[math-fun] Puzzles that led to new areas of science
I'm writing an article for an upcoming special issue of Discover magazine (in Dec) devoted to puzzles. The article will be about puzzles that led to new developments in math or science. For example, solving the Bridges of Könisburg led Euler to the development of topology. I prefer examples where the puzzle statement and the solution are accessible to a lay audience, and want to include some examples that have very recent implications...for instance even though Könisburg is an old problem, there might be a recent application of Euler circuits that are newsworthy now. Anyone have any thoughts? -- Scott Kim
If by newsworthy you mean related to current events, you probably won't find much of what you are looking for. But if by newsworthy you mean having interesting effects in modern daily life, and hence the stuff of an interesting article, you will probably find more. The four-color theorem pops to mind, though I don't know of applications (real modern political maps tend to use 5 or more colors). ----- Original Message ----- From: "Scott Kim" <scott@scottkim.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Sunday, September 23, 2007 2:11 AM Subject: [math-fun] Puzzles that led to new areas of science I'm writing an article for an upcoming special issue of Discover magazine (in Dec) devoted to puzzles. The article will be about puzzles that led to new developments in math or science. For example, solving the Bridges of Könisburg led Euler to the development of topology. I prefer examples where the puzzle statement and the solution are accessible to a lay audience, and want to include some examples that have very recent implications...for instance even though Könisburg is an old problem, there might be a recent application of Euler circuits that are newsworthy now. Anyone have any thoughts? -- Scott Kim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun -- No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.5.488 / Virus Database: 269.13.28/1021 - Release Date: 9/21/2007 2:02 PM
Cryptography, an area of science based on puzzles? Christian. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de David Wilson Envoyé : dimanche 23 septembre 2007 10:56 À : math-fun Objet : Re: [math-fun] Puzzles that led to new areas of science If by newsworthy you mean related to current events, you probably won't find much of what you are looking for. But if by newsworthy you mean having interesting effects in modern daily life, and hence the stuff of an interesting article, you will probably find more. The four-color theorem pops to mind, though I don't know of applications (real modern political maps tend to use 5 or more colors). ----- Original Message ----- From: "Scott Kim" <scott@scottkim.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Sunday, September 23, 2007 2:11 AM Subject: [math-fun] Puzzles that led to new areas of science I'm writing an article for an upcoming special issue of Discover magazine (in Dec) devoted to puzzles. The article will be about puzzles that led to new developments in math or science. For example, solving the Bridges of Könisburg led Euler to the development of topology. I prefer examples where the puzzle statement and the solution are accessible to a lay audience, and want to include some examples that have very recent implications...for instance even though Könisburg is an old problem, there might be a recent application of Euler circuits that are newsworthy now. Anyone have any thoughts? -- Scott Kim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun -- No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.5.488 / Virus Database: 269.13.28/1021 - Release Date: 9/21/2007 2:02 PM _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Knight tours and Hamiltonian circuits could be added to the list (traveling salesman problem, etc.) Loren ----- Original Message ----- From: "Scott Kim" <scott@scottkim.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Sunday, September 23, 2007 1:11 AM Subject: [math-fun] Puzzles that led to new areas of science I'm writing an article for an upcoming special issue of Discover magazine (in Dec) devoted to puzzles. The article will be about puzzles that led to new developments in math or science. For example, solving the Bridges of Könisburg led Euler to the development of topology. I prefer examples where the puzzle statement and the solution are accessible to a lay audience, and want to include some examples that have very recent implications...for instance even though Könisburg is an old problem, there might be a recent application of Euler circuits that are newsworthy now. Anyone have any thoughts? -- Scott Kim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I'm writing an article for an upcoming special issue of Discover magazine (in Dec) devoted to puzzles. The article will be about puzzles that led to new developments in math or science. For example, solving the Bridges of Könisburg led Euler to the development of topology. I prefer examples where the puzzle statement and the solution are accessible to a lay audience, and want to include some examples that have very recent implications...for instance even though Könisburg is an old problem, there might be a recent application of Euler circuits that are newsworthy now. Anyone have any thoughts?
I like to think of Goedel's theorems as resulting of a precise formali zation of the "liar's paradox", which is a puzzle of sorts. -- Andy.Latto@pobox.com
Is it true that the Fibonacci numbers were derived as a solution to a puzzle about the total number of rabbits in a herd of rabbits, where the starting state of the herd is a single breeding pair? Or was that an example that Fibonacci wrote up, after the fact? Or is the whole rabbit connection apocryphal, added on by a later day math popularizer like E.T.Bell? In any case, if it is true, and you haven't already thought of it, then it is an example. (Unrelated to math-fun: Is "herd" right? It's the first term that came to my mind, but what's *really* the right term for a group of rabbits? a flock?), Sun, 23 Sep 2007 10:01:23 -0500 "Loren and Liz Larson" <lllarsson@earthlink.net> Knight tours and Hamiltonian circuits could be added to the list (traveling salesman problem, etc.) Loren ----- Original Message ----- From: "Scott Kim" <scott@scottkim.com> Sent: Sunday, September 23, 2007 1:11 AM ... The article will be about puzzles that led to new developments in math or science.
