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Vi Hart has a bone to pick with Nickelodeon, in that the show Spongebob Squarepants does not represent the world the way it really is to children. Does she complain about the talking kitchen sponge who wears pants? The squid who runs an underwater hamburger stand? The squirrel in scuba gear? No, it’s the pattern drawn in the pineapple that Spongebob lives in. -via Metafilter
With this equation, of course:
Graph that and you'll get this:
via Krulwich Wonders
See also: I Heart Math T-Shirt over at the NeatoShop
Wanna play Skyrim at school without getting in trouble? Well now you can play on your TI-84 graphing calculator. Sure it might not be as fun as the original, but hey, how often can you play your favorite game in the middle of class?
If you ever wondered why it is so important to be exact in math, particularly in engineering math, then take a look at cases in which a math error resulted in deaths. Remember the Hyatt Regency disaster in Kansas City some 30 years ago?
When designing their newest hotel to be built in downtown Kansas City, the fine people at Hyatt Regency wanted all the bells and whistles in it. The architectural firm in charge of the building design came up with a series of aerial walkways suspended from the ceiling so that guests could people-watch from a heightened vantage point. All in all, it was a pretty nifty feature. Until it suddenly collapsed and killed more than a hundred people.
Now they know what design flaw caused it, and my mouth dropped open to see how simple it was. Read the rest of the story and others at Cracked. Link -via Digg
Who
ya callin' birdbrained? Researchers at the University of Otago in New
Zealand found that the lowly pigeon is actually quite brilliant at math:
Scarf and her colleagues began their search for mathematical ability in pigeons by training subject birds to recognize groups of one, two or three objects on a screen and peck at them in proper numerical sequence. This, admittedly, was not an easy lesson to get across. It took about a year of practice and rewards before the pigeons could be said with certainty to have gotten the idea. The birds may have actually understood earlier, but the researchers had to make sure they were indeed responding to the number of items, as opposed to their color, shape or relative size. As a result the pigeons had to be trained with random selections of ovals, triangles, rectangles and even computer clip art before it was clear they had their counting skills down cold.
Link (Photo: William van der Vliet)
Jen Clarke of West London opened four eggs in a row that were all double-yolked. The odds of such a thing happening must be astronomical -or are they?
According to the British Egg Information Service, one in every thousand eggs on average is a double-yolker. They’re not sure how they’ve come to this figure but you would like to think that the British Egg Information Service was able to supply useful information about British Eggs, so let’s give them the benefit of the doubt.
So, if the probability of finding an egg with two yolks is 1/1000 – then to find the likelihood of discovering four in a row you simply multiply the probabilities together four times. One thousand to the power of four brings us to the grand total of one trillion – that’s the new-school US-style trillion with 12 zeroes.
If true that would mean the event that occurred in Jen’s kitchen was a trillion-to-one event. But is it true? No is the short answer.
Many factors can affect these odds, like the possibility that a certain chicken or flock laying several eggs that ended up in one carton, or the sorting of eggs by size. There are other factors as well, explained in this BBC article. Link -via Metafilter
You can understand why someone would want to make a giant pie, but why make a fractal pie? Because the bigger a pie gets, the more the crust becomes overwhelmed by the filling. It’s simple math. Instructables member turkey tek solved that problem by using the fractal shape of the Koch snowflake. At this size, the pie had to be baked in a custom-made outdoor oven. The cake pie is 50 inches in diameter at its widest point, but could have been bigger if the materials for the cooking process were more readily available. Yes, I will have a slice, thank you very much. Link -via Everlasting Blort
(Image credit: Wikipedia user Salix alba)
In 2002, a reclusive Russian genius named Grigori Perelman put an end to more than 100 years of suffering in the mathematical community. He solved the most difficult math problem of the 20th century -the Poincaré Conjecture. Its siren call had lured generations of mathematicians to intellectual graves. It first, its simplicity would seduce them, and they’d become convinced the answer was near. But as years passed, they’d be left with nothing to show for their lives’ toil but dead ends. By the time Grigori Perelman proved the Conjecture, the solution was worth $1 million.
THE MAN BEHIND THE MADNESS
Henri Poincaré
In 1885, all of Europe was talking about Henri Poincaré, a 30-year-old genius who’d mathematically proven why the solar system holds together. When a hole appeared in his calculations, he plugged it up by essentially inventing chaos theory: Kings were tripping over themselves to make him a knight· and Sweden gave him a small fortune in prize money. To this day; Poincare holds the record for the most physics Nobel Prize nominations, though he never actually won one.
