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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
more …
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
Vi Hart calls herself a “recreational mathemusician”, which sounds like fun! In this video, she teaches more about math than she missed by doodling during class. See more of this sort of thing at her website. Link -Thanks, David Israel!
Just imagine Homer Simpson’s response to this brilliant tee shirt by John Sumrow, “mmm…infinite bacon.”
Link via Laughing Squid
Psst! Wanna be better at math? The answer may be shockingly simple: just give your noggin a little jolt!
The electricity generated by a 9-volt battery might be all there is between you and the mathematical brilliance of a Newton or an Einstein.
OK, we can’t guarantee you’ll be that smart, but, amazingly, British scientists have now shown that low voltage current applied to the right part of the scalp can spark changes that boost the brain’s math abilities. What’s more, that mild jolt can lock in your improved mathematical prowess for as long as six month, according to new research published in this month’s issue of Current Biology.
The findings come too late for those of us who already suffered through middle school algebra, but maybe future generations will benefit.
The researchers, led by Roi Cohen Kadosh from the University of Oxford, suspected that a little electricity directed at the right parietal lobe – a brain region at the top of the head and known to play a role in numerical calculations – might juice up a person’s math ability.
This is a perfect tool for teaching my kids their algebraic order of operations! Oh, they can do them, but I think this will help them understand the concept better. Find this “s’more formula” on a t-shirt at W00t. Link -via Laughing Squid
In researching the earlier post A Non-Math Look at Math Objects, I found that there is what a non-math person like me would call an infinite number of strange terms in geometry and topology that refer to shapes, objects, and patterns both imaginary and usable in the real world. Someone who is not used to this kind of higher thinking can only absorb so many of them at a time! Here are seven more.
What mathematicians call a hyperboloid of one sheet is a really cool structure that is made up of many (actually an infinite number) of perfectly straight lines that look to us like a curved structure. First, imagine that you have a cube. Stand it on one of its corners and spin it like a top, then look at it from the side -the sides seem to be curved, but you know they aren’t. Now, take a handful of uncooked spaghetti noodles. Use two hands, and twist the strands loosely. It forms the shape of a hyperboloid structure, which looks like a cooling tower at a nuclear reactor. All the spaghetti noodles are still straight, but the shape of the handful is curved. In architecture, this idea enables builders to produce curved structures by using straight line supports.
An Apollonian gasket is a fractal generated when you mash as many round soap bubbles together as you can. At least, that’s what it looks like. The pattern is based on threes: every circle touches two other circles. As you add more circles in the smaller spaces, they also touch two existing circles (and eventually many smaller ones). The number of smaller circles that can be added is mathematically infinite. Frothing soap bubbles can help us picture the Appolonian gasket, but the analogy is flawed, because real world soap bubbles do not like empty spaces. There is a limit to the volume of soap, and surface tension will connect round bubbles and flatten them against each other. This fractal is named for the ancient Greek mathematician Apollonius of Perga. The 3-dimensional fractal of this sort is called the Apollonian sphere packing, which is a pretty descriptive name for a math term.
When I was very young, first or second grade, my father told me he could make a piece of paper with only one side. Then he took a strip of paper, gave one end a half-twist, and taped the ends together. Then he showed me how he could draw one line down the strip without stopping and it covered the whole strip, no matter which way you turned it! I couldn’t wait to show the Möbius strip to my friends at school. When I did, they just stared at me and told me I was weird.
Maybe “continuous plane” is a better description than “one sided paper”. The Möbius strip is named for August Ferdinand Möbius who discovered it in 1858. Johann Benedict Listing also came up with the concept around the same time and actually published his work, but maybe someone thought calling it a “Listing strip” would be confusing. Anyway, the Möbius strip does have some real-world applications. For example, conveyor belts and recording tapes with a half-twist last twice as long as they would otherwise because the entire surface is used instead of just one side of a two-sided strip. It’s also an attention-getter in art and even architecture.
I found out something neat about three-dimensional shapes. Many strange mathematical solids are constructed by rotating the plane of a two-dimensional shape around an imaginary axis. Think of the flat holiday decorations you fold out around its spine/axis. Once I understood what is called a “surface of revolution” in my mind, the construction of many odd mathematical shapes began to make sense.
Superegg
(Image credit: Sir48 at da.wikipedia)
A superegg is a mathematical shape constructed by rotating a superellipse around an axis to the formula of |x/a|2.5 + |y/b|2.5 = 1, where a/b = 4/3. (If you search for “superegg formula”, you are liable to find something completely different.) But you don’t want to bother with formulas, do you? Just look at it! From the side, the superegg looks a bit like a cylinder, but has no corners. If you cut one horizontally, the cross-section will be a circle. However, unlike a natural egg, you can stand the superegg on its end -either end, as a matter of fact, as it is vertically as well as horizontally symmetrical, although it has no straight lines that you can find -although the curvature is zero at the ends, the “ends” are actually quite small and appear to be rounded. The superegg was popularized by Danish mathematician and physicist Piet Hein, who used the shape in designs for household items such as furniture, ice cubes, and candles, as well as a novelty toy (sometimes referred to as a stress-reliever) by itself.
