Chapter 1 Notes - Mathematics in the Modern World - GEMATH 1

Mathematics in the Modern World GEMATH 1 CENTRAL PHILIPPINE UNIVERSITY College of Arts and Sciences UNIT 1. Mathematics in Our World / MTH101  UNIT 1...

Mathematics in the Modern World GEMATH 1 CENTRAL PHILIPPINE UNIVERSITY College of Arts and Sciences UNIT 1. Mathematics in Our World / MTH101  UNIT 1 Math in our WORLD All photos and gifs/videos credit to the owners UNIT 1. Mathematics in Our World / MTH101  Learning Outcomes: In this unit, you should be able to: 1. Identify patterns in nature and regularities in the world; 2. Argue about the nature of mathematics, what it is, how it is expressed, represented and used; 3. Articulate the importance of mathematics in one’s life; and 4. Express appreciation for mathematics as a human endeavor. CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS  Patterns and Getting to Importance of Numbers in Nature Know Mathematics and the World Mathematics CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS  Patterns and Numbers in the Nature and the World Lesson 1.1 CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS  Our Universe of Patterns https://www.wallpaperflare.com/ UNIT 1. Mathematics in our World/MTH101 UNIT 1. Mathematics in Our World / MTH101 https://www.wallpaperflare.com/ UNIT 1. Mathematics in our World/MTH101 UNIT 1. Mathematics in Our World / MTH101 UNIT 1. Mathematics UNIT 1. Mathematics in our World/MTH101 in Our World / MTH101 CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Nature’s Patterns as Clues https://rare-gallery.com/uploads/posts/543840-pattern-texture.jpg UNIT 1. Mathematics UNIT 1. Mathematics in our World/MTH101 in Our World / MTH101  Waves and Dunes https://www.wallpaperup.com/13438/Water_landscapes_waves_sand_dunes_africa_namib_d https://www.shutterstock.com/tr/video/clip-3293060-sand-dunes-desertsahara-desert-dunessand-wavesarabian-landscapedesert CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Tiger’s Stripes and Hyena’s Spots https://africa.cgtn.com/2016/11/27/man-in-zimbabwe-found-with-hyena-nose-tail-in-his-undergarments/ https://www.latimes.com/world/la-fg-c1-china-siberian-tiger-20131001-dto-htmlstory.html CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Rainbow CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Nature’s Patterns are Numerical https://rare-gallery.com/uploads/posts/543840-pattern-texture.jpg UNIT 1. Mathematics UNIT 1. Mathematics in our World/MTH101 in Our World / MTH101 https://www.permaculturenews.org/2017/06/09/patterns-natural-world-nature-measure/  Nature’s Patterns are Numerical 1. In 28 days, the phases of the moon make a complete cycle from new moon to full moon and back again. 2. Approximately, there are 365 days in a year. 3. Number of legs of some creatures: people – 2 insects- 6 cats- 4 spiders- 8 4. Clover normally has 3 leaves. A four-leaf clover brings luck according a superstition. This reflects a deep-seated belief that exceptions to patterns are special. CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Nature’s Patterns are Numerical 5. A pattern also occurs in the petals of flowers. The number of petals is one of the numbers that occurs in the sequence 3, 5, 8, 13, 21, 34, 55, 89. Below is a list of flowers with their corresponding number of petals. Lily-3 petals Buttercup-5 petals Daisy-8 petals Marigold-13 petals Chicory-21 petals CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Nature’s Patterns are Numerical 5. A pattern also occurs in the petals of flowers. The number of petals is one of the numbers that occurs in the sequence 3, 5, 8, 13, 21, 34, 55, 89. Below is a list of flowers with their corresponding number of petals. Shasta Daisy-34 petals Michaelmas Daisy-55 petals Asteraceae Daisy-55 petals CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  These numbers can also be found in the spiral patterns of seeds in the head of a sunflower and these are the very numbers existing in a sequence called Fibonacci sequence. CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Numerical Patterns NATURE’S PATTERNS THE FIBONACCI SPIRAL CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Numerical Patterns NATURE’S PATTERNS THE FIBONACCI SPIRAL CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Geometric Patterns https://www.pinterest.ph/pin/44965696269016833/ UNIT 1. Mathematics UNIT 1. Mathematics in our World/MTH101 in Our World / MTH101  Rainbow http://www.ceravoloimages.com/gallery3/atmospheric_optics/rainbows/chasing_rainbows.html CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Ripples https://www.canadiancontractor.ca/voices/the-unexpected-ripple-effect-of-mandatory-wsib-in-ontario/attachment/ripples-in-a-pond/ CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Human