But his most legendary achievement was something no one noticed until much, much later. At the turn of the century: Poincaré invented an entirely new field called algebraic topology; and today, it’s one of the most complicated and vibrant branches of mathematics. Think of it as a twisted version of geometry, in which shapes stretch, bend, and fold inside out. Poincaré’s goal was to classify objects by identifying their basic form, much the same way botanists classify new species of plants. In the process of creating topology, Poincaré tossed out a conjecture that seemed to be true. It was a side note to a larger problem, and he figured he’d work out the details later. Little did he know; his side note would become one of the greatest challenges in the mathematical world.
THE VICTIMS
Poincaré’s conjecture seemed simple enough. It claimed that any object without a loop is essentially a sphere. Think of a knife made out of Play-Doh. Without punching a hole in it or closing a loop, can you squish it into a ball? Yes, of course. Now picture a pair of Play-Doh scissors. No matter how hard you try, you can’t crush it into a ball without closing up the finger holes. It’s impossible. Poincare believed that objects like the knife were related to spheres, while objects with holes and loops in them were not.
Poincaré thought the conjecture would be easy to prove, and he even published a solution. But then, he saw a flaw in his work and retracted it. After his death in 1912, the question lay dormant for decades, until an Oxford professor named J.H.C. Whitehead rediscovered it in the late 1930s. J,H.C. (known to his students as “Jesus, he’s confusing”) also published a solution. But he, too, found a mistake and retracted it. However, his work sparked interest in the problem. By the 1950s, the Poincaré Conjecture was one of the best-known challenges in the math community:
Christos Papakyriakopoulos
That’s when two Princeton students, Edwin Moise and Christos Papakyriakopoulos (commonly known as Papa), decided to try their hands at it. Moise in particular looked like the guy to do it. Young and brash, he liked to announce his next big problem like a batter calling his shot. Twice that included one of the toughest problems in topology; and twice he returned with the solution. Then, he set his sights on Poincaré.
Papa was vastly different. A self-taught political refugee from Greece, he was famous for his odd, obsessive nature. Legend has it that when he came to Princeton, he checked into a motel and never checked out. He never even unpacked his bags. He simply fell into a routine that he followed every day; down to the minute, which always included a midday nap on top of his desk.
Throughout the 1950s, the two geniuses dueled with each other over Poincaré. Papa would announce a proof, and Moise would shoot it down. Then Moise would announce a proof, and Papa would shoot it down. This went on for years, while neither man worked on almost anything else.
more …
Biola University professor Matthew Weathers does it again! He p[resented entertaining lectures for Halloween and April Fool’s Day that we’ve seen, and now Thanksgiving gets the treatment. -via reddit
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Dr. Levin's golden grid.
A mathematical gauging of a smile
by Alice Shirrell Kaswell, Improbable Research staff
Dr. Eddy Levin of Harley Street puts a golden ratio, not just golden teeth, into his patients’ mouths. Dr. Levin has been at this for a while. It was he who in 1978 wrote a study called “Dental Esthetics and the Golden Proportion,” which graced pages 244–52 of that year’s September issue of The Journal of Prosthetic Dentistry.1
The golden ratio is a special number that has caught the eye and imagination of mathematicians, of artists, and now, thanks to Dr. Levin, of dentists. Some call it the “golden mean” (philosophers, though, use that phrase to mean something else). Some call it the “golden section.” Some Germans call it, evocatively, the “goldener Schnitt.” Almost everyone calls it beautiful.
The golden ratio is the number you get when you compare the lengths of certain parts of certain perfectly beautiful things (among them: snail shell spirals, the Parthenon in Athens, and Da Vinci’s painting “The Last Supper”). You’ll find that the ratio of the bigger part to the smaller equals the ratio of the combined length to the bigger. That ratio, that number, is always the same, ever so slightly bigger than 1.6180339.
If doing sums causes you pain, just go find someone who has perfect teeth and who won’t mind you staring into his or her mouth.
