21. Math Forum - Ask Dr. Math Unsolvable and unsolved problems. Date 02/19/98 at 181657 From DJitsu Subject11th Grade Research Paper Dear Dr. math, I need help getting started on a http://mathforum.org/library/drmath/view/52540.html

Associated Topics Dr. Math Home Search Dr. Math Unsolvable and Unsolved Problems Date: 02/19/98 at 18:16:57 From: D-Jitsu Subject: 11th Grade Research Paper Dear Dr. Math, I need help getting started on a research paper, as well as on doing the project. The topic of my report is "The Impossible and Unsolved in Mathematics (Goldbach's Conjecture, Squaring the Circle, etc.). I was just wondering if I could get some references, tips, or ideas on how to get started. This is for a pre-calculus class. http://ug.cs.dal.ca/~campbell/colllink.html http://mathforum.org/dr.math/ Associated Topics High School History/Biography High School Number Theory Search the Dr. Math Library: Find items containing (put spaces between keywords): Click only once for faster results: [ Choose "whole words" when searching for a word like age. all keywords, in any order at least one, that exact phrase parts of words whole words Submit your own question to Dr. Math Math Forum Home Math Library Quick Reference ... Math Forum Search Ask Dr. Math TM http://mathforum.org/dr.math/

22. About "Unsolved Problems In Function Theory" unsolved problems in Function Theory. Library Home Full Table of Contents Suggest a Link Library Help Visit this site http//www.math.purdue.edu http://mathforum.org/library/view/16365.html

Unsolved Problems in Function Theory Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.math.purdue.edu/~eremenko/uns.html Author: Alexandre Eremenko Description: Files available in PDF format: Some constants studied by Littlewood; Meromorphic functions satisfying certain differential equations (E. Hille); Does every universe contain a place where you can stay at rest? (Lee Rubel); Holomorphic curves with few inflection points; Exceptional set in Gross' Theorem; Modified Cartan's Conjecture. Levels: College Research Languages: English Resource Types: Problems/Puzzles Math Topics: Functional Analysis Suggestion Box Home The Math Library ... Search http://mathforum.org/ webmaster@mathforum.org

23. Deniz Yuret - Math > Unsolved unsolved Home math unsolved. These are the 24 problems from the wonderful book Old and new unsolved problems in plane geometry and number theory by Victor http://home.ku.edu.tr/~dyuret/math/unsolved.html

Unsolved Home Math These are the 24 problems from the wonderful book "Old and new unsolved problems in plane geometry and number theory" by Victor Klee and Stan Wagon, MAA, 1991. Some problems are too cryptic to understand without the book. I'll type more explanations some day. Plane Geometry Is each reflecting polygonal region illuminable? (Imagine a room in a 2-D universe. If the walls form a polygonal shape and they reflect light, can you always illuminate the whole room with a single light source?) A point P inside a closed convex curve C is called equichordal if every chord of C drawn through point P has the same length. Is there a curve with two equichordal points? (Marek Rychlik kindly informed me of his solution to this problem. His homepage has references for the published work.) When congruent disks are pushed closer together, can the area of their union increase? If a convex body C contains a translate of each plane set of unit diameter, how small can C's area be? What is the smallest number f(n) such that any set of f(n) points (non-collinear) always contains the vertices of some convex n-gon? If n points are not collinear, must one of them lie on at least n/3 connecting lines?

24. Deniz Yuret - Math unsolved Old and new unsolved problems in plane geometry and number theory Theseare the problems from the MAA Related links A collection of math links. http://home.ku.edu.tr/~dyuret/math/

Deniz Yuret's Math Problems Home Please mail any interesting problems you find to deniz.yuret@alum.mit.edu . I cited the people I heard the problems from, they are not necessarily the originators. The unsolved flag just means that the problem is yet unsolved by me. Send me a solution if you find one. Problems This is a list of elementary problems I like for one reason or another from various branches of mathematics. Probability twisters Click here for a number of problems that will puzzle your probabilistic intuition. These are my favorites. Choose between several different arguments that lead to different answers for each problem. Unsolved Old and new unsolved problems in plane geometry and number theory: These are the problems from the MAA book by Victor Klee and Stan Wagon (1991). Related links A collection of math links. Sun Jan 12 13:05:39 EET 2003

