Nature of Mathematics: Part 1 & 2 PDF

Our lady of Fatima university COLLEGE OF ARTS AND SCIENCES Math and Physics Department Pampanga Campus MATM111 NATURE OF MATHEMATICS: Mathematics in Our World Jerica Nicole R. Flores, MAEd Lecturer I. Nature of Mathematics: Mathematics in Our World...

Our lady of Fatima university COLLEGE OF ARTS AND SCIENCES Math and Physics Department Pampanga Campus MATM111 NATURE OF MATHEMATICS: Mathematics in Our World Jerica Nicole R. Flores, MAEd Lecturer I. Nature of Mathematics: Mathematics in Our World 1.1. Patterns 1.2. 1.3. Golden and Numbers Fibonacci Ratio in Nature Sequence and in World Learning Outline  I. Nature of Mathematics: Mathematics in Our World At the end of the chapter the students are expected: To argue about the nature of mathematics, what it is, how it is expressed, presented, and used. To express appreciation for mathematics as human endeavor. Learning Outcomes Nature of Mathematics Patterns and Numbers  Nature of Mathematics Patterns and Numbers ▪ What is it? ▪ Where is it? ▪ What is it for? ▪ How it is done? ▪ Who uses Mathematics? ▪ Why is it important to learn or know? Nature of Mathematics Patterns and Numbers Nature of Mathematics Patterns and Numbers Nature of Mathematics Patterns and Numbers  Nature of Mathematics Patterns and Numbers PATTERNS AND NUMBERS IN NATURE AND THE WORLD PATTERN defined as: ❑ Regular ❑ Repeated ❑ Recurring forms or designs ❑ Identify relationships ❑ Find logical connections to form generalizations Nature of Mathematics Patterns and Numbers Nature of Mathematics Patterns and Numbers RECITATION RECITATION RECITATION Nature of Mathematics Patterns and Numbers  Nature of Mathematics Fibonacci Sequence ▪ His real name was Leonardo Pisano Bogollo, and he lived between 1170 and 1250 in Italy. ▪ "Fibonacci" was his nickname, which roughly means "Son of Bonacci". ▪ As well as being famous for the Fibonacci Sequence, he helped spread Hindu-Arabic Numerals (like our present numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) through Europe in place of Roman Numerals (I, II, III, IV, V, etc). That has saved us all a lot of trouble!.  Nature of Mathematics Fibonacci Sequence Fibonacci Sequence ▪ Fibonacci number: is an integer in the infinite sequence 1, 1, 2, 3, 5, 8, 13, … of which the first two terms are 1 and 1 and each succeeding… ▪ It displays unique mathematical properties that make it useful in fields as diverse as astronomy (distances between planets and the sun, and the shape of galactic spirals), botany (growth patterns of plants and trees), and financial markets (price movements of securities). Nature of Mathematics Fibonacci Sequence Nature of Mathematics Fibonacci Sequence Fibonacci Sequence In Nature Fibonacci Sequence And several Biological Settings Fibonacci Sequence And several Biological Settings Fibonacci Sequence In Computer Science  Nature of Mathematics Fibonacci Sequence ▪ The Fibonacci Sequence can be written as a "Rule“ ▪ First, the terms are numbered from 0 onwards like this: ▪ So term number 6 is called x6 (which equals 8). ▪ Simple Rule: Add the last two terms to get the next. Nature of Mathematics Fibonacci Sequence ▪ So we can write the rule:  Nature of Mathematics Fibonacci Sequence ▪ Where in: RECITATION  RECITATION 1. Let Fib(n) be the nth term of the Fibonacci sequence with Fib(2)= 1, Fib(3) =1, Fib (4)=2 and so on, find the following: (a) Fib(10) (b) Fib (11) (c) if Fib(23)= 17,711 and Fib(25)= 46,368, what is Fib(24)? Nature of Mathematics The Golden Ratio The Golden Ratio Nature of Mathematics The Golden Ratio Nature of Mathematics The Golden Ratio ▪ And here is a surprise. When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio "φ" which is approximately 1.618034... ▪ In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation. ▪ The Golden Ratio is also sometimes called the golden section, golden mean, golden number, divine proportion, divine section and golden proportion. Nature of Mathematics The Golden Ratio  RECITATION Marvel the minds of the ancient world as you discover the wonders of the golden ratio. TRUE/FALSE Directions: Read each statement below carefully. Place a T on the line if you think a statement, it TRUE. Place an F on the line if you think the statement is FALSE. If you have questions, raise your hand and ask your teacher. _______ 1.) The golden ratio is a mathematical term given to the phenomena of when two lengths, when divided via a formula, is equal to the number phi (φ). _______ 2.) A golden ratio occurs when the formula equation equals the number phi, which is roughly 1.618033, however, this number has an infinite number of decimal places. _______ 3.) The golden ratio was likely first discovered by mathematicians of Ancient Greece, including Pythagoras and Euclid, and studied by later folk such as the Italian Leonardo Bonacci (Leonardo of Pisa). _______ 4.) Circles can be created via the golden ratio, known as ‘golden rectangles’, that have sides of a 1:1.618 ratio, and they are widely accepted as being more aesthetically pleasing than rectangles of random sizes. GO FLEX!