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Show The Park Record C-12 STROHM ART & ANTIQUES PARK CITY, UT* Web Site www.strohmartandantiques.com WALTER LARSEN ANTIQUE SHOW SANDY CONVENTION CENTER,JUNE I0-II-I2 Fri. & Sat, 11 am - 8pm, Sun 11:00 - 4:00 Victorian Glass, Pickle Castors, Fine Antiques SIGNED PRINTS AND ETCHINGS INCLUDING: Marc Chagall Salvador Dali Joan Miro Vassilly Kandinsky Pablo Picasso OIL PAINTINGS INCLUDING: Maynard Dixon George Ottinger Edward Redfield Robert Wood ALL ITEMS GUARANTEED I FREE ADMISSION TO SHOW WITH THIS AD H, u,p fjtfr tub 7580 fopU Sheet &U Thettt Cmiti (7 $ t l Golden ratio manifests beauty By DOUGLAS BROWN MediaNews Group Wire Service WILL BE EXHIBITING AT THE ) -940-6866 ART. ASK FOR MORE. For more information about the importance of arts education, please contact www.AmericansForTheArts.org. What thrills mathematicians, inspires artists, electrifies authors and has captivated at least one cosmetic surgeon? 1.6180339887. ' The number is phi, also called the golden ratio, the golden section, the golden number and a host of other terms. People have studied, probed, played and nearly worshiped it for at least 2,000 years. They have argued about phi too. Do people enjoy the Mona Lisa, the Greek Parthenon or the smiling face of Cameron Diaz because each revolves around phi? Does phi have anything to do with these exemplars of beauty? Even if it does, could the number somehow take credit for the enthusiastic way people respond to them? The meaning of phi has engaged people around the world for centuries, and the quest charges ahead into the 21st century. Some declare the ratio an instance of mathematics that explains different aspects of existence, including the appreciation of art. Critics embrace the number as a compelling piece of mathematics, but dismiss notions that it underlies anyone's feeling of awe during a long gaze at a van Gogh. Either way, phi is a number unto itself, probably the only ratio with the power to summon and swell its own ideological, spiritual and commercial ecosystems. It beguiles. It surges with simplicity and complexity at the same time. It's an enigma. It inspires. The book "The Da Vinci Code," which has sold more than 25 million copies, fixed on phi. Denver sculptor Theresa Stroup Ferg was in her mid-40s when she first encountered phi. The number charmed her, persuading her to spend the next five years deep in foreign territory - mathematics - in pursuit of a master's degree in integrated sciences at the University of Colorado at Denver. Her master's thesis, which she completed this year, centers on a study of people's' responses to "golden ratio" images. The study, she says, suggests the evidence for connections between the golden ratio, which she calls dynamic symmetry, and art are strong. For the study, she placed series of shapes - like rectangles or stars - in front of volunteers and with each type of shape, one of them would be based on "golden-ratio" proportions. • Study participants were asked to select which rectangle, star and other shapes were the most pleasing. The golden-ratio shapes were the most popular among the participants. "The information from the study helps us to understand that dynamic symmetry exists in nature, as well as in humans, and Pass . things we respond to more powerfully than anything else, Devlin says. But the persistence of people's embrace of phi as aesthetic foundation "says to me that deep in our psyches, we know numbers are very important. They shaped our entire world. Numbers, when they were invented, changed the whole world." There are numbers, however, and then there's phi, the engine behind a blizzard of books, research papers and Web sites, as well as at least smatterings of paintings, sculptures, buildings - even flower arrangements. What is it about phi that has enchanted people since its discovery? Take a line. There will be one spot roughly two-thirds of the way down that will divide the line into golden-ratio proportions. Break the line at the golden ratio spot. Compare the size of the larger line to the whole line _ both pieces as they were before being divided. Now compare the larger of the two lines to the smaller line. The ratios will be the same, an irrational number, one that cannot be captured in a fraction and thus has no end. Digits proceed infinitely after the decimal point, without falling into patterns. One of phi's hallmarks is that its application in the physical world lets things grow and contract infinitely while retaining their geometric proportions. A five-sided star based on phi, for example, will maintain its proportions, regardless of. whether it expands to the size of an elephant or shrinks to the size of an ant. Phi is the only ratio that permits this infinite growth or diminution while keeping shape static. Nautilus shells, the arrangement of seeds in sunflowers and pine cones, DNA molecules _ all of them and many more examples from nature exhibit manifestations of phi. While there are other