25. Math Education: Newsletter: MFIN 2.22, MathPro Unsolved Problems URL Change Hi . Tony Thrall very kindly points out that the URL given in this week's MathForum Internet News for the MathPro unsolved problems archive breaks. http://www.math.yorku.ca/Who/Faculty/Monette/MathEd/0011.html

Newsletter: MFIN 2.22, MathPro Unsolved Problems URL change Sarah Seastone ( sarah@forum.swarthmore.edu Sat, 31 May 1997 22:28:40 -0400 (EDT) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Sarah Seastone: "Newsletter: Math Forum Internet News No. 2.23 (June 9)" Previous message: Sarah Seastone: "Newsletter: Math Forum Internet News No. 2.22 (June 2)" Hi - Tony Thrall very kindly points out that the URL given in this week's Math Forum Internet News for the MathPro Unsolved Problems archive breaks. MathPro seems to have updated its site this week and I didn't re-check the URL before I e-mailed the newsletter. I should know better. Here's the updated information: (2) UNSOLVED PROBLEM OF THE WEEK ARCHIVE - MATHPRO PRESS http://www.mathpro.com/math/puzzles/unsolvedMathProblems/archive.html Postings of some difficult yet interesting problems that mathematicians are investigating, with references to more information about the topics. http://www.mathpro.com/math/puzzles/unsolvedMathProblems/references.html Although these problems can be understood by the average person, mathematicians have been unsuccessfully working

26. Math Education: Newsletter: Math Forum Internet News No. 2.22 (June 2) MathPro unsolved problems URL change ; Previous message Sarah Seastone NewsletterMath Forum Internet News, No. 2.19 (May 12) . 2 June 1997 Vol.2, No.22. http://www.math.yorku.ca/Who/Faculty/Monette/MathEd/0010.html

Newsletter: Math Forum Internet News No. 2.22 (June 2) Sarah Seastone ( sarah@forum.swarthmore.edu Sat, 31 May 1997 19:23:29 -0400 (EDT) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Sarah Seastone: "Newsletter: MFIN 2.22, MathPro Unsolved Problems URL change" Previous message: Sarah Seastone: "Newsletter: Math Forum Internet News, No. 2.19 (May 12)" 2 June 1997 Vol.2, No.22 THE MATH FORUM INTERNET NEWS From the CONNECTED CURRICULUM PROJECT MATHEMATICAL MODELING IN A REAL AND COMPLEX WORLD by Frank Wattenberg http://ascc.carroll.edu/ccp/modeling/topic.htm "Among the first customers for a new car are engineers from competing companies. They need to know what their competition is doing and how. One of the most important tools for figuring out how a competitor's product works is reverse engineering. Engineers have a general idea of the tools used by their competitors and they can use their own ideas to try to reconstruct what competing engineers have done. This course is about modeling, or reverse

27. My Favorite Open Problems unsolved problems from Bondy and Murty. see my math links page forlinks to other sites with unsolved problems. Back to my homepage. http://www.math.princeton.edu/~matdevos/open/open.html

Open Problems in Discrete Math Prizes Flows on Graphs Tutte's 3-flow, 4-flow, and 5-flow conjectures The 2+epsilon flow conjecture Jaeger's modular orientation conjecture Bouchet's 6-flow conjecture ... Unit vector flows Cycle Covers The cycle double cover conjecture The circular embedding conjecture Conjectures on (m,n)-cycle-covers Faithful circuit covers ... Circuit decompositions of Eulerian graphs Choosability for Ax=y A nowhere-zero point in a linear mapping The additive basis conjecture The permanent conjecture The Alon-Tarsi basis conjecture Edge Coloring The Berge-Fulkerson conjecture The Petersen coloring conjecture Packing T-joins Acyclic edge-coloring ... Conjectures on edge-connectivity Vertex Coloring Homomorphisms of planar graphs Homomorphisms to the circuit of length 5 Directed Graphs Seymour's second neighborhood conjecture Reversing edges in digraphs Packing dijoins Topological Graph Theory Grunbaum's conjecture Embedding digraphs Conway's thrackle conjecture Matroid Theory Bases of many weights Stable bases Additive Number Theory Kneser's critical problem Sets with distinct subset sums Miscellaneous Problems The lonely runner conjecture please feel free to email me if you know of unmentioned progress (possibly a solution) to any of these problems.