Dr. Levin explains on his website2 that many years ago he was both studying math and trying to find out what made teeth look beautiful. “It was at a moment,” he writes, “like when Archimedes got into his bath, that I suddenly realized that the two were connected — the Golden Proportion and the beauty of teeth. I began to put this into practise and started testing my ideas on my patients. My first case was a young girl in a hospital, where I was teaching, whose front teeth were in a terrible state and needed crowning. Despite the scepticism of the other members of staff and the unenthusiastic technicians with whom I had to work and whose co-operation I depended upon, I crowned all her front teeth, using the principles of the Golden Proportion. Everybody, including the young lady herself, agreed that her teeth now looked magnificent.”
Most important, in Dr. Levin’s reckoning, is the simple tooth-to-tooth ratio: “The four front teeth, from central incisor to premolar are the most significant part of the smile and they are in the Golden Proportion to each other.”
Dr. Levin created an instrument called the “golden mean gauge.” Made of stainless steel 1.5 millimeters thick, and retailing for £85, it shows whether the numerous major dental landmarks “are in the Golden Proportion,” and it is suitable for autoclaving.
Dr. Levin also offers a larger version that is “useful for full face measurements” and “useful to measure larger objects or bigger pictures of furniture etc.”
(Thanks to Stanley Eigen for bringing this to our attention.)
1. “Dental Esthetics and the Golden Proportion,” E.I. Levin, Journal of Prosthetic Dentistry, vol. 40, no. 3, September 1978, pp. 244–52.
_____________________
The article above is from the May-June 2009 issue of the Annals of Improbable Research. You can download or purchase back issues of the magazine, or subscribe to receive future issues. Or get a subscription for someone as a gift!
Visit their website for more research that makes people LAUGH and then THINK.
(Image credit: Flicker user stephanie vacher)
by Marc Abrahams, Improbable Research staff
The Ham Sandwich Theorem has been a treat and a spur to mathematicians for more than half a century. It first cropped up in a branch of mathematics called algebraic topology. The theorem describes a particular truth about certain shapes. Most published papers on the topic make a hash of explaining it to anyone who is not an algebraic topologist. But the authors of a 2001 paper called “Leftovers from the Ham Sandwich Theorem” wrapped up an important little leftover: they put the idea into clear language.
“Leftovers from the Ham Sandwich Theorem,” Graham Byrnes, Grant Cairns, and Barry Jessup, The American Mathematical Monthly, vol. 108, no. 3, March 2001, pp. 246-9.
The authors are at La Trobe University, Melbourne, Australia, and University of Ottawa, Ottawa, Canada. The Ham Sandwich Theorem, they wrote, “rescues the careless sandwich maker by guaranteeing that it is always possible to slice the sandwich with one cut so that the ham and both slices of bread are each divided into equal halves, no matter how haphazardly the ingredients are arranged.”
For a while, most ham sandwich theorizing dealt with simple cases. A paper called “Computing a Ham-Sandwich Cut in Two Dimensions,” published in 1986, is typical.
Detail from the Edelsbrunner/Waupotitsch study “Computing a Ham-Sandwich Cut in Two Dimensions.”
“Computing a Ham-Sandwich Cut in Two Dimensions,” H. Edelsbrunner and R. Waupotitsch, Journal of Symbolic Computation, vol. 2, no. 2, June 1986, pp. 171–8.
It considered only ham sandwiches that had been flattened flatter than even the chintziest cook would dare devise. Mathematicians often do things this way, first considering the extreme cases, digesting those thoroughly, and only then moving on to more substantial versions. Indeed, the “Computing a Ham-Sandwich Cut in Two Dimensions” paper itself contains a section called “Getting Rid of Degenerate Cases”.
People did solve the mystery of slicing a thick ham sandwich. And inevitably, they developed a hunger for more substantial problems.
more …
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It’s in the name, pizza was just invented to be delicious based on mathematical formulas. It makes so much sense now. Kind of reminds me of our puntastically fun Pi shirt in the Neatoshop.
I’ll take two! This was on Neatorama’s Facebook page. Link
The Oatmeal has a hilarious collection of things we should have learned in school, but my favorite is the math lesson above. After all, we’ve all been in that frustrating situation before.
There’s not much to say about this infinity tentacle other than it was created by DeviantArt user Andrew Strauss and that it is so delightfully geeky that it had to be featured here on Neatorama.
Link Via Laughing Squid
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Mathematician Pierre de Fermat was born 410 years ago today, as we learn from the Google doodle of the day. The doodle recreates Fermat’s Last Theorem, which he left scribbled in the margin of a book.
