  4. Geometry growing;: Early and later proofs of famous theorems by William Richard Ransom, 1961
  6. THE WORLD'S MOST FAMOUS MATH PROBLEM. [The Proof of Fermat's Last Theorem & Othe by Marilyn Vos Savant, 1993-01-01
  7. 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
  8. 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

1. 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.
Quadratic Curves ( Conics ) There are the curve which appears when cone is cut in the plane which doesn't contain a vertex with rigth circular cone.
We knows these conics by names found in Apollonius (BC 247?-205?).



Famous Theorems in Plane Geometry When it was the 19th century, the geometrical nature of Conics was researched as the development of projective geometry.The followings are intimate relations of conics.



2. Famous Theories
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. A presentation of one of the most famous theorems ever solved.
document.write('<');document.write('! '); home hypographies links quizzes ... about Tuesday, March 18, 2003 Not logged in Famous Theories
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
Last updated September 14 2001
Viewed 4895 times.
Kepler's Conjecture is all about packing spheres into a box. Do you think it is a worthy topic for scientific study?

Most of us have heard about these theories, or at least some of them. But although they may be famous, they are not necessarily easy to understand.
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.
Another great idea is Drake's Equation, which is meant to show that there is a good possibility that there are aliens out there. It is perhaps the least scientific of all the ideas we feature below, but it is also much easier to understand than the rest. Not to mention Fermat's Last Theorem, of course, which haunted mathematicians for ages until it was finally proven in the 1990s.

3. Gödel's Theorems And Truth
Gödel's Theorems and Truth Author Dan Graves Subject Mathematics Probability Famed mathematician Kurt Gödel proved two extraordinary theorems. His two famous theorems changed mathematics, logic, and even the way we look at our universe.
Gödel's Theorems and Truth Author: Dan Graves
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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".

4. Famous Theorems/Developments
famous theorems/Developments. Proofs of the Pythagorean Theorem
Famous Theorems/Developments
Proofs of the Pythagorean Theorem Commensurability and the Problem of Irrational Numbers Regular Polyhedra Golden Ratio Conic Sections Methods of Computing The Fundamental Theorem of Arithmetic Development of Plane Trigonometry Development of Spherical Trigonometry Development of Analytical Geometry Development of Probability Theory Fermat’s Last Theorem Fundamental Theorem of Algebra The Fundamental Theorem of Calculus Development of Non-Euclidean Geometry Development of Set Theory

5. Mathematicians
Mathematicians Guide picks. Everything you wanted to know about mathematicians.Biographies, information, famous theorems and women mathematicians.
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Guide picks Everything you wanted to know about mathematicians. Biographies, information, famous theorems and women mathematicians.
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. Algebraists Excellent information about the famous algebraists throughout the centuries. 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.

6. 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
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.
Table of Contents
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.

7. Math Forum - Mathematics Teacher Bibliography: Circles
A Unification Of Two famous theorems From Classical Geometry Eli Maor Looks atthe product of the lengths of segments of intersecting secants of a circle.
Mathematics Teacher
Geometry Bibliography: Circles
Hubert Ludwig, Ball State University
Back to Geometry Bibliography: Contents

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8. Proseminar II, SS 03
Chapter 20 Buffon's needle problem. Chapter 21,6 Sperner's Lemma (and the Brouwerfixed point theorem); Chapter 22 Three famous theorems on finite sets.

Proseminar II - Analysis and Geometry
SS 03, in English, Mondays, 11:40-13:20, S1 03/12
The book
The Proseminar is based on an attractive book: Proofs from THE BOOK by M. Aigner and G. Ziegler; make sure you get the second edition (Springer 2001). In the preface, the authors explain what made them to collect the material for the 32 self-contained chapters, and they explain the title: Paul Erdos liked to talk about The Book , in which God maintains the perfect proofs for mathematical theorems. [...] We have no ... characterization of what constitutes a proof from The Book ; all we offer here is examples ..., hoping that our readers will share our enthusiasm about brilliant ideas, clever insights, and wonderful observations. [...] A limiting factor for our selection of topics was that everything in this book is supposed to be accessible to readers whose backgrounds include only a modest amount of technique... A little linear algebra, some basic analysis [...] should be sufficient to understand and enjoy everything in this book.
The main goal is a good presentation. The chapters leave room for a choice of material to present: You can select from alternative proofs, skip or add material, present the problem by experiment or with additional examples, build a model to illustrate, etc.

