The contest starts today and will run from July 22nd at 11 AM ET until Wednesday, August 5th at 10:59 AM ET.
The contest starts today and will run from July 22nd at 11 AM ET until Wednesday, August 5th at 10:59 AM ET.
Nikola Tesla was born on this day in 1856. Here are 10 facts from Tesla: Inventor of the Electrical Age by W. Bernard Carlson:
1. Tesla has two meanings in Serbian: it can refer to a small ax called an adze or to a person with protruding teeth, a common characteristic of people in Nikola Tesla’s family.
2. The night Tesla was born there was a severe thunderstorm. The fearful midwife said, “He’ll be a child of the storm.” His mother responded, “No, of light.”
3. Initially Tesla wanted to be a teacher, but he switched to engineering in his second year at Joanneum Polytechnic School in order to work on building a spark-free motor.
4. One of his favorite hobbies was card-playing and gambling. “To sit down to a game of cards, was for me the quintessence of pleasure.”
5. When Tesla came to New York for the first time after living in Prague, Budapest, and Paris, he was shocked by the crudeness and vulgarity of Americans.
6. In 1886, Tesla was abandoned by his business partners and could not find work—he took a job digging ditches to get by. A patent he filed that year for thermomagnetic motor helped him get back on his feet.
7. In April of 1887, he formed the Tesla Electric Company with his two business partners, Alfred S. Brown and Charles F. Peck. His first lab was located in New York’s financial district.
8. Mark Twain was a good friend of Tesla’s.
9. Tesla suffered from periodic bouts of depression. He treated it by administering electroshock therapy to himself.
10. Tesla told a reporter that he did not want to marry because he thought it would compromise his work. He did not have any known relationships with women.
If you would like to learn more, you can preview the introduction of Tesla: Inventor of the Electrical Age.
July 4, 2015 may be about Independence Day in the United States, but in Oxford, it’s about one of the great heroes of fiction, a young girl who followed a white rabbit, met a hookah-smoking caterpillar and asked, “Who are you?”
In July 1865, 150 years ago, Charles Lutwidge Dodgson, a professor of mathematics and Anglican deacon, published Alice’s Adventures Underground, a story about a little girl who tumbles down a rabbit hole into a world of nonsense, but keeps her wits about her. With this the world was first introduced to Alice (who was inspired by a real child named Alice Liddell) and her pseudonymous creator, Lewis Carroll. To commemorate the anniversary, the rare first edition recently went on display in Oxford. Princeton University Press is honored to publish our own beautiful new edition of Alice’s Adventures in Wonderland, with rarely seen illustrations by none other than Salvador Dalí.
Of course, Alice doesn’t just have a whimsical adventure full of anthropomorphic creatures. She falls into a world that is curiously logical and mathematical. Carroll expert Mark Burstein discusses Dalí’s connections with Carroll, his treatment of the symbolic figure of Alice, and the mathematical nature of Wonderland. In addition, mathematician Thomas Banchoff reflects on the friendship he shared with Dalí and the mathematical undercurrents in Dalí’s work.
Explore chapter one in full here, view the best illustrations over the years on Brain Pickings, or click here for a list of anniversary-related events. If you’re here in New Jersey, Washington Crossing’s Open Air Theater will be performing Alice in Wonderland in the park today at 11 and tomorrow at 4.
Happy birthday, Alice!
Frank A. Farris teaches mathematics at Santa Clara University and is a former editor of Mathematics Magazine, a publication of the Mathematical Association of America. He is also the author of the new Princeton University Press book Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. The book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry.
Frank Farris gave Princeton University Press a look at why he wrote Creating Symmetry, where he feels this book will have major contributions, and what comes next.
What inspired you to get into mathematical writing?
FF: After editing Mathematics Magazine for many years, I developed a passion for communicating mathematics: I didn’t want dry accounts written by anonymous authors; I wanted stories told by people. I wasn’t so interested in problems and puzzles, but in the stories that bring us face to face with the grand structures of mathematics.