Fermat’s claim left mathematicians puzzled for over 350 years — as mathematicians proved it true for many sets of possible values of n — until the general case was finally proved by Andrew Wiles in 1995. The story about the proof is told in Simon Singh’s book Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem.
Did Fermat really have a proof? Most likely not, since the techniques Wiles used to prove it weren’t developed until several centuries after Fermat’s death — and since, in the 30 years he lived after writing the note, he never wrote about the general case of the proof again — but nobody will ever know for sure. I’ll leave that, as they say, as an exercise for the reader.
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Actually, string theory is something completely different, but it’s a cute title for this geometry problem at Futility Closet. A boy has his toy boat in the water, and he is pulling it to shore by a string. If he pulls in one yard of string, will the boat advance a yard, or less than a yard, or more than a yard? The answer may surprise you. Link -via TYWKIWDBI
A while back we posted a video of actual Miss USA contestants being asked “Should Evolution Be Taught in Schools?” Now someone has posed an even greater question to some would be “Miss USA contestants.” Should math be taught in schools? Their answers may shock you. Watch second video at bottom of link post.
Etsy seller Nausicaa Distribution sells these precious statistical distribution graph plushies that are just perfect for any Neatorama reader. Of course, if you’re looking for cute nerdy plushes, the Neatoshop is also a great place to go shopping.
Link Via Laughing Squid
Comments Off Josh Sundquist shares some charts and graphs about fireworks, pie, and other Independence Day traditions. -via Buzzfeed
Brain Candy Toys came up with a great advertising strategy by simplifying nursery rhymes and fairy tales into adorable little math equations. Check out the rest on the ad company’s site.
Link via Laughing Squid
The date today is 6/28, which is Tau Day. The number Tau is 2pi, or 6.28 (followed by many more decimals). Geek Are Sexy has an explanation of tau, which is kind of like pi, only more so. And since tau is 2pi, you should celebrate Tau Day by baking two pies. One for me, and one for you. And not to throw at each other! Link
See also: The Pi is a Lie
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A schoolbook that both postdated and outlived its time.
by Stephen Drew, Improbable Research staff
Mathematics teaching has been cocked up — well and properly and officially — for a good long while, thanks to Edward Cocker and his amply-titled textbook Cocker’s Arithmetick: Being a Plain and Familiar Method Suitable to the Meanest Capacity for the Full Understanding of That Incomparable Art, As It Is Now Taught by the Ablest School Masters in City and Country.
Published in 1667, and later reprinted in more than 100 editions, the book was a standard in British grammar schools for several generations. Foreign schoolteachers also took Cocker to their bosom.
A Man of Words, Word, and More Words, Plus More Words
The 34-word title exemplifies the book’s approach to explaining things clearly. One could (although the author would probably not) sum it up in three words: don’t be terse.
Here, for example, is how the book takes the student in hand — nearly in handcuffs, really — to explain the so- called “Rule of Three.” This passage appears on page 88 of the book’s 47th edition, published in the year 1736:
Observe, that of the three given numbers, those two that are of the same kind, one of them must be the first, and the other the third, and that which is of the same kind with the number sought, must be the second number in the rule of three; and that you may know which of the said numbers to make your first, and which your third, know this, that to one of those two numbers there is always affixed a demand, and that number upon which the demand lieth must always be reckoned the third number.
The book’s very first page accustoms the student to what lies ahead. You might enjoy reading this aloud:
Unit is number; for the part is of the same matter that is his whole, the unit is part of the multitude of units, therefore the unit is of the same matter, that is the multitude of units; but the matter of the multitude of units is number; therefore the matter of units is number; or else, if from a number given no number but subtracted, the number given remaineth; as suppose 3 the given number, if as some suppose, 1 be no number, then if you subtract 1 from 3, there must remain 3 still; which is very absurd.
Words After Death
Scholars now debate whether Edward Cocker actually wrote the book (the first edition was published nine years after his death). Some suggest the whole thing is just a pastiche of other people’s writings, issued by a greedy publisher. No matter. Like many of today’s textbooks, authorities deemed it authoritative, and it came to enjoy widespread use. In that respect, as perhaps in others, this antique textbook is a very 21st-century piece of work.
References
Cocker’s Arithmetick: Being a Plain and Familiar Method Suitable to the Meanest Capacity for the Full Understanding of That Incomparable Art, As It Is Now Taught by the Ablest School-Masters in City and Country, Edward Cocker, 1677, John Hawkins [publisher], London.