essentially on Bland's 2 minimal index rule. The famous theorems of Farkas, Weyl and Minkowski are proved by using

10. PlanetMath: Three Theorems On Parabolas
By any of many very famous theorems (Euclid book II theorem twentysomething, Cauchy-Schwarz-Bunyakovski (overkill),
Math for the people, by the people. Encyclopedia Books Papers Expositions ... Random Login create new user name: pass: forget your password? Main Menu the math Encyclop¦dia



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Feedback Bug Reports information Docs Classification News Legalese ... TODO List 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 is . The corresponding right-bisector will also pass through and will have slope . Its equation is therefore Equivalently

11. Read This: Proofs From THE BOOK
The section on Combinatorics includes chapters (20) Pigeonhole and double counting,(21) Three famous theorems on finite sets, (22) Cayley's formula for the
Read This!
The MAA Online book review column
Proofs from THE BOOK
by Martin Aigner and Günter M. Ziegler
Reviewed by Mary Shepherd
In the preface of Proofs from THE BOOK , we read that "Paul Erdös often talked about The Book, in which God maintains the perfect proofs of mathematical theorems." As I read through the preface to this book, I began to ask some questions. What constitutes a "beautiful" proof? How about a "perfect" proof? Is there any such thing as a "perfect" proof? I don't know the answer to these questions. This book was inspired by Erdös and contains many of his suggestions. It was to appear in March, 1998 as a present to Erdös on his 85th birthday, but he died in the summer of 1997, so he is not listed as a co-author. Instead the book is dedicated to his memory. In the Number Theory section, the chapters are: (1) Six proofs of the infinity of primes, (2) Bertrand's postulate, (3) Binomial coefficients are (almost) never powers, (4) Representing numbers as sums of two squares, (5) Every finite division ring is a field, and (6) Some irrational numbers. I found most of these chapters to be somewhat difficult, requiring some background in algebra and analysis and even topology to be easily understandable. My favorite of these chapters was (4) because of the simplicity of statement of this theorem by Fermat, and the use of geometry to help visualize part of the solution. There was also a series of annoying but minor errors in chapter (6) in the reductions of the fractions on page 31.

12. Wilson Stothers' Cabri Pages
Classical theorems. Here are some Cabri *.fig files written to illustratefamous theorems of geometry. In each case, the screen shows
Classical theorems
Here are some Cabri *.fig files written to illustrate famous theorems of geometry. In each case, the screen shows how the figure looks in Cabri, but you can't drag the points around!

13. Theorem - Wikipedia
believed to be true but has not been proven is known as a conjecture.See mathematics for a list of famous theorems and conjectures.

14. 1. Introduction
In particularly, we generalized wellknown Classical Waring's Problem, generalizedand proved the famous theorems of Hilbert, Lagrange, Wieferich
]: "... Continuum Hypothesis is a rather dramatic example of what can be called (from our today's point of view) an absolutely undecidable assertion, ..." (p.13). The complete absence of any progress in the Continuum Hypothesis proof (or dispoof) on the way of modern meta-mathematics during last decades confirms the validity of Cohen's pessimism. So, it is obviously that new ways are necessary here. One of such new ways - a NON-meta-mathematical
and NON-mathematical-logic way based on a so-called scientific cognitive computer visualization technique - to a new comprehension of the Continuum Problem itself is offered below.
]. For example, in classical Number Theory (NT) such the main feature giving rise to many famous NT-problems (such as Fermat's, Goldbach's, Waring's problems) is, by B.N.Delone and A.Ya.Hintchin, a hard comprehended connection between two main properties of natural numbers - their additivity and multiplicativity. Nevertheless, by means of CV-approach, we visualized this twice abstract connection in the form of color-musical 2D-images (so-called pythograms) of abstract NT-objects, and obtained really a lot of new NT-results. In particularly, we generalized well-known Classical Waring's Problem, generalized and proved the famous theorems of Hilbert, Lagrange, Wieferich, Balasubramanian, Desouillers, and Dress, discovered a new type of NT-objects, a new universal additive property of the natural numbers and a new method, - the so-called Super-Induction method, - for the rigorous proving of general mathematical statements of the form

