Vi Hart: Math Doodling Remember that video about doodling dragons and fractals and stuff? I finally finished part 2! Here is a magnet link so you can dowload it via torrent. Here it is on YouTube: You can tell I worked on it for a long time over many interruptions (travelling and other stuff), because in order to keep myself from hating what was supposed to be a quick easy part 2, I had to amuse myself with snakes. Part of working on part 2 was working on part 3 and other related material, so the next one should go faster. Here was part 1, via Torrent or YouTube. Square Dancing I bet I can guess your favorite math subject in high school. It was geometry. So many people I’ve met over the years have expressed affection for that subject. Arithmetic and algebra — not many takers there. But geometry, well, there’s something about it that brings a twinkle to the eye. Is it because geometry draws on the right side of the brain, and that appeals to visual thinkers who might otherwise cringe at its cold logic? But my best hunch (and, full disclosure, I personally love geometry) is that people enjoy it because it marries logic and intuition. To illustrate the pleasures of geometry, let’s revisit the Pythagorean theorem, which you probably remember as a2 + b2 = c2. The Pythagorean theorem is concerned with “right triangles” — meaning those with a right (90-degree) angle at one of the corners. And since rectangles come up often in all sorts of settings, so do right triangles. They arise, for instance, in surveying. Anyway, here’s how the theorem works. Notice the word “on.”
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.
Power Tools If you were an avid television watcher in the 1980s, you may remember a clever show called “Moonlighting.” Known for its snappy dialogue and the romantic chemistry between its co-stars, it featured Cybill Shepherd and Bruce Willis as a couple of wisecracking private detectives named Maddie Hayes and David Addison. While investigating one particularly tough case, David asks a coroner’s assistant for his best guess about possible suspects. “Beats me,” says the assistant. “But you know what I don’t understand?” (Click image to play clip.) That pretty well sums up how many people feel about logarithms. The same is true of many of the other functions discussed in algebra II and pre-calculus. To show you what I mean, let’s plot the graph of the equation You may remember how this sort of activity goes: you draw a picture of the xy plane with the x-axis running horizontally and the y-axis vertically. The droopy shape of the curve is due to the action of mathematical pliers. 1.
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. 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. Yoruba, a Niger-Congo language spoken in West Africa, also has a base-20 system, but it is complicated by the fact that for each 10 numbers you advance, you add for the digits 1-4 and subtract for the digits 5-9. 4. 5. 6. 7. 8. 9. 10. 11.
Change We Can Believe In Long before I knew what calculus was, I sensed there was something special about it. My dad had spoken about it in reverential tones. He hadn’t been able to go to college, being a child of the Depression, but somewhere along the line, maybe during his time in the South Pacific repairing B-24 bomber engines, he’d gotten a feel for what calculus could do. Every year about a million American students take calculus. Calculus is the mathematics of change. But within that bulk you’ll find two ideas shining through. More in This Series Next week’s column will explore that astonishing connection, as well as the meaning of integrals. Derivatives are all around us, even if we don’t recognize them as such. Every field has its own version of a derivative. Their confusion is understandable. Like slopes, derivatives can be positive, negative or zero, indicating whether something is rising, falling or leveling off. My high school calculus teacher, Mr. Another strategy is to head straight from A to B.
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. 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. Now, Friedmann and Carl Hagen, a theoretical physicist at U of R in New York, have found a surprisingly easy way to derive the formula using a three-page calculation involving the hydrogen atom.
It Slices, It Dices Mathematical signs and symbols are often cryptic, but the best of them offer visual clues to their own meaning. The symbols for zero, one and infinity aptly resemble an empty hole, a single mark and an endless loop: 0, 1, ∞. And the equals sign, =, is formed by two parallel lines because, in the words of its originator, Welsh mathematician Robert Recorde in 1557, “no two things can be more equal.” In calculus the most recognizable icon is the integral sign: Its graceful lines are evocative of a musical clef or a violin’s f-hole — a fitting coincidence, given that some of the most enchanting harmonies in mathematics are expressed by integrals. Historically, integrals arose first in geometry, in connection with the problem of finding the areas of curved shapes. Today we still ask budding mathematicians and scientists to sharpen their skills at integration by applying them to these classic geometry problems. Still, picturing the shape is merely the first step. More in This Series