Bonus
Cocker’s Life and productive death are the subject of an essay called “Who Was Cocker,” in the July 1884 issue of The Bibiliographer. You can read it online.
_____________________
This article is republished with permission from the July-August 2010 issue of the Annals of Improbable Research. You can download or purchase back issues of the magazine, or subscribe to receive future issues. Or get a subscription for someone as a gift!
Visit their website for more research that makes people LAUGH and then THINK.
Detail from the Darke/Holmes study
by Michael Berry
H.H. Wills Physics Laboratory,
University of Bristol, Bristol, UK
The applications of mathematics can be bizarre. Soon after I arrived in Bristol in the 1960s, a senior colleague called me, saying that someone in the veterinary school needed help with mathematics — or was it physics? — and I seemed just the person to help. Cursing inwardly, I agreed to see the fellow. He was Peter Darke, a graduate student near the end of a Ph.D. studying horses’ hearts.
He showed me a paper by Gabor (Dennis Gabor, who invented holography) and Nelson1 and asked me to explain it. It took a while to understand. The idea is that a heart is like a little battery, pushing weak electric currents in a three-dimensional pattern round the body. The battery has a strength and a direction: it acts as a current dipole, represented as a little arrow — the heart vector. During each heartbeat, the vector (tip of the arrow) draws a loop – the heart loop — whose shape is a powerful diagnostic of health. Therefore it is useful to measure this loop, in a way that doesn’t involve killing the horse. Gabor’s paper gave the theory of a way to do that, inferring the heart vector by measurements of the electric potential on the surface of the horse. It is an ingenious application of Gauss’s theorem.
The Darke/Holmes study, which used the Berry approach to integrate over the surface of a horse.
Peter had spent three years preparing to implement this idea. He enveloped his horse in a coat he had made, of several hundred potentiometers, with electronics to measure the potential at each of them, fifteen times during each heartbeat, and he had arrived at the point where he had a huge file of all these measurements. But there was a difficulty: he knew only the most elementary high-school mathematics and so had no way to understand the formulas in Gabor’s paper. His specific question was: does the theory apply to a real horse, or only to an ideal cylindrical horse? Unlike the physicists’ mythical ‘spherical cow,’ this was real.
I learned that the formulas work for a horse of any shape, but they do assume uniform conductivity — a better approximation, apparently, for horses than for people. (Actually, it doesn’t have to be accurate: who cares whether the loop describes the real dipole inside the real horse? To be useful for diagnosis, it is necessary only that the loop be reproducible.)
The formulas involved integration, and Peter didn’t know what an integral was, so it was hard to explain how to add up all those measurements. A complication was that what had to be inferred was a vector, so he needed to know, at each point on the horse, the components of the perpendicular to the surface of the horse with respect to the three symmetry directions of the horse. After some discussion, we made a ‘cos-theta-meter,’ and I left him to it, and never saw him again.
Further detail from the Darke/Holmes study.
But a year later, I received two papers from him,2 reporting the outcome of all that arithmetic. To my surprise, he had indeed calculated fifteen vectors for each heartbeat, and thereby deduced the heart loops for several horses in different states of health. At the end of the paper were the usual acknowlegements to colleagues and funding agencies. For technical help, he thanked me; and for financial support, he thanked the Horserace Betting Levy Board (financed by racecourse gamblers).
The moral of this is that applications of mathematical knowledge can be unexpected; you may find yourself taking a surface integral over a horse.
References
1. “Determination of the Resultant Dipole of the Heart from Measurements on the Heart Surface,” D. Gabor and C.V. Nelson, Journal of Applied Physics, vol. 25, 1954, pp. 413-6.
2. “Studies on the Equine Cardiac Electric Field. I. Body Surface Potentials, II. The Integration of Body Surface Potentials to Derive Resultant Cardiac Dipole Moments,” P.G.G. Darke and J.R. Holmes, Journal of Electrocardiology vol. 2, 1969, pp. 222-234 and 235-244.
_____________________
This article is republished with permission from the July-August 2010 issue of the Annals of Improbable Research. You can download or purchase back issues of the magazine, or subscribe to receive future issues. Or get a subscription for someone as a gift!
Visit their website for more research that makes people LAUGH and then THINK.