Eyes https://www.fertility-docs.com/programs-and-services/pgd-screening/choose-your-babys-eye-color.php CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Circles on Butterfly’s Wings https://www.youtube.com/watch?v=1BcRs9OCaTs CHAPTER 1.inTHE UNIT 1. Mathematics NATURE Our World / MTH101 OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  https://www.khou.com/article/news/local/the-beaches-are-ripe-for-rips/314551505 CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  https://mirjamglessmer.com/tag/ship-generated-waves/ CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  https://www.indiatoday.in/educationtoday/gkcurrent affairs/story/tsunami india 359485 201612 26 CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  https://www.jagranjosh.com/generalknowledge/what is a tidalbore 1556004787 1 CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  https://www.awajishimakanko.jp/en/uzushio/ CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  https://pixabay.com/photos/waterfallrapids river water2420715/ CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  https://www.pinterest.com/pin/286119382546282937/ CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Wave Patterns on Land https://www.wallpaperflare.com/close-up-photo-of-sand-land-wave-pattern-backgrounds-sand-dune-wallpaper-gsmas/download/1920x1080 UNIT 1. Mathematics in Our World / MTH101  Transverse Dunes https://www.researchgate.net/figure/Transverse-dunes-in-the-Caraveli-Province-of-Peru-Note-the-almost-perfect-alignment_fig3_309719801 CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Barchanoid Ridges https://www.flickr.com/photos/rwolf/4988415995/in/photostream/ CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Parabolic Dunes https://www.worldatlas.com/articles/types of sand dunes.html CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  https://www.haikudeck.com/desert-visual-dictionary-education-presentation-Qqo9gOEsPS#slide2 CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Questions to think about… UNIT 1. Mathematics in Our World / MTH101  Why do so many shells form spirals? http://4-designer.com/2013/09/Shells-and-starfish-02-HD-picture/#.XUgIB2YRXIU CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Why are starfish equipped with a symmetric set of arms? http://4-designer.com/2013/09/Shells-and-starfish-02-HD-picture/#.XUgIB2YRXIU CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Why do so many viruses assume regular geometric shapes, the most striking being that of an icosahedron- a regular solid formed from twenty equilateral https://www.britannica.com/science/icosahedral-virus triangles? CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Why are so many animals bilaterally symmetric? https://hemantmore.org.in/science/biology/criteria-animal-classification/1149/ CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Why is that symmetry so often imperfect, disappearing when you look at the detail, such as the position of the human heart or the differences between the two hemispheres of the human brain? CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Chemical Molecules https://www.wallpaperflare.com/static/686/250/370/digital-art-minimalism-texture-simple-wallpaper.jpg UNIT 1. Mathematics in Our World / MTH101 Lesson 1: Patterns and Numbers in the Nature and the World  Methane Benzene https://www.dreamstime.com/stock-illustration-benzene-structure-consists-carbon-hydrogen-vector- http://chemistry.elmhurst.edu/vchembook/204tetrahedral.html CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Buckminsterfullerene https://bcachemistry.wordpress.com/tag/buckminsterfullerene/ https://mathworld.wolfram.com/TruncatedIcosahedron.html CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Patterns of Movements https://bestwallpapers.net/desktop/photo/birds-flock-sunset-wallpapers-free-download UNIT 1. Mathematics in Our World / MTH101 Lesson 1: Patterns and Numbers in the Nature and the World  Human Walk UNIT 1. Mathematics UNIT 1. Mathematics in Our World /in our World/MTH101 MTH101 Lesson 1: Patterns and Numbers in the Nature and the World  Tiny Bacteria UNIT 1. Mathematics UNIT 1. Mathematics in Our World /in our World/MTH101 MTH101 Lesson 1: Patterns and Numbers in the Nature and the World  Flight of Birds UNIT 1. Mathematics UNIT 1. Mathematics in Our World /in our World/MTH101 MTH101 Lesson 1: Patterns and Numbers in the Nature and the World  New Kinds of Pattern UNIT 1. Mathematics in Our World / MTH101  Fractals Fractals are geometric shapes that repeat their structure on ever-finer scales. Although fractals are very complex, they are made by repeating a simple process. Fractals are found in nature, for