Fibonacci Number The Fibonacci numbers are the sequence of numbers defined by the linear recurrence equation with . The Fibonacci numbers for , 2, ... are 1, 1, 2, 3, 5, 8, 13, 21, ... Fibonacci numbers can be viewed as a particular case of the Fibonacci polynomials Fibonacci numbers are implemented in the Wolfram Language as Fibonacci[n]. The Fibonacci numbers are also a Lucas sequence , and are companions to the Lucas numbers (which satisfy the same recurrence equation). The above cartoon (Amend 2005) shows an unconventional sports application of the Fibonacci numbers (left two panels). A scrambled version 13, 3, 2, 21, 1, 1, 8, 5 (OEIS A117540) of the first eight Fibonacci numbers appear as one of the clues left by murdered museum curator Jacque Saunière in D. The plot above shows the first 511 terms of the Fibonacci sequence represented in binary, revealing an interesting pattern of hollow and filled triangles (Pegg 2003). ends in zeros. The Fibonacci numbers give the number of pairs of rabbits is given by .
Gorgeous Sunrise Photography Sunrise is the instant at which the upper edge of the Sun appears above the horizon in the east. Nature is very beautiful, and if caught by a talented photographer in photographs is worth watching and incomparable to any other form of beauty! Just to gather this beautiful phenomenon in pictures, many photographers get up early and find places to catch it. Here i have gathered some of the most beautiful Sunrise Photos from 1x.com, 500px.com , flickr and Deviant Art. Hope you will find it inspiring and take some exceptional pictures your self! Sunrise by Matjaz Cater Divine Light by Christolakis Heal Me by Sun rise V by Daniel Hasselberg The Valley by Roger Arleryd Sun shower by Christolakis Sun Tree by ~Hassan9 Sun Rise by =DennisChunga Golden Gate Bridge – Into The Mist by PatrickSmithPhotography Autumn Sun rise by Gary McParland The fabulous sunrise by Michal Ostrowski Taj Mahal Sun rise Reflectivity by Heather Hartkamp Let There Be Light by [ Rodelicious ] Dawn by Stefan Nielsen sun rays by ~noobs
100 Incredible Open Lectures for Math Geeks While many math geeks out there may have been teased for their love of numbers, it’s math that makes the world go round, defining everything from the economy to how the universe itself operates. You can indulge your love of mathematics in these great lectures and lecture series, which are a great diversion for those diligently working toward traditional or online master’s degree programs in mathematics. Some are meant to review the basics and others will keep you on the cutting edge of what renowned researchers are doing in the field, but all will help you expand your knowledge and spend a few hours enjoying a topic you love. Basic Math These lectures cover some pretty basic mathematical issues that can be a great review or help younger math lovers get a handle on a subject. Such lectures are an excellent resource for students who are completing online degrees in applied mathematics with the intention of entering careers as mathematics educators in middle schools and high schools. Algebra
70 Photos That Will Take Your Breath Away We here at DPShots believe that the easiest way to learn photography is to learn it by example. Every now and then we come up with some amazing photography examples that take your breath away. This post is no different. We have collected some of the most amazing, most awesome and THE most beautiful photography we could ever get our hands on. This post will help a lot of budding photographers to see where they are headed. It shows what is possible with Photography and a bit of creative thinking. From wildlife to magic to a guy sleeping on the back of a buffalo, this post has photographs for all kinds of photographers to take inspiration from. We have collected over 70 majestic photographs that are simply to good to miss. We hope you like this post and endless others that you will get to checkout in future if you are subscribed to our RSS. The Fearless Cat Dael Giraffe says Hi!. Idealists…foolish enough to throw caution to the winds…have advanced mankind and have enriched the world. Kry Love
Mysterious number 6174 March 2006 Anyone can uncover the mystery The number 6174 is a really mysterious number. At first glance, it might not seem so obvious. But as we are about to see, anyone who can subtract can uncover the mystery that makes 6174 so special. Kaprekar's operation In 1949 the mathematician D. It is a simple operation, but Kaprekar discovered it led to a surprising result. When we reach 6174 the operation repeats itself, returning 6174 every time. We reached 6174 again! A very mysterious number... When we started with 2005 the process reached 6174 in seven steps, and for 1789 in three steps. Only 6174? The digits of any four digit number can be arranged into a maximum number by putting the digits in descending order, and a minimum number by putting them in ascending order. 9 ≥ a ≥ b ≥ c ≥ d ≥ 0 and a, b, c, d are not all the same digit, the maximum number is abcd and the minimum is dcba. which gives the relations for those numbers where a>b>c>d. For three digit numbers the same phenomenon occurs. and
