tag:blogger.com,1999:blog-362699732021-04-21T17:06:02.573-05:00The Mathematical TouristMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.comBlogger1863125tag:blogger.com,1999:blog-36269973.post-63179148598872248302021-04-21T17:06:00.000-05:002021-04-21T17:06:02.242-05:00Diamond Back Chair (for Imperial Hotel, Tokyo, Japan) by Frank Lloyd Wright. Virginia Museum of Fine Arts, Richmond, Virginia, 2017.Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-43093266756036270652021-04-20T15:15:00.000-05:002021-04-20T15:15:33.020-05:00Wrong-Way Yield Atalaya Trail, Santa Fe, New Mexico, 2021.Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-24615890230400071822021-04-17T14:43:00.001-05:002021-04-20T15:15:47.023-05:00Stained Glass Stained-glass window by Jacques Grüber. Virginia Museum of Fine Arts, Richmond, Virginia, 2017.Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-24339130517143966992021-04-16T07:00:00.002-05:002021-04-20T15:16:03.755-05:00Window Geometry Two windows for the Avery Coonley Playhouse in Riverside, Illinois, by Frank Lloyd Wright. Virginia Museum of Fine Arts, Richmond, Virginia, 2017.See also "Wright Window."Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-42586730876946591892021-04-15T14:39:00.001-05:002021-04-20T15:16:16.182-05:00Double Curve Double Curve by Ellsworth Kelly. Minneapolis Sculpture Garden, Walker Art Center, Minneapolis, Minnesota, 2010.See also "Folded Disk" and "Stele II."Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-45448735456133528502021-04-13T07:00:00.044-05:002021-04-20T15:16:33.087-05:00Fibonacci Matrix in Bronze Fibonacci Matrix (miniature) by Helaman Ferguson.See also "Hyperbolic Five," "Minimal Snow," "Hyperbolic Quilt," "UmbilicTorus, Writ Large," "Double Torus Stonehenge," "Four Canoes," "Fractal Drum," "Torus with Cross-Cap," "Eightfold Way," and "Barn Studio." Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-27311242502345573582021-04-12T14:49:00.002-05:002021-04-20T15:16:46.993-05:00Round Head Watercarrier by Allan Houser (detail). Santa Fe Botanical Garden, Santa Fe, New Mexico, 2021.See also "Water Carrier" and "Welcome Ramada."Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-69719197972935268592021-03-18T12:58:00.000-05:002021-03-18T12:58:47.853-05:00How to Prove a Theorem So No One Else Can Claim ItThe trouble with sitting down at a computer keyboard to enter a password is that someone may be looking over your shoulder. Because your password could be stolen as you type it, the computer system isn't completely secure.But if you could somehow provide the computer with information that persuades the computer you know the password without actually giving away the password itself, you would be Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-79740222925245979312021-03-16T14:17:00.000-05:002021-03-16T14:17:33.121-05:00Form Plus FunctionNestled beside a national wildlife refuge, the Noyes Museum of Art in Oceanville, N.J., seemed an unlikely place for an exhibit featuring art rooted in mathematical concepts. Nonetheless, in 2006, its galleries (now closed at this location) featured works by four contemporary artists whose art had a strong mathematical element.The Noyes Museum of Art in Oceanville, N.J. Photo by I. Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-22094829905814238402021-03-15T17:29:00.001-05:002021-03-16T14:19:00.918-05:00Fractal Roots and Artful MathThe term "mathematical art" for many people might conjure up images of M.C. Escher's endless staircases, Möbius-strip ants, and mind-boggling tilings. Or it might remind you of the intimate intertwining of mathematics and art during the Renaissance with the development of perspective painting and eye-teasing stagecraft.A view of the groundbreaking 2002 MathArt/ArtMath show at the Selby Gallery inMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-15688121832579375302021-03-14T14:12:00.002-05:002021-03-16T14:19:53.219-05:00Quilting PiWhen John Sims contemplates a number, he sees color and shape. And an intriguing, enigmatic number such as pi, the ratio of a circle's circumference to its diameter, conjures up vivid patterns that belong on quilts.Starting with 3.14159265, the decimal digits of pi run on forever, and there's no discernible pattern to ease the task of compiling (or memorizing) these digits. Computer scientists Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-68956721165633355172021-03-10T08:00:00.015-05:002021-03-10T08:00:12.709-05:00Welcome Ramada Ramada, Welcome Garden, Santa Fe Botanical Garden, Santa Fe Botanical Garden, Santa Fe, New Mexico, 2021.Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-65514380256996462462021-03-09T08:00:00.022-05:002021-03-09T08:00:04.392-05:00Mountain Spirits Dance of the Mountain Spirits I (detail) by Allan Houser. Santa Fe Botanical Garden, Santa Fe, New Mexico, 2021.Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-53380355154852336592021-03-08T08:00:00.031-05:002021-03-08T08:00:09.388-05:00Iced Claret Cup Claret cup cactus (Echinocereus triglochidiatus), Santa Fe Botanical Garden, Santa Fe, New Mexico, 2021.Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-6357854952141221302021-03-07T16:15:00.000-05:002021-03-07T16:15:15.371-05:00Moon Shot Santa Fe, New Mexico, 2021.Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-60444137240228539912021-03-03T14:53:00.000-05:002021-03-03T14:53:08.547-05:00Patterns and RandomnessWhen we see patterns—whether in the arrangement of stars in the sky (see "Spying Pi in the Sky") or in the distribution of guests at a dinner party (see "Party Games")—we are constantly tempted to think of these patterns as existing for a purpose and being the effect of a cause. Ramsey's theorem (see "Playing Fields of Logic") suggests otherwise. Patterns can, and indeed must, arise out of pure Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-22035566731578519752021-03-01T15:13:00.004-05:002021-03-03T14:53:55.194-05:00Group Thoughts Mathematical research is generally thought to be a solitary pursuit. You might even imagine a mathematician squirreled away in a dingy garret, an isolated wilderness cabin, or a sparsely appointed cubicle, thinking deeply, scrawling inscrutable equations across scraps of paper, to emerge from a self-imposed exile at last with a proof in hand.A few mathematicians do spend their professional livesMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-52260466840492532522021-02-25T17:00:00.000-05:002021-02-25T17:00:28.151-05:00Dartboard EstimatesThrowing darts at a target may sound like a curiously haphazard way to solve a mathematical problem. Properly applied as a kind of intelligent guessing, however, it can become a highly effective technique for obtaining answers to certain problems in Ramsey theory (see "Playing Fields of Logic") and in other areas of mathematics.Suppose that instead of the usual rings and diagonals, a dartboard Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-9064047423424434272021-02-24T17:11:00.001-05:002021-02-24T17:11:47.173-05:00Puzzling Groups and Ramsey NumbersThroughout his long, itinerant life, Paul Erdős (1913-1996) spent most of his waking hours and, apparently, all his sleeping hours doing mathematics. He was a superb problem solver, and his phenomenal memory allowed him to cite exact references to thousands of mathematical papers, including their page numbers."If you don't know how to attack a particular problem, ask Erdős" was the constant Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-44018464973181561622021-02-22T16:46:00.001-05:002021-02-24T17:12:56.958-05:00Planes of BudapestNearly every Sunday during the winter of 1933 in Budapest, a small group of students would meet somewhere in the city at a park or cafe to discuss mathematics. The gathering typically included Paul Erdős (1913-1996), George Szekeres (1911-2005), and Esther Klein (1910-2005).In addition to feeding their passion for mathematics, the students enjoyed exchanging personal gossip and talking politics. Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-68654458989738488712021-02-21T13:38:00.001-05:002021-02-21T23:53:49.660-05:00Playing Fields of LogicRamsey theory owes it name to Frank Plumpton Ramsey, an English mathematician, philosopher, and economist. His father, Arthur Stanley Ramsey, was a professor of mathematics and the president of Magdalene College at the University of Cambridge.Frank Ramsey (1903-1930). MAA Convergence Portrait Gallery.Frank Ramsey was born in 1903 and spent nearly his entire life in Cambridge. After he graduated Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-35939085301487429532021-02-18T14:13:00.000-05:002021-02-18T14:13:46.026-05:00Pigeonhole CongestionSorting the mail that comes into an office generally requires that each piece be slipped into the appropriate slot of an array of pigeonholes—one for each employee. Suppose that a small business needs ten such slots. When 11 pieces of mail arrive, one or more of the slots will have to contain at least two items.So, if there are more pigeons than holes, some of the pigeons have to double up. Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-56335232185614888332021-02-11T17:25:00.001-05:002021-02-11T17:38:46.109-05:00The Long RunQuite often, in a race game governed strictly by chance, the player who starts out ahead stays ahead for most, if not all, of the race. This striking feature is worth examining more closely.In a two-player coin-flipping game, heads and tails will each win half the time, on average (see "Rolls and Flips"). But in a game of a thousand flips, when the total number of heads versus the total number ofMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-69256124278160340942021-02-09T13:26:00.000-05:002021-02-09T13:26:49.723-05:00Change of Face The serious gamblers in casinos hang out at the craps tables. The basic rules of this two-dice game are simple, but the bewildering array of options for betting on various outcomes creates a fast-paced, insidiously seductive pastime, in which a heady brew of chance, intuition, experience, calculation, and superstition come into play.The shooter tosses two dice. If a total of seven or eleven Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-21721613048327263272021-02-08T13:36:00.000-05:002021-02-08T13:36:21.251-05:00Climbing and SlidingThe origins of the game of Chutes and Ladders (or its Snakes and Ladders counterpart) go back many centuries to India and a board game called moksha patam (a Hindu concept that is akin to heaven and hell). Designed as a way of instructing children in religious values, the game graphically depicts the coexistence of good and evil and illustrates the impact of chance on human affairs.In the game, Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0