irrational numbers, few if any are as compelling as phi. "The golden ratio is an irrational number, but it also is in some sense the most irrational of irrational numbers," says Mario Livio, an astronomer with the Hubble Telescope in Maryland and author of the 2002 book "The Golden Ratio: Tne Story 6i Phi, the World's Most Astonishing Number." "This number is extraordinarily fascinating," he says. "You see pi (in contrast to phi), for example, is a very fascinating number. It appears in math and the sciences, but it has not crossed over into the arts." Great debate swirls around the existence - or not - of golden-ratio principles in works of art. Phi promoters say they have found the ratio in a variety of works of art, from ancient buildings to modern paintings. Critics say claims of phi in many works of art are exaggerat- ed. Phi patrons force their favorite ratio into everything they examine, critics say. In reality, they say, few works of art are based on phi. Phi was employed in the design of the Villa Emo, a classic Italian villa built in 1559, says Rachel Fletcher, an independent interior-design consultant and scholar in Massachusetts who lectures on the use of goldenratio principles in design. "You see it at every level of subdivision," she says of the villa. "You see it everywhere. It's quite precise." She uses the golden ratio in design because "it gives you a sense of well-being, a sense of, if you enter a room, all of the individual facets have a relation to one another," she says. "When you are in an environment where that is taking place, you feel the world is right, nothing is out of pface." Fletcher maintains that phi probably stirs everyone in mysterious ways. She has followed debates about phi for 25 years, she says, and doesn't spend much time anchored to either camp. "The fact that it has persisted for centuries over history, I think,, is very compelling," she says. "If it isn't a wonderful proportion, it's one we all want to be a wonderful proportion." Stephen Marquardt, a retired cosmetic surgeon in Huntington Beach, Calif., has dedicated years to the study of the golden ratio in the human face, and now in the body. He has appeared on The Learning Channel, the Discovery Channel and other media outlets to talk about his research. Frustrated with an absence of scientific answers to the question "What is beauty?" Marquardt set out to find keys to physical attraction. His search quickly led to the golden ratio, and he immersed himself in phi. Using a complicated set of golden-ratio measurements and proportions, Marquardt created a beauty "mask" that shows where, for example, eyes will ideally sit in relation to the tip of the nose. The mask, he says, is an objective and scientific portrayal of universal beauty. With the mask as a benchmark, he says he can study a woman's face and quickly under-' stand what does not fit within the golden ratio. This makes decisions about what to do with lips or noses much easier. Vladimir Konecni, a University of California at San Diego psychology professor, has dedicated years to studying intersections of the golden ratio and aesthetics, and he celebrates the number, which he says is one proportion among others that translates into pleasing aesthetics. It's not built into our genetic code. Instead, the golden ratio is "something you have to think of in art as an interesting proportion that was passed from father to son, teacher to pupil, over the centuries," he says. between a mother and her son whom she does not love, won Shriver the $54,730 prize. Praised by judges as a "courageous work," the novel is a series of letters written by the main character Eva to her estranged husband. Eva explores how she came to despise her son, whom she blames for the souring of her perfect marriage. "'We Need to Talk About Kevin' is a book that acknowledges what many women worry about but never express - the fear of becoming a mother andthe terror of what kind of child one might bring into the world," Orange Prize judge Jenni Murray said. Shriver, 33, dedicated her win to other struggling writers. "I've had a number of very lean and very hard years," said Shriver, who was born Margaret Ann but changed her name to Lionel at the age of 15. "I'd like to accept this prize on behalf of the hundreds, if not thousands, of writers who are incredibly talented and work incredibly hard and never quite get the recognition «they deserve." One of the book world's most lucrative awards, the Orange Prize is open to any novel by a woman published in English. Mudslides block Yellowstone road RED LODGE, Mont. (AP) A series of huge landslides has blocked the scenic Beartooth Highway, a major tourist magnet that winds through a high mountain pass into Yellowstone National Park, likely closing it all summer. Construction crews plowed a path around the lowest mud and rock slide south of Red Lodge on Tuesday and prepared to attack the next slide in the series, but that work only serves to clear a route for contractors who will have to make millions of dollars in repairs. 