28. Sci.math FAQ: Unsolved Problems Vorherige Nächste Index sci.math FAQ unsolved problems. Subject sci.mathFAQ unsolved problems; From alopezo@neumann.uwaterloo.ca (Alex Lopez-Ortiz); http://www.uni-giessen.de/faq/archiv/sci-math-faq.unsolvedproblems/msg00000.html

Index sci.math FAQ: Unsolved Problems Subject : sci.math FAQ: Unsolved Problems From alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz) Date : Fri, 17 Nov 1995 17:15:13 GMT Newsgroups sci.math sci.answers news.answers Sender news@undergrad.math.uwaterloo.ca (news spool owner) Summary : Part 18 of many, New version, Index: Index sci-math-faq.unsolvedproblems

29. Mathematical Problems In various subjects, compiled by Torsten Sillke.Category Science math Research Open problems...... or the diameter of GL(n,F2); Combinatorial Games unsolved problems (by RK OftenShould You Beat Your Kids; Expectation Linearity - problems solved by math-News. http://www.mathematik.uni-bielefeld.de/~sillke/problems.html

Mathematical Problems Graph Theory Stable sets - The number of stable/independent sets of a graph Planar Graphs - Special embeddings of planar graphs Graph Parameter - The Rank and the Chromatic Number Cograph (P4 free Graphs) - Graphs with maximal rank Nordhaus type question - eigenvalues Number Theory Lucas-Lehmer series - Factors and Period length Partial anwers: K Brown 1 K Brown 3 Chapman Some Properties of the Lucas Sequence (2,4,14,52,194,...) of Kevin Brown Reputnics - when are they squares? (Chris Thompson) x^3 + y^3 + z^3 - Representations by sum of Cubes (Noam Elkies) FLT++ - x^r + y^s = z^t Combinatorics Hadamard Matrices - Maximizing Determinants - M. Hudelson, V. Klee, D. Larman; Largest j-Simplices in d-Cubes: Some Relatives of the Hadamard Maximum Determinant Problem (1996) GKL - P. Gritzmann, V. Klee, D. Larman; Largest j-Simplices in n-Polytopes (unpublished) A Library of Hadamard Matrices - N. J. A. Sloane Grid-avoidance problems - A collection of problems Gray Codes - Gray Codes with few Tracks Distance Sets - Sets with equal Distances register swap - or the diameter of GL(n,F2)

30. NZ problems. mathFAQ) The Hilbert ~ (from the math-FAQ) mathematics of Knots (elementary)The trisection of an angle (from the math-FAQ) unsolved ~ (from the http://cage.rug.ac.be/~hvernaev/catN-Z.html

The Math Catalog: N-Z A-M N-Z Newsgroups sci.math sci.math.num-analysis sci.math.research sci.math.symbolic Nonstandard Analysis Homepages of Nonstandard Analysis People (a local version is behind this button) Number Theory Some Web-sources Prime Numbers: from the Math-FAQ Caldwell's List of the Largest ~ Primality tests (a local version is behind this button) Mersenne-primes (a local version is behind this button) Short history (elementary introduction to number theory) Fermat's Last Theorem (FLT): from the Math-FAQ from the University of St Andrews a (Dutch) newspaper-article a DVI-file : introduction to FLT Probability of 2 numbers being coprime Fibonacci numbers and the Golden Section Olympiads International Mathematical Olympiad IMO-problems (1959 - now) International Mathematical Olympiad 1993-96 Dutch IMO-site (with info about other Math Olympiads, too) Math competitions archive Math problems archive Argentina Math Olympiad Bulgarian Math Olympiad ... Estonian Math Olympiad (Estonian) Flanders Math Olympiad (VWO) Iberoamerican Math Olympiad (Spanish) Irish Math Olympiad Italian Math Olympiad (Italian) Mexican Math Olympiad (Spanish) Dutch Math Olympiad Norwegian Math Olympiad (`Niels Henrik Abels matematikk-konkurranse') Polish Math Olympiad Romanian Math Olympiad Singaporean IMO-team South-African IMO-team ... Russian Math Olympiad An excerpt from questions (mostly) from the Dutch Math Olympiad (Dutch) See also: Contests Organisations A list of ~ American Mathematical Society (AMS) Canadian Mathematical Electronic Services (Camel)