Why did you write this book?
FF: Many years ago, I asked the innocent question: What is a wallpaper pattern, really? Creating Symmetry is the story of my dissatisfaction with standard answers and how it led me on a curious journey to a new kind of mathematical art. I took some risks and let my personality show through, while maintaining an honest, mathematically responsible approach. I hope readers enjoy the balance: real math told by a person.
What do you think is the book’s most important contribution?
FF: Most people who see my artwork say they’ve never seen anything like these images and that pleases me immensely. Of course, people have seen wallpaper patterns before, but the unusual construction method I use—wallpaper waves and photographs—gives my patterns an intricacy and rhythm that people wouldn’t create through the usual potato-stamp construction method, where the patterns is made from discrete blocks.
What is your next project?
FF: I am working on a “wallpaper lookbook,” a book for the simple joy of looking at patterns. Creating Symmetry tells people how to make the patterns, and there’s quite a lot of mathematical detail to process. Not everyone who likes my work wants to know all the details, but can still appreciate the “before and after” nature of the images.
Who do you see as the audience for this book?
FF: There are three audiences and they will read the book in different ways. The general reader, who knows some calculus but may be a little rusty, should find a refreshing and challenging way to reconnect with mathematics. Undergraduate mathematics majors will enjoy the book as a summer project or enrichment reading, as it makes surprising connections among topics they may have studied. The professional mathematician will find this light reading—a chance to enjoy the amazing interconnectedness of our field.
Tipping Point Tuesday takes on a global debate!
The United States and Canada use paper that is 8.5 inches by 11 inches, called US letter. However, the rest of the world officially uses A4 paper, which has a different aspect ratio. Which paper size is better, US letter or A4? Find the mathematical answer with the help of Marc Chamberland in a video from his YouTube channel Tipping Point Math.
Today’s Tipping Point Tuesday gives us a behind the scenes look at how mathematics can be used in unique ways in the workplace.
Here’s the scenario: In busy museums, guards keep an eye on the priceless works of art. Suppose a museum wants to schedule the fewest number of guards per museum shift without leaving any art display unmonitored. Marc Chamberland explains how a museum manager could use mathematics to calculate the ideal number of guards per shift.
Marc Chamberland is the Myra Steele Professor of Natural Science and Mathematics at Grinnell College. He is also the creator of the popular YouTube channel Tipping Point Math, which strives to make mathematics accessible to everyone. Continuing on his mathematics mission, Marc Chamberland has authored Single Digits: In Praise of Small Numbers, a book that looks at the vast numerical possibilities that can come from the single digits. Over the course of the coming weeks, we will be exploring the single digits in real life math situations with the author himself by featuring a series of original videos from Tipping Point Math.
Recently Chamberland gave the press a look at the inspiration behind the book, along with some personal insights on being a mathematician, and more:
What was the motivation behind your Tipping Point Math website?
MC: I have long felt that many people are sour on math because they think it is all technical stuff that leads to nowhere. I felt that if they could be exposed to the rich ideas and beauty of mathematics presented in an interesting way, their negative opinion could change.
I had wondered for a while how YouTube could be used since it is such a popular medium. In 2013, I reconnected with Henry Reich, a former student of mine, who created the highly successful channels MinutePhysics and MinuteEarth. With his inspiration and advice, I was convinced that a similar channel for mathematics was possible. Thus the concept of Tipping Point Math was born.
What is the biggest misunderstanding people have about your mathematics profession?
MC: Besides my remarks about people thinking that math is only about technical stuff, there is also the misconception that all of mathematics is known. This is not the case at all. New mathematics is being developed every day. This ranges from very abstract ideas to applications such as signal processing, medical imaging, population modeling, and computer algorithms.
What would you have been if not a mathematician?
