tag:blogger.com,1999:blog-362699732020-10-26T07:00:03.212-05:00The Mathematical TouristMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.comBlogger1788125tag:blogger.com,1999:blog-36269973.post-38682030342970259852020-10-26T07:00:00.011-05:002020-10-26T07:00:02.951-05:00WestportWestport, Ontario, 1992.Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-81876874012003086202020-10-25T07:00:00.001-05:002020-10-25T07:00:02.341-05:00Geometry out of Latvia and AfricaBoth of my parents were born and grew up in the tiny Baltic country of Latvia. I remember, as a young child in northern Ontario, intently watching my father painstakingly color in tiny squares of a grid to create a symmetric design. Using yarn and needle, my mother would then transfer that geometric pattern to cloth, creating a wall hanging, a pillow cover, or some other decorative Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-414045647435367542020-10-24T07:00:00.018-05:002020-10-24T07:00:08.784-05:00Aspen Gold Aspen Vista trail, Santa Fe National Forest, New Mexico, 2020.Photos by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-49051463075448399612020-10-23T07:00:00.005-05:002020-10-23T07:00:00.601-05:00Moebius ScarfMöbius Scarf by Cliff Stoll.A Möbius strip is a one-sided, one-edged surface. You can make one by giving a strip of paper a half-twist, then taping the ends together. The scarf is knitted so that it forms a loop with one continuous surface.See also "Immersed in Klein Bottles" and "Folding a Klein Bottle."Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-73410122548731572502020-10-22T07:00:00.009-05:002020-10-22T07:00:03.258-05:00Icosahedral Slices1,2 Icosahedron by Steve Morse.The icosahedron is one of the five Platonic solids. Its twenty faces are equilateral triangles, with five meeting at each corner. In the model above, each face is further divided into six congruent 30-60-90 triangles, for a total of 120 triangles. The model is constructed from 15 slotted rings lying in 15 planes.Photos by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-75247138676755794392020-10-21T07:00:00.033-05:002020-10-21T07:00:06.157-05:00Purse of FortunatusFortunatus X by Susan Goldstine.According to legend, the purse of Fortunatus continually replenished itself as coins were withdrawn from it.A story by Lewis Carroll (Charles L. Dodgson) describes how to make such a purse from four handkerchiefs. The resulting form is a model of a topological structure known as the projective plane.A projective plane can be constructed by gluing both pairs of Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-8554098419783205312020-10-20T07:00:00.000-05:002020-10-20T07:00:07.101-05:00Medieval HarmonyPhilippe de Vitry (1291-1361) was one of the most prominent figures in medieval music. He was the author of an important music theory text, Ars Nova, which introduced new rhythmic schemes and musical notation. He had a deep knowledge of philosophy, rhetoric, and mathematics.In many ways, de Vitry's interests and accomplishments reflected the Pythagorean view that music is a subdivision of Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-38756985690863273062020-10-19T07:00:00.146-05:002020-10-19T07:00:06.472-05:00Moebius AccordionIn 2001, artist Susan Happersett came up with a novel twist on the venerable Möbius strip: a playful, eye-catching creation she described as a Möbius accordion.The Happersett Accordion by Susan Happersett.A Möbius strip, or band, is the remarkable one-sided surface that results from joining together the two ends of a long strip of paper after twisting one end 180 degrees. Mathematicians, Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-22751211394992141952020-10-18T07:00:00.029-05:002020-10-18T07:00:04.244-05:00Pierre Elliott Trudeau (1919-2000)Prime Minister Pierre Elliott Trudeau (1919-2000) (with Marion McGaw), Liberal Party of Canada reception, Ottawa, Ontario, 1970.Photo by I. PetersonPierre Trudeau autograph, Toronto, Ontario, 1970.Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-23961343644053069822020-10-17T07:00:00.017-05:002020-10-17T07:00:02.127-05:00Alpha 'n' Beta IMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-88981371188294467602020-10-16T07:00:00.099-05:002020-10-16T07:00:05.450-05:00A Magic Knight's TourFor as long as the game of chess has existed, there have been puzzles involving chessboards and chess pieces. Some of the most enduring conundrums have involved knights.According to the rules of chess, a knight makes an L-shaped move that shifts its position by a single square in one direction and two squares in a perpendicular direction. Indeed, the knight is the only chess piece that covers an Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-57684923211421479622020-10-15T07:00:00.065-05:002020-10-15T07:00:06.878-05:00Geometry in CourtThe TV series Numb3rs highlighted how mathematics can play a role in solving crimes.Even though the episodes were sometimes rather fanciful, they still illustrated ways in which various types of math can help illuminate mysteries, confirm conjectures, and point to villains.In real life, math can also be relevant in the courtroom or come up in legal disputes.In 2005, the Pythagorean theorem was a Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-90874277533719919532020-10-14T07:00:00.001-05:002020-10-14T07:00:04.659-05:00Morning HikeBlack Canyon trail, Santa Fe National Forest, New Mexico, 