The Making of a Fly by Peter Lawrence is a well-regarded reference book on fruit flies used by those who study genetics. You can get a used copy for about $35. But recently a new copy was spotted on Amazon for the price of $1,730,045.91! Michael Eisen was intrigued, and looked into why it was so expensive. He found there were two vendors selling the book new, bordeebook and profnath, and they seemed to be in a price war of sorts, with the prices rising daily by a steady algorithm. Profnath’s price was always lower, but both sellers raised their price automatically in response to the other’s price change.
The behavior of profnath is easy to deconstruct. They presumably have a new copy of the book, and want to make sure theirs is the lowest priced – but only by a tiny bit ($9.98 compared to $10.00). Why though would bordeebook want to make sure theirs is always more expensive? Since the prices of all the sellers are posted, this would seem to guarantee they would get no sales. But maybe this isn’t right – they have a huge volume of positive feedback – far more than most others. And some buyers might choose to pay a few extra dollars for the level of confidence in the transaction this might impart. Nonetheless this seems like a fairly risky thing to rely on – most people probably don’t behave that way – and meanwhile you’ve got a book sitting on the shelf collecting dust. Unless, of course, you don’t actually have the book….
My preferred explanation for bordeebook’s pricing is that they do not actually possess the book. Rather, they noticed that someone else listed a copy for sale, and so they put it up as well – relying on their better feedback record to attract buyers. But, of course, if someone actually orders the book, they have to get it – so they have to set their price significantly higher – say 1.27059 times higher – than the price they’d have to pay to get the book elsewhere.
The price went as high as $23,698,655.93 (plus $3.99 shipping) on April 18th when someone apparently noticed, and manually adjusted the price. Read the whole story at Eisen’s blog. Link -via reddit
This is good, but the moves get really explicit once you start into calculus. If you know who’s responsible for this great cartoon, let us know in the comments.
via Geekosystem | Previously: Math Dances and Other College Application Videos
Can you figure out what movie each of these mathematical equations represents? I couldn’t. There are a lot of good guesses in the comments at Spiked Math Comics, but no definitive answer list. Link -via Geeks Are Sexy
Last year, John Farrier wrote a great Neatogeek post about geeky love songs. While the twelve listed were great, there were still plenty more great geek ballads out there. Here are ten more love songs sure to get your nerd juices flowing.
How is it nerdy? This is the song that inspired me to write this list. It’s an ultimate geek love song in that a woman is able to seduce her love interest not through her looks but through chemistry and other scientific fields.
Choice lyrics: It’s poetry in motion/And now she’s making love to me/The spheres are in commotion/The elements in harmony/She blinded me with science/”She blinded me with science!”/And hit me with technology
Video:
How is it nerdy? It might just be impossible to write a romantic song with more Dungeons and Dragons references.
Choice lyrics: I picked up spell resistance from the enchanted school/So I could bend up all these magic pretences/And though always use it as a general rule /This time I’m lowering all my defences
Video: There’s no official video for the song, but here’s a YouTube video with the song.
Video link
How is it nerdy? MC Chris is one of the biggest stars of the nerdcore hip hop scene and this serenade to a nerd shows just how geeky he can be, even when discussing matters of the heart.
Choice lyrics: She’s romantic, known to panic/With anxiety attacks/Literary, it’s so scary/Reading Brontes back to back/She’s playing Ragnarok on her mom’s Magnavox/She’s underneath my skin like a million nanobots
Video:
How is it nerdy? It’s not even about a girl, it really is about loving a computer and how the computer is far better than a real girlfriend.
Choice lyrics: I’ve never been quite so happy/all I need to do is click on you/and we’ll be joined/in the most soul-less way/and we’ll never/ever ruin each other’s day
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Vi Hart, who knows more about math than I ever will, made a video and two pies especially for Pi Day, which she says we should call Half-Tau Day. She lost me when she said a pie is really 2pi, because I never took that class. I will take a slice of cherry, if you don’t mind. Link -via The Daily What
Tom Beddard of subblue created this nifty little Flash application where you can draw your own mathematical butterfly:
Taken from Clifford Pickover’s book, Computers and the Imagination, is this experiment that creates butterfly like curves.
The formula is expressed in polar coordinates as:
By changing the A, B, a, b and c parameters you can get some nice results.
It’s fun to change the parameters to see what you get: Link – via Cliff Pickover’s Reality Carnival