1\iesday was the second day of moving the highly unstable debris by crews from JTL Group crews. "We know it's going to slide. We'll try and control it," said company representative Jay Steinmasel. 5aveJ3LG over daily drop-in rates. One pass lets seven days a week, ail summer long. Valid May 28th-Octieth this knowledge can guide us to better understand ourselves," wrote Ferg in an e-mail. "This current study is strongly supportive of the original premise that the human aesthetic appeal is connected to the mathematical concept of dynamic symmetry." Ferg teaches sculpture and now uses the golden ratio when she's showing students how to transform blocks of clay into heads and faces. "My notion about doing art was Michelangelo with a big block of rock and a chisel," says Ellen Stevens, an educational psychology professor at CUDenver who has taken Ferg's class. "To work with Theresa to actually see how much the mathematics were there, it was an eye-opener for me. ... I think she's a renaissance woman, frankly." People respond most favorably to faces, shapes, buildings, paintings and other things that are based on the ratio, advocates say. Golden ratio studies of Leonardo Da Vinci's art are the most common - phi proponents hail Da Vinci as a.prophet of phi - but many others, including the French painter Georges Seurat and the Renaissance sculptor and painter Michelangelo, have been linked to phi. The number, phi lovers argue, speaks to something deep inside everyone. Some phi fanatics also claim the mysterious number must be a divine gift. Others attack notions of phi as a universal aesthetic code as hocus-pocus. "Almost all of the studies are spurious," says Stanford University mathematician Keith Devlin, author of the recent book "The Math Instinct" and National Public Radio's "Math Guy." "It is true that there is a strong connection between math and aesthetics and beauty. You can look at symmetries. There are connections. You can look at things we find beautiful and analyze them mathematically. Math has its own beauty. They go together in many ways. Unfortunately, many people whose knowledge of math is very basic ... extract from the idea of math and beauty some simplistic notions like the golden ratio, which they wishfully impose onto the world around them." University^ of Maine mathematician George Markowsky even dedicated at least one scholarly paper to debunking golden-ratio claims. In "Misconceptions About the Golden Ratio," Markowsky writes that statements about the golden ratio "have achieved the status of common knowledge, and are widely repeated. Even current high school geometry textbooks ... make many incorrect statements about the golden ratio." "It would take a large book to document all of the misinformation about the golden ratio," he writes. Physical echoes of phi are not Author Lionel Shriver wins prize for fiction LONDON (AP) American author Lionel Shriver won the Orange Prize for fiction by women on Tuesday for her book about the aftermath of a fictional school shooting. "We Need to Talk About Kevin," a dark novel which explores the relationship AMERICANS Sat/Sun/Mon/Tues, June 11-14,2005 " Family of Three (3) $185 Additional Family Member $39 Pool Pass goodforleisure pool lap swim pool andhormS, use. ~ki> " Facility passes also available which include :;,k?V M*V*S, emrdlo,fitness,gymnasium & pools. \ \ Swim Lessv n ^Morning & Evening Classes startJune 13th J CosUaer 2 week session: $50 The late journalist Charles Kuralt called the Beartooth "the most beautiful roadway in America." The mountainside highway is closed part of the year by snow and typically opens during the Memorial Day weekend. But on May 19-20 the slides and washouts damaged or destroyed 13 segments of a 12-mile stretch. No one was injured. State officials estimated more than 500 million tons of debris cascaded down the mountainsides. The slides were blamed on snowmelt and heavy rain, and water is still flowing across the highway in spots The r o between Red Lodge and Yellowstone National Park, via Cooke City, is expected to remain closed through mid-October. State Department of Transportation officials said they hope to award a bid for rebuilding the damaged portions of the highway this month. The highway winds over 10,940-foot Beartooth Pass, eventually reaching Yellowstone's northeast entrance. The Wyoming side of the road remains open to traffic and the park's northeast entrance is still open. The closure is a major concern for Red Lodge, which depends on business from tourists who use the highway. Officials have touted as an alternative the longer Chief Joseph Scenic Highway, saying that drive time to Yellowstone is similar to that of the Beartooth Highway. \Free Day Jbirius for a FREE DAY of POOL PLAY Jiirie 11th • Everyone's Invited . 435-615-5401 www.parkcilyrecrcnlion.org • 12G0 L t l l c K a l e R a a c l , P a r k C i t y PARK C I T Y RACQUET CLUB ///(•/ \jiarf, I.t'l\ P/tiy www.parkrecord.com |