On Sep 23, 2007, at 8:48 AM, greenwald@cis.upenn.edu wrote:
(Unrelated to math-fun: Is "herd" right? It's the first term that came to my mind, but what's *really* the right term for a group of rabbits? a flock?),
According to Wikipedia (http://en.wikipedia.org/wiki/List_of_animal_names ) rabbits may be any of warren, nest, colony, bevy, bury, drove, or trace. Apparently for animals these are referred to as terms of venery. See also http://en.wikipedia.org/wiki/Collective_noun for a more general discussion. Oddly, a quick perusal uncovers no specific word for a collection of collective nouns. I have to assume I've just missed it. And a collection of those words would be...? (JZ)
Hello M. Scott Kim, what about tiling pbs ? Best, E. ________________________________ De: math-fun-bounces@mailman.xmission.com de la part de Scott Kim Date: dim. 23/09/2007 08:11 À: math-fun Objet : [math-fun] Puzzles that led to new areas of science I'm writing an article for an upcoming special issue of Discover magazine (in Dec) devoted to puzzles. The article will be about puzzles that led to new developments in math or science. For example, solving the Bridges of Könisburg led Euler to the development of topology. I prefer examples where the puzzle statement and the solution are accessible to a lay audience, and want to include some examples that have very recent implications...for instance even though Könisburg is an old problem, there might be a recent application of Euler circuits that are newsworthy now. Anyone have any thoughts? -- Scott Kim _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun <http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
Scott, Speaking of "Bridges of Koningsberg", I believe that Euler's solution has had an important application in biology. During a series of talks by Leroy Hood at Penn State around 15 years ago, he mentioned a breakthrough by Pavel Pevzner, then Penn State, now UCSD (http://www.cse.ucsd.edu/~ppevzner/), in which Pevzner applied the Euler path algorithm to genome sequencing chips. Briefly, the genome is cut up with enzimes, the pieces bind to spots on the surface of a microchip, and finally a computer algorithm is used to work out the original sequence. According to what I remember from the lecture, before Pevzner suggested using Euler paths, people had been using Hamiltonian paths for finding the original sequence.... Pevzner's realization apparently made him a lot of money (from coroperate consultation) and accolades. Pevzner might be be an interesting interview for the article. Doug Bowman
I'm writing an article for an upcoming special issue of Discover magazine (in Dec) devoted to puzzles. The article will be about puzzles that led to new developments in math or science. For example, solving the Bridges of Könisburg led Euler to the development of topology. I prefer examples where the puzzle statement and the solution are accessible to a lay audience, and want to include some examples that have very recent implications...for instance even though Könisburg is an old problem, there might be a recent application of Euler circuits that are newsworthy now. Anyone have any thoughts? -- Scott Kim
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1. Solution of the cubic & quartic algebraic equations were "puzzles" circa 1500. 2. Logical problems were parlor games circa 1900. These became the basis of Russell's & Goedel's work. 3. Permutation puzzles in the late 1800's -- Polya's/Burnside's theory of counting, etc. 4. Ropes & knots -- "knot theory" Maxwell, Tait, etc. http://www.southalabama.edu/mathstat/personal_pages/silver/scottish.pdf 5. Weaving & looms -- http://en.wikipedia.org/wiki/Jacquard_loom -- led to Babbage & the Census Bureau & to IBM punch cards. 6. Tiles & tiling & especially Penrose-type tilings. 7. Betting games & problems with infinite variance. Huge amounts of work required to pin down the nature of probability density functions, etc. 8. Mobius strips, Klein bottles, etc., and advances in physics. 9. All sorts of puzzle-like things have been found to lead to undecidability or to "NP-completeness". E.g., "knapsack"-type puzzles. 10. Various games that can be solved with "information theory" -- minimum number of weighings, etc. 11. "Rock, paper, scissors" & non-transitive voting preferences. 12. All kinds of mechanical linkages circa 1900. 13. Number theory was the basis of puzzles circa 2000BCE: http://www.amazon.com/Number-History-Classics-Science-Mathematics/dp/0486656... 14. Visual puzzles / optical delusions, etc. Insight into how the brain works, how robot vision should work, etc. At 11:11 PM 9/22/2007, Scott Kim wrote:
I'm writing an article for an upcoming special issue of Discover magazine (in Dec) devoted to puzzles. The article will be about puzzles that led to new developments in math or science. For example, solving the Bridges of Könisburg led Euler to the development of topology. I prefer examples where the puzzle statement and the solution are accessible to a lay audience, and want to include some examples that have very recent implications...for instance even though Könisburg is an old problem, there might be a recent application of Euler circuits that are newsworthy now. Anyone have any thoughts? -- Scott Kim
On Sat, 22 Sep 2007, Scott Kim wrote:
I'm writing an article for an upcoming special issue of Discover magazine (in
I used a bin packing algorithm to see how big of a trailer my grandmother needed to store her furniture when she moved out of her house. That problem seems to have some puzzle background to it.
participants (11)
-
Andy Latto -
Christian Boyer -
David Wilson -
Douglas Bowman -
Eric Angelini -
greenwald＠cis.upenn.edu -
Henry Baker -
Jason -
Jon Ziegler -
Loren and Liz Larson -
Scott Kim