Amazing Roads Photos | Beautiful Places - Geniusbeauty.com: Magazine for Beautiful Women Today I decided to add some more beautiful pictures to the “Beautiful Places” category. And this time it’s going to be amazing photos of roads. Yes, I really mean it, because even roads can be beautiful. These are absolutely different roads: roads in forests, asphalt roads, railroads. If the copyright of any wallpaper or stock photo belongs to you, contact me and I’ll remove it! Nick's Mathematical Puzzles Welcome to my selection of mathematical puzzles. What's new? See puzzle 160. The math puzzles presented here are selected for the deceptive simplicity of their statement, or the elegance of their solution. They range over geometry, probability, number theory, algebra, calculus, trigonometry, and logic. Explaining how an answer is arrived at is more important than the answer itself. Each puzzle is assigned a level of difficulty of between one and four stars, with four being the most difficult. The source for each problem is given at the bottom of the solution page. I welcome feedback of any kind. Some brief biographical information. Nick Back to top
40 Incredible Digital Painting Portraits Get the FlatPix UI Kit for only $7 - Learn More or Buy Now As I’m browsing through portfolios on sites like devianART, some of the work that amazes me the most are the digital paintings and portraits of highly-skilled artists. In this post we’ll feature 40 outstanding examples. Digital Portrait Showcase: Captain Jack Sparrow Elena Formal Portrait Chris Ali G Jimi Hendrix Scarlett Johansson Lisa Edelstein Eyes Water Self Portrait Study Carlzon Portrait Portrait Drawing Natalie Portman Gerard Butler Pink Girl with the Blues Mood1 Desire Pintura Digital Sirnyx Portrait Comission Portrait Portrait 4 Scarlett Johansson Search for the Hiro Another Portrait Portrait of a Madman Liv Tyler Nancy Botwin Nancy Botwin 2 Nami Tamaki Kurt Cobain Josh Holloway Mr. Ryan Adams Tatsuya Christina Aguilera Keira Knightley Johnny Depp John Lennon Carlo Angry Look 3D Digital Portrait For more design inspiration, please see: About Steven Snell Stephen Snell is the owner and editor of Vandelay Design.
50 Stunning Examples Of Reflective Photography Using reflections in photography can lead to some amazing effects and beautiful images. Using water, windows, mirrors or any sort of reflective surface can change an image into a work of art. The wonderful thing about using reflections when taking photos is that they can completely alter the image from something fairly straightforward to something richer or abstract or otherwise more artistic. Sometimes reflections can be annoying and certainly not artistic. But creativity and good-quality photos depend on the photographer being able to see things differently, rather than seeing only one part of a larger whole. Also, using reflected light can vastly improve the quality of lighting available. Whether you choose to use reflection in an artistic way or as a source of lightning, learning to use reflections in photography will help take your photographic skills to the next level. Below we present over 50 beautiful examples of reflective photography. Showcase Of Photos With Reflections: Mik13
35 Beautiful Examples Of Rain Photography Advertisement Most photographers do not feel comfortable in taking photographs in bad weather. Yet bad weather sometimes presents the perfect opportunity to get most out of our skills. In particular, in the beginning of autumn rain can provide the perfect opportunity to capture wonderful photos. Shooting in rain produces dramatic atmosphere and soft romantic scenes. Below we present over 35 beautiful examples of rain photography. All photos are linked and lead to the sources from which they were taken. You may want to take a look at the following related posts: Rain Photography Marcel Germain Maria Sauh vijayal Tim Hearud muha Dreamer-Soul Cody26 Muha J Rutledge black&white Victor Eredel Ben Visbeek Agnieszka Borkowska unknown Artem Tschaikowsky unknown Cody26 Time Magazine Curtis Forrester Zasu Yauheni Attsetski Séverine Cousot aka Sey DeDaniel Ahmed Zahid 3amfromkyoto Hau Si Yuan Julian Borbély Márk Zaniac Suketoketchi Chospatis Soumya DenesG1 Max Further Articles and Related Resources Related posts It's done. Yay!
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