31. F. Conjectures (Math 413, Number Theory) A collection of easily stated conjectures which are still open. Each conjecture is stated along with Category Science math Number Theory Open problems......F. Conjectures. Number Theory, math 413, Fall 1998. Refs unsolved problems, Klee Wagon, 1991, Sect 17; Elementary Number Theory, Jones Jones, 1998, Chap 9; http://www.math.umbc.edu/~campbell/Math413Fall98/Conjectures.html

F. Conjectures Number Theory, Math 413, Fall 1998 A collection of easily stated number theory conjectures which are still open. Each conjecture is stated along with a collection of accessible references. The Riemann Hypothesis Fermat Numbers Goldbach's Conjecture Catalan's Conjecture ... The Collatz Problem The Riemann Hypothesis Def: Riemann's Zeta function, Z(s), is defined as the analytic extension of sum n infty n s Thm: Z( s )=prod i infty p i s , where p i is the i th prime. Conj: The only zeros of Z( s ) are at s s Thm: The Riemann Conjecture is equivalent to the conjecture that for some constant c x )-li( x c sqrt( x )ln( x where pi( x ) is the prime counting function. Refs: Unsolved Problems Elementary Number Theory http://www.utm.edu/research/primes/notes/rh.html (notes in Chris Caldwell's Prime Pages) http://match.stanford.edu/rh/ (Dan Bump's notes) Def: n is perfect if it is equal to the sum of its divisors (except itself). Examples are 6=1+2+3, 28, 496, 8128, ... Def: The n th Mersenne Number, M n , is defined by M n n Thm: M n is prime implies that n n is perfect. (Euclid)

32. Unsolved Problems Hi! We're E and Pi, here to introduce you to Jon Bettencourt's webpage on unsolved math problems. It's his final project for COSMOS http://www.geocities.com/jonrelay/cosmos/

Hi! We're E and Pi, here to introduce you to Jon Bettencourt's web page on unsolved math problems. It's his final project for COSMOS, the math and science program he's in. Is he going to be surprised when he sees what we've done! Our favorite problem is the one about e (pi* n) being close to integers, since it involves us! Although Pi says she likes the formula for any digit of pi better (of course). To which Jon responds... I'm gonna get them for this! If E and Pi keep messing with this page, I'll have to get Bromine to get them off my back, and I know they don't want that! More information on E and Pi (the characters, not the numbers) Anyway, I have been gathering information on unsolved problems from the Internet and other sources. Here are a few of the problems I have found and some information on some of them. Some of these problems seem very simple, but end up with no simple proof or solution to them. As an example, Fermat's Last Theorem was very simple, but it took hundreds of years and some parts from very advanced branches of mathematics to solve it. So if one seems simple, don't try to solve it unless you know a lot of math. More information about unsolved problems can be found with a search for unsolved problems on Google.com

33. Maine Math Talent Search : Math Links unsolved problems; Meeroh's math problems; Interactive problems; mathOracle; math contests; unsolved math problems; math olympiad; Ask http://www.geocities.com/CollegePark/Center/1539/p89.htm