Torus
I learned about the torus from crossword puzzles. If the clue says “donut shape”, the answer is torus. The solid is produced by rotating a circle around an imaginary axis, but in this surface of revolution, the axis is outside the circle. The resulting shape is a ring torus. Other torus shapes are produced when the axis is touching or slightly inside the circle. Some really strange mathematical shapes are produced when the rotating plane of the circle is not quite round, or is itself rotating around a point in the plane. A toroid is a ring or donut shaped solid produced by a surface of revolution not necessarily limited to a circle. For example, a square used in this manner will produce a ring that would be uncomfortable on your finger. A toroidal polyhedron is a torus constructed with or converted into flat surfaces, with the shape dependent on how many flat surfaces you use. Toroidal Polyhedron would be a cool name for a band.
Gömböc
You might remember Weebles -they wobble, but they don’t fall down. However, if the heavy weight in the bottom of the toy ever came loose, you had a Weeble that fell down. In 1995, Russian mathematician Vladimir Arnold questioned whether there could be a 3-dimensional shape that would always return to its original position without the help of internal weights. If a shape could be found that had as few as two points of equilibrium, one stable and one unstable, the shape would naturally return to balancing on the one stable point. For a long time, mathematicians thought the shape was impossible. But in 2006, Gábor Domokos and Péter Várkonyi developed the gömböc. This odd shape has only two points it could possibly balance upon, and the point on top is too “pointed” to be stable. So, if you roll a gömböc around, it will soon right itself, returning to an upright position because of its shape, not because of any internal irregularities. It’s a Weeble that doesn’t wear out! Objet Geometries made the first fabricated gömböcs. They were numbered as a limited series (inside, using transparent materials of the same density as the rest of the object) and professor Arnold was presented with number one. You can buy one of your own.
Declaring war on limp fish, bone crusher, politician and other types of handshakes, Chevrolet UK commissioned a study to determine the perfect handshake. After all, there's nothing more important to closing the deal in selling cars than the handshake:
Professor Geoffrey Beattie, who worked on the project for Chevrolet, said: "The human handshake is one of the most crucial elements of impression formation and is used as a source of information for making a judgement about another person.
"The rules for men and women are the same: right hand, a complete grip and a firm squeeze (but not too strong) in a mid-point position between yourself and the other person, a cool and dry palm, approximately three shakes, with a medium level of vigour, held for no longer than two to three seconds, with eye contact kept throughout and a good natural smile with a slow offset with, of course, an appropriate accompanying verbal statement, make up the basic constituent parts for the perfect handshake."
Just so you know this is very serious business, Professor Beattie of the University of Manchester codified the perfect handshake into mathematical formula:
(e) is eye contact (1=none; 5=direct) 5; (ve) is verbal greeting (1=totally inappropriate; 5=totally appropriate) 5; (d) is Duchenne smile - smiling in eyes and mouth, plus symmetry on both sides of face, and slower offset (1=totally non-Duchenne smile (false smile); 5=totally Duchenne) 5; (cg) completeness of grip (1=very incomplete; 5=full) 5; (dr) is dryness of hand (1=damp; 5=dry) 4; (s) is strength (1= weak; 5=strong) 3; (p) is position of hand (1=back towards own body; 5=other person's bodily zone) 3; (vi) is vigour (1=too low/too high; 5=mid) 3; (t) is temperature of hands (1=too cold/too hot; 5=mid) 3; (te) is texture of hands (5=mid; 1=too rough/too smooth) 3; (c) is control (1=low; 5=high) 3; (du) is duration (1= brief; 5=long) 3.
Dell computers have discovered what your prototypical high school student already knows: math is hard, and sometimes it can melt your brain.
After the math department at the University of Texas noticed some of its Dell computers failing, Dell examined the machines. The company came up with an unusual reason for the computers’ demise: the school had overtaxed the machines by making them perform difficult math calculations.
And I’m sure you can predict what would happen next if you continue to ship faulty computers to your customers. Five words: Dell, you’re getting a lawsuit!
See also: Dude, You’re Getting A Tequila! | Alphabet of Computing
I Reverse Polish Notation Heart T-Shirt - $9.95
Be still my geeky heart! Neatoramanaut Ana models this wonderfully geeky I Reverse Polish Notation Heart T-Shirt.
What’s a Reverse Polish notation? It’s a mathematical notation where the operator (e.g. +, -, x) follows the operands. Those of you who have the old HP-10C series calculator are probably nodding in nostalgia right now!
More I Heart T-shirts | Science T-Shirts over at the NeatoShop
San Francisco-based artist/coder Robert Hodgin of Flight 404 Blog created some of the most mesmerizing sculptures using magnetized balls and cylinders. They’re part of the Gray Area Foundation for the Arts (GAFFTA) exhibition.
