# Fibonacci Numbers, the Golden section and the Golden String

Fibonacci Numbers and the Golden Section This is the Home page for Dr Ron Knott's multimedia web site on the Fibonacci numbers, the Golden section and the Golden string hosted by the Mathematics Department of the University of Surrey, UK. The Fibonacci numbers are The golden section numbers are 0·61803 39887... = phi = φ and 1·61803 39887... = Phi = Φ The golden string is 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 ... a sequence of 0s and 1s that is closely related to the Fibonacci numbers and the golden section. If you want a quick introduction then have a look at the first link on the Fibonacci numbers and where they appear in Nature. THIS PAGE is the Menu page linking to other pages at this site on the Fibonacci numbers and related topics above. Fibonacci Numbers and Golden sections in Nature Ron Knott was on Melvyn Bragg's In Our Time on BBC Radio 4, November 29, 2007 when we discussed The Fibonacci Numbers (45 minutes). listen again online or download the podcast. and phi . The Golden Section

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The Fibonacci Numbers and Golden section in Nature - 1 This page has been split into TWO PARTS. This, the first, looks at the Fibonacci numbers and why they appear in various "family trees" and patterns of spirals of leaves and seeds. The second page then examines why the golden section is used by nature in some detail, including animations of growing plants. Let's look first at the Rabbit Puzzle that Fibonacci wrote about and then at two adaptations of it to make it more realistic. This introduces you to the Fibonacci Number series and the simple definition of the whole never-ending series.

Welcome - OeisWiki From OeisWiki Welcome to The On-Line Encyclopedia of Integer Sequences® (OEIS®) Wiki Some Famous Sequences Click on any of the following to see examples of famous sequences in the On-Line Encyclopedia of Integer Sequences (the OEIS), then hit "Back" in your browser to return here: Recamán's sequence, A005132 The Busy Beaver problem, A060843 The Catalan numbers, A000108 The prime numbers, A000040 The Mersenne primes, A000043 and A000668 The Fibonacci numbers, A000045 For some other fascinating sequences see Pictures from the OEIS: The (Free) OEIS Store

What you need to know about artificial intelligence, and the imminent robot future Do androids dream of electric sheep? That's unclear, but I know for sure that every kid dreams of intelligent, thinking robots -- certainly every kid who goes on to work at CNET, in any case. Today, my sci-fi-fuelled childhood fantasies of a bot with a "brain the size of a planet" are closer than ever to being realised. Artificial intelligence, or AI, the practice of making a machine behave in a smart way, is already changing our world and is, by my reckoning, the most fascinating field of technology right now.

Seasonal Math Activities These math activities are organized by seasons. Elementary teachers often incorporate seasonal activities as craft projects. Many of these seasonal craft projects can be mathematical as well with a little forethought. Browse the activities for projects to add that reinforce mathematical concepts and skills through seasonal and holiday themes. Back-to-School Activities Back-to-School Activities: include glyphs, math-literature connection, problem solving and daily math routines. September 2007: Back-to-School Issue includes writing in Math class, active participation, using math templates.

Robots master skills with ‘deep learning’ technique Robot learns to use hammer. What could go wrong? (credit: UC Berkeley) UC Berkeley researchers have developed new algorithms that enable robots to learn motor tasks by trial and error, using a process that more closely approximates the way humans learn. Printable Mazes for Kids These printable mazes for kids, or puzzles and mazes in general, are excellent educational worksheets for developing kids small motor skills and spacial perception skills. You can print the traditional printable mazes, counting mazes and PrintActivities exclusive . Follow the happy faces to find the path through the printed maze.

Fibonacci Leonardo Bonacci (c. 1170 – c. 1250)[2]—known as Fibonacci (Italian: [fiboˈnattʃi]), and also Leonardo of Pisa, Leonardo Pisano, Leonardo Pisano Bigollo, Leonardo Fibonacci—was an Italian mathematician, considered as "the most talented Western mathematician of the Middle Ages.".[3][4] Fibonacci introduced to Europe the Hindu–Arabic numeral system primarily through his composition in 1202 of Liber Abaci (Book of Calculation).[5] He also introduced to Europe the sequence of Fibonacci numbers (discovered earlier in India but not previously known in Europe), which he used as an example in Liber Abaci.[6] Life Fibonacci was born around 1170 to Guglielmo Bonacci, a wealthy Italian merchant and, by some accounts, the consul for Pisa.

Nick's Mathematical Puzzles Welcome to my selection of mathematical puzzles. What's new? See puzzle 160. Fibonacci number A tiling with squares whose side lengths are successive Fibonacci numbers In mathematics, the Fibonacci numbers or Fibonacci sequence are the numbers in the following integer sequence: or (often, in modern usage): (sequence A000045 in OEIS). The Fibonacci spiral: an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling;[3] this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34.

The Illusion Of Matter: Our Physical Reality Isn’t Really Physical At All Niels Bohr, a Danish Physicist who made significant contributions to understanding atomic structure and quantum theory once said: “if quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet.” Quantum physics has left scientists all over the world baffled, especially with the discovery that our physical material reality, isn’t really physical at all. “Everything we call real is made of things that cannot be regarded as real.” It seems philosophers of our ancient past were right, our senses really do deceive us.

I Love Math and Young Math ►The "I Love Math" series by TimeLife covers virtually every elementary math concept. These books can be used to explore math concepts within the stated themes, and are possibly the most-read math readers in our home library among all our kids. They are out of print, but many can be found at used booksellers at reasonable prices.

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