Math Education A must site for teachers MegaMathematics K-12 fun room Links to math education Links to great math topics ... Digital education on the net Computers and Mathematics Waterloo Maple software Symbolic computation Math software Math online ... Mathematics on the internet Problem Solving Famous problems Alphametrics Word problems for kids Online math problems ... Solving word problems History, Foundations, Logic History of mathematics Zermelo-Fraenkel axioms Goedel's theorem (hyper-textbook) Liar's paradox ... Notable women in mathematics Applied Mathematics Math in technology? Minnesota Research Associates Dynamics and complex variables Mathematics/Genome Project ... Mathematics and artificial intelligence General Math Links Math Net Math search Math organizations Cornell math gateway ... Canadian mathematical society Miscellaneous Jobs in mathematics The abacus Careers in mathematics Works of great mathematicians ... Interactive statistics Algebra, Number Theory Abstract algebra Continued fractions Prime number research Fun with numbers ... Algebraic number theory Geometry, Topology Geometry and topology examples Applications of Geometry Oswald Veblen Euler's formula ... Geometry and geneology Univ of Maine Math Courses General Service Courses Analysis Statistics Logic, Foundations, History

34. MATH-abundance More than 400 math problems in 1 file unsolved math problems. InternetCenter for mathematics problems. Many other math links. mathematics http://www.jct.ac.il/science/math/MathAbundance/

MATH-abundance Main Purpose = MATH TUTORIAL TUTORIAL : Topics; Solved and unsolved problems Math links to links to math links ... Other Tutorials ... Many other math links J.C.'s Math Home Page = http://www.ping.be/math e-mail: Johan.Claeys@ping.be Last update: 4 dec 1997 Main Purpose = MATH TUTORIAL The main purpose of this site is to provide the net with a 'upper secondary' MATH TUTORIAL The order of the topics is not random. Most of them appeal on the properties and formulas stated in previous pages. Download Since each topic is in 1 file, it is easy to download the file and to study the subject off line. See Copying Conditions TUTORIAL : Topics; Solved and unsolved problems Trigonometry Vectors Lines - orthogonality ; distance (in a plane) Complex numbers ... Miscellaneous Problems about all topics Additionally, I can give a number of math links to math related links to math links... Math links to links to math links ... Other Tutorials Lessons, Tutorials and Lecture Notes Teaching Materials Calculus Resources On-line Graphing Calculators JAVA and Other Interactive WWW Pages Mathematics and the Liberal Arts Sites with K-12 Teaching Materials in Mathematics Visual Calculus Other solved and unsolved problems on the net.

35. Mathematical Problems - Problem Solving - Mathematical Competitions (Math Links mathematics Hots (problems) by Bruno KeviusCategory Science math Recreations...... by subtracting squares (Dean Hickerson and Michael Kleber); Shack's math problemsby Michael Shackleford, ASA; unsolved mathematics problems mathsoft; unsolved http://www.abc.se/~m9847/matre/problem.html

Mathematical Resources Math Links by Bruno Kevius This list is continually under development Mathematical Problems - Problem Solving Mathematical Competitions not a complete list, only what I happened to see... The 3x+1 problem and its generalizations The 3x+1 problem, also known as the Collatz problem, the Syracuse problem, Kakutani's problem, Hasse's algorithm, and Ulam's problem by Jeff Lagarias 21st Century Problem Solving Solutions to solving word problems across the curriculum. (SureMath - hawaii.edu) Algebra Story and Word Problems A collection of simple algebra word problems (SureMath: 21st Century Problem Solving) Algebrator - an Algebra Problem Solver for Students and Teachers ALVIRNE HIGH SCHOOL PROBLEM OF THE WEEK SITE Andrei Jorza's Home Page Calculus Problems Alvirne High School in Hudson, N.H. The Cereal Box Problem by George Reese A Collection of Math-Olympiad-Problems by Hans Vernaeve Countries with Mathematical Olympiad Websites - Links to Mathematical Olympiad Websites. CRUX Mathematicorium Online The Digital Supplement to the Canadian Mathematical Society's Problem Solving Journal Ken Duisenberg's Puzzle of the Week Elementary Problem of the Week by Ruth Carver (MathForum) Fermat's Last Theorem Flanders Mathematics Olympiad The Goal Angle Problem Hilbert's Tenth Problem by Karlis Podnieks Paul Erdos: An I nfinity of Problems - Ivars Peterson (MathLand) International Mathematical Olympiad / Olympiade internationale ... International Mathematics Olympiad (IMO) Eindhoven University of Technology

