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Geometry

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CALIFORNIA | LOCAL
August 30, 1996
Urk. Euclid told Ptolemy I, "There is no royal road to geometry," not Aristotle to Alexander (letter, Aug. 13). But the anecdote's point remains valid. BILL THOMAS Lancaster
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OPINION
March 8, 2014
Re "The masterpieces of math," Opinion, March 2 As a high school math teacher, I appreciate UC Berkeley professor Edward Frenkel's enthusiasm for the abstractness and applications of math in the real world. I love projects on fractals, snowflake symmetry, logic and reasoning in advertising and more. I would do more if I had time - but I don't have time. High-school curriculum is held hostage to tests that measure those 1,000-year-old formulas and applications as a means to get into colleges.
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CALIFORNIA | LOCAL
May 23, 1988 | from Times staff and wire reports
The brain apparently uses simple geometric calculations to instantly figure out depth and distances, but researchers say they do not know if the ability is learned or inherited. Scientists at the Smith-Kettlewell Eye Research Institute in San Francisco who are studying how the nervous system enables people to see in three dimensions have found that the brain uses either innate or learned geometric principles.
OPINION
March 2, 2014 | By Edward Frenkel
Imagine you had to take an art class in which you were taught how to paint a fence or a wall, but you were never shown the paintings of the great masters, and you weren't even told that such paintings existed. Pretty soon you'd be asking, why study art? That's absurd, of course, but it's surprisingly close to the way we teach children mathematics. In elementary and middle school and even into high school, we hide math's great masterpieces from students' view. The arithmetic, algebraic equations and geometric proofs we do teach are important, but they are to mathematics what whitewashing a fence is to Picasso - so reductive it's almost a lie. Most of us never get to see the real mathematics because our current math curriculum is more than 1,000 years old. For example, the formula for solutions of quadratic equations was in al-Khwarizmi's book published in 830, and Euclid laid the foundations of Euclidean geometry around 300 BC. If the same time warp were true in physics or biology, we wouldn't know about the solar system, the atom and DNA. This creates an extraordinary educational gap for our kids, schools and society.
ENTERTAINMENT
April 5, 2002 | DAVID PAGEL, SPECIAL TO THE TIMES
Only 13 months ago, Bart Exposito made his L.A. solo debut with a series of promising paintings that appeared to be the love children of streamlined RVs and old-fashioned TVs. Rendered with the steady hand of a sign painter, these goofy fusions of abstraction and representation also added a touch of Sputnik clunkiness and a slap of skateboarder verve to their hard-edged shapes, whose homey futurism matched that of the Jetsons.
NEWS
May 11, 1989 | RICK HOLGUIN, Times Staff Writer
The problem was fairly easy for Arthur Nam, a 17-year-old geometry student at Warren High School in Downey. "A plane 15 centimeters from the center of a sphere cuts the sphere in a circle of radius 8 centimeters. Find the diameter of the sphere." Thirty-four centimeters, of course. Nam answered that problem and 28 others correctly--he missed only one--to lead Warren High to victory in the geometry division of the 1989 National Mathematics League competition. More than 430 schools from across the country entered the geometry division, said league director Diane Riley, who released the final results earlier this week.
NEWS
July 31, 1991 | THOMAS H. MAUGH II, TIMES SCIENCE WRITER
A UC Berkeley mathematician says he has proved a theorem that has mystified scientists for 380 years. The theorem, put forth by astronomer Johannes Kepler in 1611, involves the most efficient way to pack round objects in a rectangular box. Greengrocers have known intuitively for hundreds of years that the best way to pack oranges, for example, is to stagger the layers so that each orange sits in the depression formed by three oranges below it.
CALIFORNIA | LOCAL
October 21, 2010 | By Elaine Woo, Los Angeles Times
What do coastlines, clouds, cauliflower and the stock market have in common? Mathematician Benoit Mandelbrot may not have conceived the question, but he provided an answer ? one that was compelling in its originality and startling in its usefulness in fields as unrelated as geography, medicine, art and finance. Mandelbrot, 85, who died of cancer Oct. 14 in Cambridge, Mass., was the father of fractals, a term he coined in 1975 to describe a new branch of geometry that seeks to make sense of irregular shapes and processes, from the infinite zigs and zags of a seacoast to erratic fluctuations on Wall Street.
OPINION
March 2, 2014 | By Edward Frenkel
Imagine you had to take an art class in which you were taught how to paint a fence or a wall, but you were never shown the paintings of the great masters, and you weren't even told that such paintings existed. Pretty soon you'd be asking, why study art? That's absurd, of course, but it's surprisingly close to the way we teach children mathematics. In elementary and middle school and even into high school, we hide math's great masterpieces from students' view. The arithmetic, algebraic equations and geometric proofs we do teach are important, but they are to mathematics what whitewashing a fence is to Picasso - so reductive it's almost a lie. Most of us never get to see the real mathematics because our current math curriculum is more than 1,000 years old. For example, the formula for solutions of quadratic equations was in al-Khwarizmi's book published in 830, and Euclid laid the foundations of Euclidean geometry around 300 BC. If the same time warp were true in physics or biology, we wouldn't know about the solar system, the atom and DNA. This creates an extraordinary educational gap for our kids, schools and society.