That has got to take some mad skillz because I can easily envision the whole thing collapsing into a pile of magnetized blob at the slightest touch.
MAKE Blog has the gallery: Link | Robert’s official webpage
Related: Buckyballs over at the NeatoShop
ScienceBlogs, together with Serious Eats, held a Pi Day Bake-Off to celebrate Pi Day on March 14th. They received 35 pie entries, which have been narrowed down to ten finalists. Not only are these “pi pies” decorated in a mathematically clever way, they look scrumptious! Shown is Claudette’s amazing One-Hundred-Digit pie made with cherries, raspberries, blueberries, blackberries, and strawberries. Sure it’s not round, but remember, pie are square! Link to photographs. Link to voting.
The Inverse Graphing Calculator takes words and converts them into equations that would express them graphically:
The Inverse Graphing Calculator (version beta-1) is like a backwards graphing calculator. Normally, you enter an equation into your calculator and then get a graph of the curve. The way the IGC works is, you type something you’d like as your curve, like ‘Hello World’ or ‘I love you’. The IGC produces an *equation* which has this phrase as its graph!
Link via Geekologie
It makes sense that a movie has to conform to our average attention span. This way we will not get bored during the film. Cornell University psychologist James Cutting has worked out the formula for delivering a blockbuster hit.
To find out whether the length of camera shots in films might follow 1/f too, Cutting measured the duration of every shot in 150 high-grossing Hollywood movies in various genres released between 1935 and 2005. He then turned these into a series of waves for each film. He found that later films were more likely to obey the 1/f law than earlier ones (Psychological Science, in press). But he stresses that it isn’t just fast-paced action films like Die Hard II that follow 1/f. Rather, the important thing is having shots of similar length that recur in a regular pattern throughout a film.
From the Upcoming 
ueue, submitted by mrmunchies.
Is there something in our brains that make humans see the same geometric patterns during drug use, illness, or near-death experiences? Even pressing on our eyes can induce the same spirals other people see. Research by professor of Mathematical and Computational Neuroscience Paul Bressloff and his colleagues at Oxford shows that these patterns are formed in the first visual field of the brain, or V1.
An object or scene in the visual world is projected as a two-dimensional image on the retina of each eye, so what we see can also be treated as flat sheet: the visual field. Every point on this sheet can be pin-pointed by two coordinates, just like a point on a map, or a point on the flat model of V1. The alternating regions of light and dark that make up a geometric hallucination are caused by alternating regions of high and low neural activity in V1 — regions where the neurons are firing very rapidly and regions where they are not firing rapidly.
A closer look at the types of specialized neurons in the V1 field and how they interact with each other explains the geometric patterns.
Bressloff and his colleagues used a generalised version of the equations from the original model to let the system evolve. The result was a model that is not only more accurate in terms of the anatomy of V1, but can also generate geometric patterns in the visual field that the original model was unable to produce. These include lattice tunnels, honeycombs and cobwebs that are better characterised in terms of the orientation of contours within them, than in terms of contrasting regions of light and dark.
That’s about as simple as I can make it in a short blurb; the entire article explains it better. Yes, there is math involved. Link -via Metafilter
Found at Cliff Pickover’s always excellent Reality Carnival. It took me a while to get it!
Previously on Neatorama: The Math Book: Milestones in the History of Math
Photographer Nikki Graziano takes pictures and then creates graphs of mathematical functions which map nicely to elements of the image. It’s a very neat and beautiful way of combining math, nature, and art together into a single image.
Most of us can’t tell our secant from our cotangent. But the forms are everywhere, and Nikki Graziano wants to help us see them. Graziano, a math and photography student at Rochester Institute of Technology, overlays graphs and their corresponding equations onto her carefully composed photos. “I wanted to create something that could communicate how awesome math is, to everyone,” she says.
From the Upcoming ueue, submitted by thalin.
The Salary Theorem proves mathematically that those who know more make less money. Therefore, if you know nothing, you should be fabulously wealthy! Link -via Digg
Just another way I can prove to my kids that I am, in fact, a genius. -via reddit
The Fibonacci sequence, named after a 13th Century Italian mathematician, is a sequence of numbers in which every third number is the sum of the previous two numbers. This ring and others like it by Etsy seller Holmes Craft is an homage to that mathematical sequence in that the beads are organized according to the first four Fibonacci numbers.
Link via Technabob | Math Explanation | Photo: Holmes Craft
George W. Hart has brought us a milestone in breakfast-related math feats, the mobius strip bagel. Directions for making your own are on the link. The author says these are superior to regular bagels for non-math-related reasons as well.
It is much more fun to put cream cheese on these bagels than on an ordinary bagel. In additional to the intellectual stimulation, you get more cream cheese, because there is slightly more surface area.
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