MC: In my last year of high school, I developed an unquenchable thirst to explore two academic areas: mathematics and music. Since I eventually became a mathematics professor, I suppose one could say that mathematics “won”. But music was also consuming. I would ask myself, “Why does that piece of music sound so good? Why does it produce particular emotional states? How can I compose music that affects people in different ways?” To this day I still ask some of these questions, I occasionally compose short pieces, and I play the piano, guitar, and sing. Would I have been a musician? Is it too late to change?
What are you reading right now?
MC: I’m reading “The Alchemist” (by Paulo Coelho) out loud to my wife. The simple language and overflowing spirituality is stunning.
Who do you see as the audience for your book, Single Digits?
MC: My audience: those who love beauty. I did not choose topics for their depth or their technical superiority. I principally chose vignettes that I thought are beautiful.
The staff and community of Princeton University Press mourns the tragic loss of John and Alicia Nash. In 2001 we had the great privilege of publishing The Essential John Nash, a collection of Professor Nash’s scholarly articles edited by his biographer, Sylvia Nasar, and his longtime colleague and friend, Princeton mathematician Harold Kuhn, (now deceased). The Essential John Nash received impressive public exposure largely because it was published during the release of the Academy Award-winning movie version of Nash’s biography, A Beautiful Mind. Critics and readers admired The Essential John Nash as a faithful representation of Nash’s most important work, made available for a broadly intellectual audience of mathematicians and social scientists. Gratifying as this recognition was for us, during the course of publication, the staff members at PUP who worked on Professor Nash’s book had the great good fortune to get to know him and Alicia, two gentle and wonderful people. Our thoughts and prayers are with their family.
Peter J. Dougherty
From chapter eight of Marc Chamberland’s Single Digits:
How many times should you shuffle a deck of cards so that they’re well-mixed? Gamblers know that three or four times is not sufficient and take advantage of this fact. In 1992, researchers did computer simulations and estimated that seven rough riffle shuffles is a good amount. They took their research further and figured out that further shuffling does not significantly improve the mixing. If the shuffler does a perfect riffle shuffle (a Faro shuffle), in which s/he perfectly cuts the deck and shuffles so that each card from one side alternates with each card from the other side, then a standard 52-card deck will end in the same order that it started in after it is done 8 times.
The numbers one through nine have remarkable mathematical properties and characteristics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? Are there really “six degrees of separation” between all pairs of people? And how can any map need only four colors to ensure that no regions of the same color touch? In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics.
Each chapter focuses on a single digit, beginning with easy concepts that become more advanced as the chapter progresses. Chamberland covers vast numerical territory, such as illustrating the ways that the number three connects to chaos theory, an unsolved problem involving Egyptian fractions, the number of guards needed to protect an art gallery, and problematic election results. He considers the role of the number seven in matrix multiplication, the Transylvania lottery, synchronizing signals, and hearing the shape of a drum. Throughout, he introduces readers to an array of puzzles, such as perfect squares, the four hats problem, Strassen multiplication, Catalan’s conjecture, and so much more. The book’s short sections can be read independently and digested in bite-sized chunks—especially good for learning about the Ham Sandwich Theorem and the Pizza Theorem.
Appealing to high school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.
The idea of cloning a mammoth, the science of which is explored in evolutionary biologist and “ancient DNA expert” Beth Shapiro’s new book, How to Clone a Mammoth, is the subject of considerable debate. One can only imagine what the animal kingdom would think of such an undertaking, but wonder no more. PUP staffers were feeling “punny” enough to ask their best friends:
Chester can’t get past “ice age bones”.
Buddy thinks passenger pigeons would be so much more civilized… and fun to chase.
Tux always wanted to be an evolutionary biologist…
Stella thinks 240 pages on a glorified elephant is a little excessive. Take her for a walk.
A mammoth weighs how much?! Don’t worry, Murphy. The tundra is a long way from New Jersey.