36. Unsolved Math Problems unsolved math problems unsolved mathematics problems mathsoft providesan archive of unsolved math problems plus links to related sites. http://westford.mec.edu/schools/tips/unsolved.htm

Unsolved Math Problems Unsolved Mathematics Problems Mathsoft provides an archive of unsolved math problems plus links to related sites. http://www.mathsoft.com/asolve/index.html There are really impossible things ... This site includes slider puzzles as well as many other mind-numbing puzzles. http://www.cut-the-knot.com/impossible/index.html CICA Project Fermat The animation presents a popularized introduction to Fermat's Last Theorem. Three dimensional mathematical depictions are used in the beginning of the film to illustrate the meaning of the mathematical ideas involved. The second half of the film makes a transition to show a remarkable family of four dimensional surfaces related to Fermat's theorem, and projects them to three dimensions for display using standard rendering and shading techniques. http://www.cica.indiana.edu/projects/Fermat/index.html Unsolved Problems Here you'll find Goldbach's and Collatz's conjectures and the number of twin primes. http://abel.math.umu.se/~frankw/unsolved.html

37. Unsolved Problems References. unsolved problems in Number Theory. Richard K Guy. Springer, ProblemE16. GT Leavens and M. Vermeulen 3x+1 search programs Comput. math. Appl. http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node30.html

Next: Mathematical Games Up: Famous Problems in Mathematics Previous: Which are the 23 Unsolved Problems Does there exist a number that is perfect and odd? A given number is perfect if it is equal to the sum of all its proper divisors. This question was first posed by Euclid in ancient Greece. This question is still open. Euler proved that if N is an odd perfect number, then in the prime power decomposition of N , exactly one exponent is congruent to 1 mod 4 and all the other exponents are even. Furthermore, the prime occurring to an odd power must itself be congruent to 1 mod 4. A sketch of the proof appears in Exercise 87, page 203 of Underwood Dudley's Elementary Number Theory. It has been shown that there are no odd perfect numbers Collatz Problem Take any natural number n : = m; repeat n is odd) then n : = 3*n + 1 ; else n : = n/2 until ( n==1 Conjecture 1. For all positive integers m, the program above terminates. The conjecture has been verified for all numbers up to References Unsolved Problems in Number Theory.

38. Unsolved Problems next up previous contents Next Does there exist a Up Famous problemsin Mathematics Previous Which are the. unsolved problems. http://db.uwaterloo.ca/~alopez-o/math-faq/node59.html

Next: Does there exist a Up: Famous Problems in Mathematics Previous: Which are the Unsolved Problems Does there exist a number that is perfect and odd? Collatz Problem Goldbach's conjecture Twin primes conjecture Alex Lopez-Ortiz Mon Feb 23 16:26:48 EST 1998

39. The State News - Www.statenews.com Leonard Ford at Wells Hall. math problems left unsolved By LESLIE ESCOBARThe State News. When journalism freshman Marshall Weinbaum http://www.statenews.com/article.phtml?pk=7165

40. Math Digest This article concerns the legacy of unsolved problems that Erdos leftbehind and the cash prizes associated with those problems. http://www.ams.org/new-in-math/mathdigest/200205-erdos.html

Mathematical Digest Short Summaries of Articles about Mathematics in the Popular Press "Erdos's Hard-To-Win Prizes Still Draw Bounty Hunters," by Charles Seife. Science, 5 April 2002, pages 39-40. Paul Erdos, with an output of more than 1500 papers during his lifetime, has had 62 papers bearing his name published since his death. This article concerns the legacy of unsolved problems that Erdos left behind and the cash prizes associated with those problems. People who solve a problem receive a cash award, the size of which depends on the difficulty of the problem. In 1993, Ron Graham had Erdos sign some of Graham's checks "to be filled out later." These checks are intended as souvenirs for those who solve a problem, but Graham also sends out real checks (bearing his signature). He has sent out about $3000 so far and estimates that the remainder of the unsolved problems have awards totalling about $25,000. The article concludes with a quote from Graham regarding Erdos' unsolved problems: "These problems serve as Socratic gadflies, reminding us of how much we have to learn." - Mike Breen

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