mgf1107lecture25 - This characteristic growth pattern is...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 25 Spiral Growth in Nature When discussing the golden ratio in Lecture 23, it was claimed that it often occurs in nature. While this fact may at first seem coincidental, it can be explained using the concept of a gnomon from Lecture 24, in particular Fibonacci rectangles. Fibonacci Rectangles If we start with a 1 x 1 square, and successively add a square equal in length to the longest side of the previous shape (rectangle in all but the first case), we build a series of rectangles whose sides have the length of two consecutive Fibonacci numbers. Since we know that the ratio of two Fibonacci numbers quickly converges to the Golden Ratio, the difference between the Fibonacci rectangles above and the Golden rectangles discussed in Lecture 24 becomes increasingly small. Now consider a living organism continually growing in a spiral shape inside each successive Fibonacci rectangle.
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Unformatted text preview: This characteristic growth pattern is common to seashells, flowers, fruits, and trees, and explains why the Fibonacci sequence is often seen in nature. Chapter 10 – The Mathematics of Money This chapter will explain the mathematics behind some common financial products such as savings accounts, loans, credit cards, mortgages, and annuities. Since these concepts are often phrased in terms of percentages, it is beneficial to review this basic notion before moving on. Percentages Fact 1: In order to turn a fraction into a percentage we multiply by 100. Ex. Fact 2: In order to turn a percentage into a fraction we divide by 100. Ex. Fact 3: If you start with a quantity Q and increase it by x% then the resulting quantity is Ex. (10.A.9) Ex. (10.A.13) Fact 4: If you start with a quantity Q and decrease it by x% then the resulting quantity is Ex. (10.A.7) Ex. (10.6) Ex. (10.A.19)...
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This note was uploaded on 09/22/2011 for the course MAC 2311 taught by Professor Evinson during the Spring '08 term at University of Central Florida.

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mgf1107lecture25 - This characteristic growth pattern is...

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