We are teaming with Corbis Entertainment to offer this terrific giveaway through their official Albert Einstein Facebook page. Contest details below, but please head over to the “official Facebook page of the world’s favorite genius” to enter!
Paul Nahin is the author of many books we’ve proudly published over the years, including An Imaginary Tale, Dr. Euler’s Fabulous Formula, and Number Crunching. For today’s installment in our Math Awareness Month series, he writes about his first encounter with √-1.
Electrical Engineering and √-1
It won’t come as a surprise to very many to learn that mathematics is central to electrical engineering. Probably more surprising is that the cornerstone of that mathematical foundation is the mysterious (some even think mystical) square-root of minus one. Every electrical engineer almost surely has a story to tell about their first encounter with √-1, and in this essay I’ll tell you mine.
Lots of different kinds of mathematics have been important in my personal career at different times; in particular, Boolean algebra (when I worked as a digital logic designer), and probability theory (when I wore the label of radar system engineer). But it’s the mathematics of √-1 that has been the most important. My introduction to √-1 came when I was still in high school. In my freshman year (1954) my father gave me the gift of a subscription to a new magazine called Popular Electronics. From it I learned how to read electrical schematics from the projects that appeared in each issue, but my most important lesson came when I opened the April 1955 issue.
It had an article in it about something called contra-polar power: a desk lamp plugged into a contra-polar outlet plug would emit not a cone of light, but a cone of darkness! There was even a photograph of this, and my eyes bugged-out when I saw that: What wondrous science was at work here?, I gasped to myself —I really was a naive 14-year old kid! It was, of course, all a huge editorial joke, along with some nifty photo-retouching, but the lead sentence had me hooked: “One of the reasons why atomic energy has not yet become popular among home experimenters is that an understanding of its production requires knowledge of very advanced mathematics.” Just algebra, however, was all that was required to understand contra-polar power.
Contra-polar power ‘worked’ by simply using the negative square root (instead of the positive root) in calculating the resonant frequency in a circuit containing both inductance and capacitance. The idea of negative frequency was intriguing to me (and electrical engineers have actually made sense of it when combined with √-1, but then the editors played a few more clever math tricks and came up with negative resistance. Now, there really is such a thing as negative resistance, and it has long been known by electrical engineers to occur in the operation of electric arcs. Such arcs were used, in the very early, pre-electronic days of radio, to build powerful AM transmitters that could broadcast music and human speech, and not just the on-off telegraph code signals that were all the Marconi transmitters could send. I eventually came to appreciate that the operation of AM/FM radio is impossible to understand, at a deep, theoretical level, without √-1.
When, in my high school algebra classes, I was introduced to complex numbers as the solutions to certain quadratic equations, I knew (unlike my mostly perplexed classmates) that they were not just part of a sterile intellectual game, but that √-1 was important to electrical engineers, and to their ability to construct truly amazing devices. That early, teenage fascination with mathematics in general, and √-1 in particular, was the start of my entire professional life. I wish my dad was still alive, so I could once again thank him for that long-ago subscription.
These are the best-selling books for the past week.
|Alan Turing: The Enigma, The Book That Inspired the Film The Imitation Game by Andrew Hodges|
|Tesla: Inventor of the Electrical Age by W. Bernard Carlson|
|The Rise and Fall of Classical Greece by Josiah Ober|
|The Transformation of the World: A Global History of the Nineteenth Century by Jürgen Osterhammel|
|Pedigree: How Elite Students Get Elite Jobs by Lauren A. Rivera|
|The Original Folk and Fairy Tales of the Brother’s Grimm: The Complete First Edition by Jacob & Wilhelm Grimm, Translated and edited by Jack Zipes|
|On Bullshit by Harry G. Frankfurt|
|How to Clone a Mammoth: The Science of De-Extinction by Beth Shapiro|
|Irrational Exuberance by Robert J. Shiller|
|1177 B.C.: The Year Civilization Collapsed by Eric H. Cline|
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