PPT-Fibonacci Numbers

F n F n1 F n2 F 0 0 F 1 1 0 1 1 2 3 5 8 13 21 34 Straightforward recursive procedure is slow Why How slow Lets draw the recursion tree Fibonacci Numbers 2. DOTS AND DASHES. James . Tanton. MAA Mathematician-at-Large. jtanton@maa.org. Curriculum Inspirations: . www.maa.org/ci. Mathematical Stuff: . www.jamestanton.com. Mathematical Courses: . www.gdaymath.com. The Power of Visualization. James . Tanton. MAA Mathematician-at-Large. t. anton.math@gmail.com. . Curriculum Inspirations: . www.maa.org/ci. Mathematical Stuff: . www.jamestanton.com. Mathematical Courses: . Kristijan Štefanec. The golden ratio. Also called. φ. Two quantities a and b are said to be in golden ratio if = =. φ. The second definition of . φ. is: . φ. -1=. From this one, we can easily calculate . The Power of Visualization. James . Tanton. MAA Mathematician-at-Large. t. anton.math@gmail.com. . Curriculum Inspirations: . www.maa.org/ci. Mathematical Stuff: . www.jamestanton.com. Mathematical Courses: . Fibonacci. . numbers. The . Fibonacci. . Numbers. :. 1, 1, 2, 3, 5, 8, 13, 21, 34. a, a, (. a+a. ), a+(. a+a. ), (. a+a. ) + (. a+a+a. ) etc.. Term = . sum. of 2 . preceding. terms. = GOLDEN RATIO. b.wikkerink@csgliudger.nl. Programming. a strategy game. What. we do:.  . Explore a game.  . Use mathematics to find a winning strategy.  . Make a program in TI-Basic. But first . ….  . Charlotte Kiang. May 16, 2012. About me. My name is Charlotte Kiang, and I am a junior at Wellesley College, majoring in math and computer science with a focus on engineering applications.. What I hope to accomplish today. Emma Stephens, Charlotte Evans, Kenneth Mcilree, Lisa Yuan. What are the Fibonacci numbers?. The Fibonacci sequence is a recursively defined sequence where,. F. 1 . = 1 and F. 2 . = 1 . Alannah McGregor. Gudrun Mackness. Brittany Kozak. Background Information. Grades 6-7. Mathematics: patterning and algebra. Time frame: 30 min. Lesson environment. Inquiry-based exploration. Exploration of a complex number pattern that results in a sequence that is found in nature and has been translated into art. 1175 – 1250 AD. Best remembered for a problem he posed in Liber Abaci dealing with RABBITS!. The Rabbit Problem. At 2 months, the rabbits can reproduce a pair of bunnies. . How many pairs at k months?. Math 2700. Spring 2010. History of the Fibonacci Sequence. From . Fibonacci’s. . Liber. Abaci. , Chapter 12. . How Many Pairs of Rabbits Are Created by One Pair in One Year. . . A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear also.. Lecture #11 : Recursion II. Instructor : Sean Morris. Security Flaws in your OS. http://. www.nytimes.com. /2013/07/14/world/. europe. /. nations-buying-as-hackers-sell-computer-flaws.html?pagewanted. Maria Murphy. Central Florida Math Circle. University of Central Florida . Department of Mathematics . What is a Palindrome? . A palindrome is a word or phrase that reads the same forwards and backwards. . Maths. in Nature. Patterns in nature. are visible regularities of form found in the natural world. These . patterns. recur in different contexts and are . modelled. mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, arrays, cracks and stripes. Early Greek philosophers studied these patterns, with .