2020.Photo by N. HendersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-73246991517468133022020-10-13T07:00:00.226-05:002020-10-13T07:00:10.053-05:00Mastering MastermindGames offer wonderful playing fields for developing mathematical problem-solving skills.For educator Mathew Mitchell, the preferred training ground is a classic game called Mastermind. "Students young and old are fascinated by simple yet challenging games," he wrote in his book Mastermind Mathematics: Logic, Strategies, and Proofs.Mastermind involves hypothesis testing and deductive reasoning, Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-79274916406761282182020-10-12T07:00:00.080-05:002020-10-12T07:00:02.450-05:00Absolutely AbnormalIdentifying the normal (or even the abnormal) in mathematics can pose serious difficulties.In 1909, mathematician Émile Borel (1871-1956) introduced the concept of normality as one way to characterize the resemblance between the digits of a mathematical constant such as pi (the ratio of a circle's circumference to its diameter) and a sequence of random numbers.Émile Borel. MAA Convergence Photo Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-50735505898578823242020-10-11T07:00:00.074-05:002020-10-11T07:00:04.805-05:00Probabilities in BingoOne of the little pleasures of our annual winter vacation is an evening Bingo party. After a day of sledding and cross-country skiing, it's relaxing to indulge in a social game that requires minimal thought, affords young and old the same chance of winning, and has a strong element of suspense.To play Bingo, each player has one or more cards divided into squares. Each card has five rows and five Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-19909155465866884312020-10-10T07:00:00.145-05:002020-10-10T07:00:02.586-05:00Testing for DivisibilityThe crisp new dollar bill that I have just taken from my wallet bears the serial number 24598176. It's easy to tell that the number is exactly divisible by 2 but not by 5. Is it divisible by 3? by 4? by 11? In a 1962 Scientific American article, Martin Gardner noted that during the 15th and 16th centuries in Renaissance Europe, the rules for checking whether one number is divisible by another Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-50373283418802771102020-10-09T07:00:00.078-05:002020-10-09T07:00:03.953-05:00Playing Pig OptimallyThe simple dice game known as Pig is surprisingly complex when you're trying to find an optimal strategy for playing it.The game's object is to be the first player, rolling a die, to reach a total of 100 points. On each turn, a player rolls a die as many times as he or she wishes, totaling the score of the rolls until the player decides to end the turn and pass the die to his or her Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-63670858165612677812020-10-08T07:00:00.122-05:002020-10-08T07:00:07.412-05:00A Measure of BeautyMathematician George David Birkhoff (1884–1944) is best known for his work on differential equations and dynamics. His ergodic theorem gave the kinetic theory of gases a rigorous basis. He solved important problems in celestial mechanics and made contributions to the mathematical foundations of relativity theory and quantum mechanics.Birkhoff also had a keen interest in aesthetics—the qualities Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-92133459931789462102020-10-07T07:00:00.100-05:002020-10-07T07:00:04.502-05:00Squaring CirclesThere's no telling where thoughts about a seemingly simple, even trivial, question may lead.Consider the problem of turning a circle into a square. Cut a circle out of a sheet of paper. Then cut the circle into pieces so that the pieces, when fitted back together, form a square having the same area as the original circle.The task seems impossible: How do you get rid of the curves?But there is a Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-23534731461965951612020-10-06T07:00:00.017-05:002020-10-06T07:00:11.688-05:00Cubic Star RedStar by Bob Sidenberg. Mathematical Art Exhibit, Joint Mathematics Meetings, Boston, 2012.See also "Quarthead."Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-24356540825439973302020-10-05T07:00:00.029-05:002020-10-05T07:00:05.010-05:00Torus Eversion Symmetrical Half-way Point for Torus Eversion by Carlo Sequin. Mathematical Art Exhibit, Joint Mathematics Meetings, Boston, 2012.See also "Borromean Twists," "Borromean Soap Film," and "Trefoil Klein-Knottle"Photos by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-31598510686949313952020-10-04T07:00:00.021-05:002020-10-04T07:00:02.286-05:00Round Moebius Round Möbius Strip by Harry Segerman. Mathematical Art Exhibit, Joint Mathematics Meetings, Boston, 2012.Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-5081153559285666282020-10-03T07:00:00.038-05:002020-10-03T07:00:05.878-05:00Beaded Star Weaves Beaded Star Weaves: Five Bracelets by Gwen Fisher. Mathematical Art Exhibit, Joint Mathematics Meetings, Boston, 2010.See also "A Tetrix at Burning Man," "Symmetries of Beaded Beads," "Beady Deltahedron," and "Chaos and Order in Beads." Photos by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-58237075307930371142020-10-02T07:00:00.019-05:002020-10-02T07:00:01.618-05:00Magic Square Still LifeStill Life with Magic Square by Sylvia Donmoyer. Mathematical Art Exhibit, Joint Mathematics Meetings, Boston, 2012.Photos by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0