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Fibonacci in Nature

Fibonacci in Nature
The Fibonacci numbers play a significant role in nature and in art and architecture. We will first use the rectangle to lead us to some interesting applications in these areas. We will construct a set of rectangles using the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, and 34 which will lead us to a design found in nature. You will need a ruler, protractor, and compass. Start by drawing two, unit squares (0.5 cm is suggested) side by side. Your construction will look like this: Now, with your compass, starting in the unit squares, construct in each square an arc of a circle with a radius the size of the edge of each respective square (Your arcs will be quarter circles.). This spiral construction closely approximates the spiral of a snail, nautilus, and other sea shells. We will next consider the use by architects and artists throughout history of the "Golden Ratio" and other geometric shapes based upon these ratios. Graphics courtesy of Dr.

2012 March 12 - The Scale of the Universe Interactive Discover the cosmos! Each day a different image or photograph of our fascinating universe is featured, along with a brief explanation written by a professional astronomer. 2012 March 12 The Scale of the Universe - Interactive Flash Animation Credit & Copyright: Cary & Michael Huang Explanation: What does the universe look like on small scales? Tomorrow's picture: dust before galaxies Authors & editors: Robert Nemiroff (MTU) & Jerry Bonnell (UMCP)NASA Official: Phillip Newman Specific rights apply.NASA Web Privacy Policy and Important NoticesA service of:ASD at NASA / GSFC& Michigan Tech.

How to create an unfair coin and prove it with math Want to make sure you win the coin toss just a little more often than you should? I certainly do, so I made some unfair coins. We’ll use the beta distribution to see just how unfair they are. While this is just a toy example problem for using the beta distribution, machine learning algorithms rely on this distribution for learning just about everything. Math is an amazing thing that way. Making the coins We’ll make our unfair coins by bending them. It’s easy to bend the coins with your teeth: WAIT! I made seven coins this way, each with a different bending angle. I did 100 flips for each coin, making sure each flip went at least a foot in the air and spun real well. Here’s the raw results: Now for the math Coin flipping is a Bernoulli process. Enter the beta distribution. x. The beta distribution takes two parameters and is the number of heads we have flipped plus one, and is the number of tails plus one. That’s exactly what we said the expectation of the next coin flip should be above. Where .

10 Awesome Online Classes You Can Take For Free Cool, but you need iTunes for nearly everything, and that gets an 'F.' Are there really no other places to get these lessons? I was sure there are some on Academic Earth. Flagged 1. 7 of them are available via YouTube. 2. iTunes is free. 1. 2. Don't worry, we're looking out for you! While I have no personal beef with iTunes, I know that many people share your sentiments — so I actually made a concerted effort to include relevant youtube links when possible.

Impress your friends with mental Math tricks & Fun Math Blog See Math tricks on video at the Wild About Math! mathcasts page. Being able to perform arithmetic quickly and mentally can greatly boost your self-esteem, especially if you don't consider yourself to be very good at Math. This article presents nine ideas that will hopefully get you to look at arithmetic as a game, one in which you can see patterns among numbers and pick then apply the right trick to quickly doing the calculation. The tricks in this article all involve multiplication. Don't be discouraged if the tricks seem difficult at first. As you learn and practice the tricks make sure you check your results by doing multiplication the way you're used to, until the tricks start to become second nature. 1. Multiplying by 9 is really multiplying by 10-1.So, 9x9 is just 9x(10-1) which is 9x10-9 which is 90-9 or 81. Let's try a harder example: 46x9 = 46x10-46 = 460-46 = 414. One more example: 68x9 = 680-68 = 612. 2. 3. Multiplying by 5 is just multiplying by 10 and then dividing by 2. 4. 5.

Brain Fitness And Memory Programs, Brain Training - CogniFit Two Suns? Twin Stars Could Be Visible From Earth By 2012 - StumbleUpon By Dean Praetorius | HuffingtonPost.com Earth could be getting a second sun, at least temporarily. Dr. Brad Carter, Senior Lecturer of Physics at the University of Southern Queensland, outlined the scenario to news.com.au. Betelgeuse, one of the night sky’s brightest stars, is losing mass, indicating it is collapsing. It could run out of fuel and go super-nova at any time. When that happens, for at least a few weeks, we’d see a second sun, Carter says. The Star Wars-esque scenario could happen by 2012, Carter says... or it could take longer. But doomsday sayers should be careful about speculation on this one. In fact, a neutrino shower could be beneficial to Earth. UPDATE: To clarify, the news.com.au article does not say a neutrino shower could be beneficial to Earth, but implies a supernova could be beneficial, stating, "Far from being a sign of the apocalypse, according to Dr Carter the supernova will provide Earth with elements necessary for survival and continuity." Top Image: Source

100 Websites You Should Know and Use In the spring of 2007, Julius Wiedemann, editor in charge at Taschen GmbH, gave a legendary TED University talk: an ultra-fast-moving ride through the “100 websites you should know and use.” Six years later, it remains one of the most viewed TED blog posts ever. Time for an update? To see the original list, click here. And now, the original list from 2007, created by Julius Wiedemann, editor in charge at Taschen GmbH. In the spring of 2007, Julius Wiedemann, editor in charge at Taschen GmbH, gave a legendary TED University talk: an ultra-fast-moving ride through the “100 websites you should know and use.” To see the original list, click here. And now, the original list from 2007, created by Julius Wiedemann, editor in charge at Taschen GmbH.

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