CALIFORNIA | LOCAL
December 22, 1999
This week's subject: Geometry Whether you're interested in measuring a bridge of exploring the intricate designs of nature, geometry offers tools to make sense of the shapes around us. By learning to use theorems--which help us make different types of calculations--geometry can help us in our daily lives and is an important part of such varied fields as engineering, navigation and even art. Learn more about geometry through the direct links on The Times' Launch Point Web site. Go to: http://www.
NEWS
September 11, 2012 | By S. Irene Virbila
Found lurking on my bookshelf: my once lost cookbook "The Geometry of Pasta" by Caz Hildebrand and Jacob Kenedy (Quirk Books, Philadelphia, 2010, $24.95). It was conceived by graphic designer Hildebrand, who kept "thinking about the Italians' preoccupation with choosing the right pasta shape to go with the right sauce. " To explore the concept further, he decided to do a book using simple geometric black-and-white drawings of the pasta shapes. And for the recipes, he approached Jacob Kenedy, co-founder of the Italian restaurant La Bocca di Lupo in London.
CALIFORNIA | LOCAL
January 10, 2012 | By Inga Saffron, Philadelphia Inquirer
Anne Tyng, a pioneering female architect whose ideas about geometry influenced Louis Kahn's modernist buildings and who later had a child with him, has died. She was 91. Tyng died Dec. 27 in Greenbrae, Calif., where she lived, said her daughter, Alexandra Tyng. Although Tyng was among the first group of women to graduate from Harvard University's architecture school in 1944, she struggled her entire career to be taken seriously. Firms would not hire her because she was a woman.
CALIFORNIA | LOCAL
October 21, 2010 | By Elaine Woo, Los Angeles Times
What do coastlines, clouds, cauliflower and the stock market have in common? Mathematician Benoit Mandelbrot may not have conceived the question, but he provided an answer ? one that was compelling in its originality and startling in its usefulness in fields as unrelated as geography, medicine, art and finance. Mandelbrot, 85, who died of cancer Oct. 14 in Cambridge, Mass., was the father of fractals, a term he coined in 1975 to describe a new branch of geometry that seeks to make sense of irregular shapes and processes, from the infinite zigs and zags of a seacoast to erratic fluctuations on Wall Street.
BUSINESS
January 17, 2010 | By Darrell Satzman
Could it be that when singer-actress Lauryn Hill covered the classic "Can't Take My Eyes Off of You" she was actually paying tribute to the sweeping coastal and city views from the home she owned in Beverly Hills' Trousdale Estates? The midcentury modern boasts a fully retractable wall of glass and a broad vista that stretches from the Palos Verdes Peninsula to Marina del Rey, taking in Century City and much of West Los Angeles. Catalina Island joins the tableau on a clear day. Adding to the property's celebrity pedigree, radio personality Tom Joyner was among the owners since Hill, according to property records.
IMAGE
June 21, 2009 | Melissa Magsaysay
A pop of coral can instantly take a simple summer item from plain to powerful, just by adding a splash of the fiery hue. From the real deal in jewelry containing the branch-like sea life to the imprint of its skeletal silhouette printed on sandals, mini-dresses and beaded maillots, coral in all forms is hitting stores in various pieces and in a refreshing range of prices.
ENTERTAINMENT
June 19, 2009 | Holly Myers
New York-based artist Peter Macapia comes to art making with weighty credentials, a vision that spans multiple fields -- including visual art, design, architecture, urban planning, geometry, physics and mathematics -- and a theoretical vocabulary that's likely to challenge even the most determined layman. His CV, indeed, is a little dizzying. He has a BFA from the Rhode Island School of Design, a master's in history from Harvard and a PhD in theory and criticism from Columbia. (His advisor was critical heavyweight Rosalind Krauss.
ENTERTAINMENT
April 8, 2001
Puzzle makers Sylvia Bursztyn and Barry Tunick are usually quite knowledgeable in their science-related clues, but in their March 18 crossword they had a little math confusion. The common clue for 35 and 77 across was "geometry abbr." The answers were COS (for cosine) and COSEC (for cosecant). However, these two terms are used in trigonometry, not geometry. JOHN LANE Stanton
OPINION
March 8, 2014
Re "The masterpieces of math," Opinion, March 2 As a high school math teacher, I appreciate UC Berkeley professor Edward Frenkel's enthusiasm for the abstractness and applications of math in the real world. I love projects on fractals, snowflake symmetry, logic and reasoning in advertising and more. I would do more if I had time - but I don't have time. High-school curriculum is held hostage to tests that measure those 1,000-year-old formulas and applications as a means to get into colleges.
BUSINESS
May 3, 2009 | Dinah Eng
Angled steel beams, walls of glass and polished concrete floors create an intricate series of geometric shapes in a contemporary-style house that's designed to follow the slope of the Malibu hillside it sits on. The home is in Point Dume, known for its panoramic ocean views, and for being an enclave for celebrities such as Julia Roberts, Kenny G and Martin Sheen. It was designed by New Mexico architect Bart Prince.
IMAGE
October 5, 2008 | Booth Moore, Times Fashion Critic
CAR WRECK prints embroidered with glass shards, aerodynamic forms frozen in motion -- Hussein Chalayan's Spring collection, titled "Inertia," captured the chaos of a week when the global economic crisis was hurtling out of control and Washington was stalled trying to fix it.
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