Chap-1-Part-3-GNED-03-ppt-2022-2023.pptx

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1. GNED 03 MATHEMATICS IN THE MODERN WORLD 1 ST Semester , AY 2022-2023 NOMER B. LAYUGAN Instructor

2. MATHEMATICS IN THE MODERN WORLD CHAPTER 1 MODULE 3 NOMER B. LAYUGAN Instructor

3. Table of Contents Part 3 Chapter 1 : Mathematics in our World A. Patterns and Numbers in Nature and the World 1. Patterns in Nature 2. People Involved in the Study of Nature B. The Fibonacci Sequence and the Golden Ratio C. Patterns and Regularities in the World as Organized by Mathematics D. Phenomena in the World as Predicted by Mathematics E. Nature and Occurences in the World as Controlled by Mathematics F. Application of Mathematics in the world

4. OBJECTIVES At the end of the chapter, the students will be able to: Articulate the importance of mathematics in ones life. Identify patterns in nature and regularities in the world Argue about the nature of mathematics, what it is, how it is expressed, represented and used Establish the relationship between the Fibonacci Sequence and the Golden Ratio Investigate the relationship of the Golden Ratio and the Fibonacci Numbers in the natural world Express appreciation of mathematics as a human endeavor

5. Patterns and Regularities in the World as Organized by Mathematics C . Patterns and Regularities in the World as Organized by Mathematics Patterns, relationships, and functions constitute a unifying theme of mathematics. So many of the beautiful phenomena observed in nature can be described in mathematical terms. Spectacular Patterns

6. C. Patterns and Regularities in the World Symmetrical Patterns

7. C. Patterns and Regularities in the World Symmetry The concept of symmetry fascinates philosophers, astronomers, mathematicians, artists, architects and physicists. The mathematics behind symmetry seems to permeate in most of the things around us. The mathematics of pendulum  is quite complicated but harmonic. Its period or the time it takes to swing back to its original position is related to its length, but the relationship is not linear. A pendulum that is suspended twice as long as another pendulum does not simply have a period that is also twice as long but mathematics can explicate it. The patterns and regularities in the swinging motion of a pendulum can be explained by mathematics.

8. c. Patterns and Regularities in the World How an image is formed by an object in a plane mirror is fascinating – the image which has exactly the same size as the object and is far behind the mirror as the object is distant from the mirror. This regularity in size and distance can be explained mathematically by the law of reflection. How an image is formed by an object in a plane mirror is fascinating – the image which has exactly the same size as the object and is far behind the mirror as the object is distant from the mirror. This regularity in size and distance can be explained mathematically by the law of reflection. How an image is formed by an object in a plane mirror is fascinating – the image which has exactly the same size as the object and is far behind the mirror as the object is distant from the mirror. This regularity in size and distance can be explained mathematically by the law of reflection. A free-falling object is an object that is falling under the sole influence of gravity. Any object that is moving and being acted upon only be the force of gravity is said to be in a state of free fall. Its motion obeys the equations of uniformly accelerated vertical motion.

9. c. Patterns and Regularities in the World In every interaction, there is a pair of forces acting on the two interacting objects. The amount of the force on the first object equals the size of the force on the second object. The direction of the force on the first object is opposite to the direction of the force on the second object. Forces always come in pairs - equal and opposite action-reaction force pairs.

10. D. Phenomena in the World as Predicted by Mathematics There are many patterns found in nature, including numerical patterns (such as Fibonacci numbers in sunflowers) and shape patterns (such as in snowflakes). Nature has symmetries at every scale, from elementary particles and atoms right up to galaxies. The role of mathematics is to describe symmetry-breaking processes in order to explain in a unified way the fact that the patterns seen in sand dunes and zebras’ stripes are caused by processes which, while physically different, are mathematically very similar. Sand dunes Zebra stripes

11. D. Phenomena in the World as Predicted by Mathematics d Mathematics is an extraordinary exercise of the human mind in abstracting the results of observation to find similarities and differences between phenomena. These relations between phenomena make it possible to organize the natural world into discrete sets of objects that can be studied using similar mathematical objects and methods. Nature, as an object of mathematical study, bridges the gap between the concreteness of the everyday environment and the abstraction of mathematics. Mathematics, in turn, allows us to summarize, formalize, interpolate, and extrapolate from observations that have been recorded ( Knickerbocker , 2016).

12. E. Nature and Occurrences in the World as Controlled by Mathematics for Human Ends Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and its intellectual challenge . For others, including many scientists and engineers, the chief value of mathematics is how it applies to their own work. Because mathematics plays such a central role in modern culture, some basic understanding of the nature of mathematics is requisite for scientific literacy. To achieve this, students need to perceive mathematics as part of the scientific endeavor , comprehend the nature of mathematical thinking, and become familiar with key mathematical ideas and skills. ( Chapter 2:  The Nature of Mathematics - Science for all Americans , 1990)

13. The application of mathematics to medicine is an exciting and novel area of research within the discipline of applied mathematics. A component in which mathematics contributes significantly to health and medicine concerns life expectancy Political scientists use math and statistics to predict the behavior of group of people. They study the population using many different applications of math, including computer science, database management, statistics and economics. Analysis and study in economics help explain the interdependent relation between different variables. Economists try to explain what causes rise in prices or unemployment or inflation.

14. F. Application of Mathematics Mathematics has everyday applications . It is a universal language in different places, in different times, in different settings and different circumstances. The physical world seems to consist of countable things and any infinity encountered is a result of extending a counting process. But of course, mathematics is not just counting but using mathematical principles. . Mathematics has everyday applications. It is a universal language in different places, in different times, in different settings and different circumstances. The physical world seems to consist of countable things and any infinity encountered is a result of extending a counting process. But of course, mathematics is not just counting. When one buys a product, follow a recipe, or decorate his room, he uses math principles. People employ these principles for thousands of years, across countries and continents. Other uses of math includes farming, planning a market list, decorating our house, inside and outside., cooking, travelling, constructions, investments, time management and many others.. Though some of the more abstract mathematical concepts seldom come into play, the essential skills developed in basic math lessons resonate throughout a student’s lifetime and often resurface to help solve various problems in real life situations in the workplace and in the world.

15. Generalizations 1. Many patterns and occurrences exist in nature, in our world and in our life. Mathematics helps make sense of these patterns and occurrences.   2. Mathematics is a tool to quantify, organize and control the world, predict phenomena and make life easier for us. End of Chapter 1 Thank you…

16. Assessment Answer the following questions in 3 to 5 sentences only.. 1. What new ideas about mathematics did you learn? 2. What is it about mathematics that might have changed your thoughts about it? 3. How useful is mathematics to humankind?