15. Math 460 (Senior Seminar) Home Page
and colorful characters who were mathematicians but most of all it's a wellwrittenpresentation of twelve interesting and famous theorems in mathematics.
Math 460 - Senior Seminar - Home Page
Journey through Genius
Instructor: Brian Shelburne 329A Science
Class Meetings: Th 2:10 - 3:40
Text: Journey Through Genius by W. Dunham
Course Objectives
This is a capstone course for mathematics majors. Its purpose is to let you think about and reflect on what mathematics is and to tie together your years of studying mathematics. Dunham's book, Journey Through Genius , covers the story of mathematics from the 5th century B.C.E. up to the 20th Century C.E. by looking at some famous problems and theorems, and the mathematicians who worked on them. The book is many things. It's a selective history of mathematics, it's a look at some of the famous and colorful "characters" who were mathematicians but most of all it's a well-written presentation of twelve interesting and famous theorems in mathematics. Through the twelve theorems, Dunham presents his idea of what makes a theorem great! . The book is well written, fun to read and it will give you a deeper appreciation of the unique endeavor we call mathematics . Enjoy!

16. Brain Teaser-home
new problems. The Famous Mathematician Quiz tests your knowledgeof the authors of famous theorems and formulas. There is also

17. 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
home stands games about ... links Number Theory
Goldbach's Conjecture Fermat's Last Theorem
Gaussian Integers
Prime Numbers
The Sieve of Eratosthenes The Fundamental Theorem of Arithmetic How Many Primes Are There?
An Infinity Of Primes Mersenne Numbers Largest Prime Numbers Famous Theorems
Diophantine Equations
Solving Diophantine Equations
Fermat's Last Theorem
History of the Theorem Proof Of The Theorem
Number Theory
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.
Goldbach's Conjecture
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.

18. Mathematics And Statistics
famous theorems, etc. Theorems are more than just something you haveto memorize in geometry class. They represent Truth in a way
The World of Numbers
This page, like the companion Science page , contains items and links that appeal to me for one reason or another. Here you will find various topics related to mathematics and statistics , including links to reference material, tutorials, Macintosh freeware, and miscellaneous tidbits as well as to other sites like this one. The list is not meant to be comprehensive and the selection is based, as always, on my personal perspective . Thus, this page will always be under construction!
It would be difficult to find any other subject, of comparable relevance and importance, about which so many are so proud of their ignorance. Even the most fastidious individuals, who would never tolerate the unforgivable solecism of a split infinitive, will not hesitate to proclaim, to one and all, their utter inadequacy when it comes to anything pertaining to numbers. This includes activities even as mundane as rescaling a recipe, reading a weather map, or computing the total cost of a mortgage. Tell people that the Sun is far away and they will nod their head and try to look intelligent. Say that it is 93,000,000 miles away and their eyes will start to glaze over as they search for some means of escape. If you are reading this page, then you are likely in that happy minority who know better. Therefore, you might find things here that you will appreciate.

19. Disproving Statements
There are many famous conjectures and famous theorems that were conjectures formany years (The 4 color theorem and Fermat's Last Theorem, for example).
Next: Types of Proof Up: NOTES ON METHODS OF Previous: Definitions and Theorems
Disproving Statements
Some conjectures are false. Verifying that a conjecture is false is often easier than proving a conjecture is true. Despite that, showing a conjecture is false may have its own challenges and usually requires a deep knowledge of the subject. Some statements are often shown to be false by a counter examples . Such statements have the form ``For all x in X conclusion ''. This is shown to be false by finding one element of X which does not satisfy the conclusion. As an example, consider the statement ``For all prime numbers p p +1 is prime''. This statement is true for the primes 2, 3 and 5. It is also true for the primes 11 and 23. However, the statement is an assertion for all primes. Clearly the statement is not true for the prime 7 (since 15 = 3 5) and we have obtained a counter example to the statement. For finite sets, statements of the form such as ``There exists an x such that conclusion '' can be refuted by example. By testing each element of the set and showing no element satisfies the conclusion we have shown the statement is false through an

20. Goedels Theorem
Pseudoaxiomatic definitions. Pseudo-philosophers The set of self-appointedphilosophers who abuse famous theorems to prove hobby horses are real.

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