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Math Fun Facts

Math Fun Facts
Did you know that it is possible to cut a solid ball into 5 pieces, and by re-assembling them, using rigid motions only, form TWO solid balls, EACH THE SAME SIZE AND SHAPE as the original? This theorem is known as the Banach-Tarski paradox. So why can't you do this in real life, say, with a block of gold? If matter were infinitely divisible (which it is not) then it might be possible. An alternate version of this theorem says (and you'd better sit down for this one): it is possible to take a solid ball the size of a pea, and by cutting it into a FINITE number of pieces, reassemble it to form A SOLID BALL THE SIZE OF THE SUN. Presentation Suggestions: Students will find this Fun Fact hard to believe. The Math Behind the Fact: First of all, if we didn't restrict ourselves to rigid motions, this paradox would be more believable. The proof involves studing group actions on the sphere, specifically, subgroups of the rotation group "SO(3)" that are free subgroups on 2 generators. Related:  Fun Facts of the DayScience!

Amazing Coincidences Weird Stuff Life is full of coincidences, some very minor, but occasionally – extraordinary. This is a list of 15 of the most incredible, unbelievable coincidences. 15. Childhood Book While American novelist Anne Parrish was browsing bookstores in Paris in the 1920s, she came upon a book that was one of her childhood favorites – Jack Frost and Other Stories. 14. In 1858, Robert Fallon was shot dead, an act of vengeance by those with whom he was playing poker. 13. On 2002, Seventy-year-old twin brothers have died within hours of one another after separate accidents on the same road in northern Finland. 12. In the 19th century, the famous horror writer, Egdar Allan Poe, wrote a book called ‘The narrative of Arthur Gordon Pym’. 11. In Monza, Italy, King Umberto I, went to a small restaurant for dinner, accompanied by his aide-de-camp, General Emilio Ponzia- Vaglia. 1. 10. 9. In 19th century Austria, a near-famous painter named Joseph Aigner attempted suicide on several occasions. 8. 7. 6.

Banach-Tarski!: Fun with some very weird math The Banach-Tarski paradox is one of the many places where higher-level math starts to sound like a stoned conversation in a Freshman college dorm room. Imagine a ball. Now imagine cutting that ball up into a finite number of pieces. Six, maybe. Or five. WTF, you may ask? So here's my proposed "intuitive" rationalization of it. Anyway, this very long introduction to a mathematical concept is necessary so that you can enjoy the funny video at the top of this post. Video Link Thank you, samurai!

Khan Academy 10 Psychological Experiments That Went Horribly Wrong Psychology as we know it is a relatively young science, but since its inception it has helped us to gain a greater understanding of ourselves and our interactions with the world. Many psychological experiments have been valid and ethical, allowing researchers to make new treatments and therapies available, and giving other insights into our motivations and actions. Sadly, others have ended up backfiring horribly — ruining lives and shaming the profession. Here are ten psychological experiments that spiraled out of control. 10. Prisoners and guards In 1971, social psychologist Philip Zimbardo set out to interrogate the ways in which people conform to social roles, using a group of male college students to take part in a two-week-long experiment in which they would live as prisoners and guards in a mock prison. 9. Wendell Johnson, of the University of Iowa, who was behind the study Theodore Kaczynski, the Unabomber, also seen top 7. 6. The Milgram Experiment underway 5. 4. 3. 2. 1.

Drunken Walker and Fly -- Math Fun Facts Imagine a drunken person wandering on the number line who starts at 0, and then moves left or right (+/-1) with probability 1/2. What is the probability that the walker will eventually return to her starting point Answer: probability 1. What about a random walk in the plane, moving on the integer lattice points, with probability 1/4 in each of the coordinate directions? What's the chance of return to the starting point? OK, now what about a drunken fly, with 6 directions to move, probability 1/6? Presentation Suggestions: Try to give a little insight by illustrating a random walk on the line for several steps. The Math Behind the Fact: A probabilist would say that simple random walks on the line and plane are recurrent, meaning that with probability one the walker would return to his starting point, and that simple random walks in dimensions 3 and higher are transient, meaning there is a positive probability that he will never return! How to Cite this Page: Su, Francis E., et al.

Health Fun Facts Absolutely True! The safest number of times to reuse a disposable razor is only 3. Disposable razors have thinner blades than other razors, and are thus more prone to producing microscopic cuts in the skin. The longer you keep using a disposable razor, the more germs it will collect, and the greater the chance that a nick will become infected. When you walk uphill, the level of harmful fats in the bloodstream goes down. 90% of the calories in cream cheese come from fat! Make sure your television set is securely supported if you have young children in your house. If you have an impaired immune system, don't eat alfalfa sprouts. Coffee does not increase the risk of heart attacks. Sweet potatoes contain no more calories than white potatoes, and virtually no fat. As people age, they burn fewer calories. If you have symptoms of a heart attack, such as chest pain, chew and swallow one adult aspirin tablet (325 mg) immediately, while you seek medical help. Watch out!

NEURO.tv - Discussion among scientists and philosophers by Diana Xie Stretch goal #1: Bring our Kickstarter to $45,000 and Dr. Jean-François Gariépy will Dance for Science after a 4-hour course with Boris Penton, one of the leading Dubstep dancers in the US. The stretch goal will allow us to buy a professional camera, buy a livecast software that will allow us to switch between guests like you would see in a professional TV show, and hire an intern to manage the technical aspects of the show. NEURO.tv is a talk show featuring leading scientists and philosophers sharing their ideas and discoveries with the general public. We believe that the fascinating discussions and debates about the brain and the mind, those that scientists and philosophers engage in, should be available online, free to download for everyone. NEURO.tv is a registered non-profit organization dedicated to public education. "One of the reasons I'm excited about NEURO.tv is the same reason that I was excited about doing my own podcast. The regular NEURO.tv t-shirts.

Integral Table Layman's Guide to the Banach-Tarski Paradox Preliminaries First of all, let's nail down what exactly we're talking about so that we're all on the same page. First and foremost, we're talking about a mathematical sphere, not a physical sphere, although I'd like to use an analogy with physical spheres to describe one possible way to intuit the Banach-Tarski Paradox. By mathematical sphere, I mean the set of points that lie within a 3-dimensional spherical area in ℜ3, where ℜ is the set of all real numbers. For simplicity, let's assume a radius of 1, so our sphere would be the set: S = {(x,y,z) | x2+y2+z2 <= 1 } One important difference between S and a real, physical sphere is that S is infinitely divisible. 2Or, to be precise, c points, where c is the cardinality of the continuum. Now let's move on to the paradox itself. The Banach-Tarski Paradox The Banach-Tarski Paradox states, basically, that it is possible to take S (as we've defined above), and cut it up into n disjoint pieces, which we shall call A1, A2, ... Bingo! Epilogue

Yawn Fun Fact By Andrew Newburg | Yawn. Go ahead: Laugh if you want (though you’ll benefit your brain more if you smile), but in my professional opinion, yawning is one of the best-kept secrets in neuroscience. Even my colleagues who are researching meditation, relaxation, and stress reduction at other universities have overlooked this powerful neural-enhancing tool. Several recent brain-scan studies have shown that yawning evokes a unique neural activity in the areas of the brain that are directly involved in generating social awareness and creating feelings of empathy. For these reasons I believe that yawning should be integrated into exercise and stress reduction programs, cognitive and memory enhancement training, psychotherapy, and contemplative spiritual practice. Why am I so insistent? As a young medical student, I was once “caught” yawning and actually scolded by my professor. But yawning doesn’t just relax you—it quickly brings you into a heightened state of cognitive awareness.

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