Khan Academy How To Slice A Bagel Along A Mobius Strip — And Why In the weeks before Doug Sohn closed down his legendary Chicago sausage joint Hot Doug’s, people were literally walking in the door and offering him a million dollars to stay open. This week on The Sporkful podcast, we’re featuring part one of our live show at the Taste of Chicago. I talk to Doug about why he walked away from all that money, and one of the top chefs in the world reveals his favorite candy bar. As part of our live show I also interviewed mathematician Eugenia Cheng, author of How To Bake Pi: An Edible Exploration of the Mathematics of Mathematics, who sliced a bagel along a Mobius strip live on stage. A Mobius strip, as you probably forgot, is a surface with only one side. If you were to start drawing a line down the middle of the strip and just keep going, you’d cover all the paper and end up right back where you started, without ever flipping it over. How did that make the bagel more delicious? “Well, it’s basically completely ridiculous,” Cheng explains.
Maths Online - Free Maths Tuition For All Australian High School Students 12 Mind Blowing Number Systems From Other Languages Today is a big day for lovers of the number 12, and no one loves 12s more than the members of the Dozenal Society. The Dozenal Society advocates for ditching the base-10 system we use for counting in favor of a base-12 system. Because 12 is cleanly divisible by more factors than 10 is (1, 2, 3, 4, 6 and 12 vs. 1, 2, 5 and 10), such a system would neaten up our mathematical lives in various ways. But a dozenal system would require us to change our number words so that, for example, what we know as 20 would mean 24 (2x12), 30 would mean 36, and so on. Does that blow your mind a little too much? 1. Photo Courtesy of Austronesian Counting The Oksapmin people of New Guinea have a base-27 counting system. 2. Tzotzil, a Mayan language spoken in Mexico, has a vigesimal, or base-20, counting system. 3. 4. Though modern Welsh uses base-10 numbers, the traditional system was base-20, with the added twist of using 15 as a reference point. 5. 6. 7. 8. 9. 10. 11. 12.
Contents, Interactive Mathematics Miscellany and Puzzles Since May 6, 1997You are visitor number E66B7E in base 20 Raymond Smullyan, a Mathematician, Philosopher and author of several outstanding books of logical puzzles, tells, in one of his books, a revealing story. A friend invited him for dinner. Having told this story, would it be wise to announce up front what this site is about? |Contact||Front page||Index||Store| Famed number π found hidden in the hydrogen atom Three hundred and sixty years ago, British mathematician John Wallis ground out an unusual formula for π, the famed number that never ends. Now, oddly, a pair of physicists has found that the same formula emerges from a routine calculation in the physics of the hydrogen atom—the simplest atom there is. But before you go looking for a cosmic connection or buy any crystals, relax: There is probably no deep meaning to the slice of π from the quantum calculation. Defined as the ratio of the circumference of a circle to its diameter, π is one of the weirder numbers going. Its decimal representation, 3.14159265358979 …, never ends and never repeats. Deriving that formula didn't come easy for Wallis, says Tamar Friedmann, a mathematician and physicist at the University of Rochester (U of R) in New York.
Touch Mathematics Great Literature Is Surprisingly Arithmetic A good book evokes a variety of emotions as you read. Turns out, though, that almost all novels and plays provide one of only six “emotional experiences” from beginning to end—a rags-to-riches exuberance, say, or a rise and fall of hope (below, top). Researchers at the University of Vermont graphed the happiness and sadness of words that occurred across the pages of more than 1,300 fiction works to reveal the emotional arcs and discovered relatively few variations. A different study coordinated by Poland's Institute of Nuclear Physics found that sentence lengths in books frequently form a fractal pattern—a set of objects that repeat on a small and large scale, the way small, triangular leaflets make up larger, triangular leaves that make up a larger, triangular palm frond (below, bottom). Why analyze the mathematics of literature?
Finding Unity in the Math Wars I usually avoid current events, but recent skirmishes in the math world prompted me to chime in. To recap, there’ve been heated discussions about math education and the role of online resources like Khan Academy. As fun as a good math showdown may appear, there’s a bigger threat: Apathy. And Justin Bieber. Educators, online or not, don’t compete with each other. Entertainment is great; I love Starcraft. What do we need? I could be walking into a knife fight with an ice cream cone, but I’d like to approach each side with empathy and offer specific suggestions to bridge the gap. The Big Misunderstanding Superheroes need a misunderstanding before working together. Bad Teacher < Online Learning < Good teacher The problem is in considering each part separately. Is Khan Academy (free, friendly, always available) better than a mean, uninformed, or absent teacher? But, really, the ultimate solution is Online learning + Good Teachers. Why Do I Care? I love learning. I was a good student. Finals came.
A quantum technique highlights math’s mysterious link to physics It has long been a mystery why pure math can reveal so much about the nature of the physical world. Antimatter was discovered in Paul Dirac’s equations before being detected in cosmic rays. Quarks appeared in symbols sketched out on a napkin by Murray Gell-Mann several years before they were confirmed experimentally. Einstein’s equations for gravity suggested the universe was expanding a decade before Edwin Hubble provided the proof. Nobel laureate physicist Eugene Wigner alluded to math’s mysterious power as the “unreasonable effectiveness of mathematics in the natural sciences.” But maybe there’s a new clue to what that explanation might be. Sign Up For the Latest from Science News Headlines and summaries of the latest Science News articles, delivered to your inbox At least that’s a conceivable implication of a new paper that has startled the interrelated worlds of math, computer science and quantum physics. Verifying a proof without actually seeing it is not that strange a concept.
Research Supporting NCTM-Standards-Based Mathematics Education Reform » Mathematically Sane Research Supporting NCTM-Standards-Based Mathematics Education Reform By admin - Last updated: Sunday, October 24, 2004 - Save & Share - Leave a Comment Prepared by Eric Hart There is a rigorous and extensive research base for NCTM-Standards-based reform in mathematics education. A brief sample of that research base, related to several major themes of reform, is included here. 1. “There is a long history of research, going back to the 1940s and the work of William Brownell, on the effects of teaching for meaning and understanding in mathematics. “Instructional programs that emphasize conceptual development, with the goal of understanding, can facilitate significant mathematics learning without sacrificing skill proficiency.” “Students who memorize facts or procedures without understanding often are not sure when and how to use what they know, and such learning is often quite fragile.” “Students who develop conceptual understanding early perform best on procedural knowledge later.” 2. 3.