PPT-Fibonacci numbers Golden Ratio,

recurrences Lecture 27 CS2110 Fall 2018 Fibonacci Leonardo Pisano 11701240 Statue in Pisa Italy Announcements A7 NO LATE DAYS No need to put in time and comments We have to grade quickly No regrade requests for A7 Grade based only on your score on a bunch of sewer systems. and Sequences. sol 6.17 . by k . woodard. and k . norman. Arithmetic Sequence. Add or Subtract. . . the . same number . each time. This is called the . common difference. examples. 2, 4, 6, 8, …. On scrap paper, each sketch or draw a rectangle. Measure the sides of your rectangle. What’s the ratio of length to width for your rectangle?. Find the average ratio for the rectangles of all class members. Old Guys and their formulas. Looking for Patterns. So what’s the pattern?. Let’s start with two numbers: 1 and 1.. Add these two values to get the next number in the sequence (pattern).. Add the last two values to get the next number. . Brandon Groeger. March 23, 2010. Chapter 18: Form. and Growth. Chapter 19: Symmetry and Patterns. Chapter 20: . Tilings. Outline. Chapter 18: Form and Growth. Geometric Similarity and Scaling. Physical limits to Scaling. Prepared By : . Murk . Altaf. Anaushey. Quratulain. Golden ratio. In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship.. 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 . 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. On scrap paper, each sketch or draw a rectangle. Measure the sides of your rectangle. What’s the ratio of length to width for your rectangle?. Find the average ratio for the rectangles of all class members. 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 . What are the Fibonacci numbers?. The Fibonacci sequence is a recursively defined sequence where,. F. 1 . = 1 and F. 2 . = 1 . F. n . = F. n-1. F. n-2 . where n>2. {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,...}. 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. Bracketing Bracketing Identifying an interval containing a local minimum and then successively shrinking that interval 2 Unimodality There exists a unique optimizer x * such that f is monotonically decreasing for recurrences. Lecture 27. CS2110 – Fall 2018. Fibonacci. (Leonardo Pisano) 1170-1240?. Statue in Pisa Italy. Announcements. A7: NO LATE DAYS. No need to put in time and comments. We have to grade quickly. No regrade requests for A7. Grade based only on your score on a bunch of sewer systems.. 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 .