instance, trees, rivers, coastlines, mountains, clouds, seashells, hurricanes. Fractals are also found in geometry and algebra referred to as mathematical fractals. CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Natural Fractals: Branching Neurons from the Human Cortex. Human Lungs https://wccftech.com/scientists-artificial-neurons-mimics-human-brain-cells/ https://fractalfoundation.org/fractivities/FractalPacks-EducatorsGuide.pdf CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Natural Fractals: Branching Lichtenberg Lightning Oak Tree River Network in China https://fractalfoundation.org/fractivities/FractalPacks-EducatorsGuide.pdf https://fractalfoundation.org/fractivities/FractalPacks-EducatorsGuide.pdf https://fractalfoundation.org/fractivities/FractalPacks-EducatorsGuide.pdf CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Natural Fractals: Spirals FossilizedAmonite Hurricane Spiral Galaxy https://fractalfoundation.org/fractivities/FractalPacks-EducatorsGuide.pdf CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Natural Fractals: Spirals Agave Cactus Turbulent motion Fiddlehead Fern https://fractalfoundation.org/fractivities/FractalPacks-EducatorsGuide.pdf CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Geometric Fractals: Sierpinski Triangle 1st 2nd 3rd 4th 5th 6th CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Geometric Fractals: Sierpinski Triangle https://www.youtube.com/watch?v=jsfxdDtYCAw CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Geometric Fractals: Koch Curve CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Geometric Fractals: Koch Curve https://www.youtube.com/watch?v=MTYW4Re_RsY CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Algebraic Fractals: Mandelbrot Set https://fractalfoundation.org/fractivities/FractalPacks-EducatorsGuide.pdf CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  Getting to Know Mathematics Lesson 1.2 CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS  The Whats of Math CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.2: Getting to Know Mathematics  https://linkiya.wordpress.com/2015/07/13/the-six-blind-men-and-the-elephant-differing-perspectives-on-grades/ CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.2: Getting to Know Mathematics  What is Mathematics? Mathematics, developed by human mind and culture, https://career.sa.ucsb.edu/students/career-planning/choosing-major/mathematical-sciences is a formal system of thought for recognizing, classifying, and exploiting patterns. -Ian Stewart https://denisegaskins.com/2015/10/26/what-is-mathematics/ CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.2: Getting to Know Mathematics  STUDY OF PATTERNS AND RELATIONSHIPS What is the NATURE of ART Mathematics? TOOL LANGUAGE PROCESS OF THINKING CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.2: Getting to Know Mathematics  Where is Mathematics? CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.3: Importance of Mathematics  Where is Mathematics? UNIT 1. Mathematics UNIT 1. Mathematics in Our World /in our World/MTH101 MTH101 Lesson 1.3: Importance of Mathematics  What is Mathematics About? Mathematics is about quantity, structure, space, and change. Also, Mathematics has a landscape. CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.2: Getting to Know Mathematics  How is Mathematics Done? ❖ with curiosity ❖ with a penchant for seeking patterns and generalities ❖ with the desire to know the truth ❖ with trial and error ❖ without fear of facing more questions and problems to solve CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.2: Getting to Know Mathematics  Who Uses Mathematics? ❖ Applied and Pure Mathematicians ❖ Scientists ❖ Engineers ❖ Medical Practitioners ❖ Data Analysts ❖ Statisticians ❖ Finance Analysts, etc. CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.2: Getting to Know Mathematics  Importance of Mathematics Lesson 1.3 CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.3: Importance of Mathematics  What is the use of Mathematics? CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.3: Importance of Mathematics  Mathematics helps us to solve puzzles. CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.3: Importance of Mathematics  Mathematics is a useful way to think about nature. CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1: Patterns and Numbers in the Nature and the World  What is Mathematics For? ❖ useful in making conclusions and/or predictions of the events of the world ❖ use to describe the natural order and occurrences of the universe ❖ use to organize patterns and regularities as well as irregularities CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.3: Importance of Mathematics  What is Mathematics For? ❖ help to control weather, epidemics ❖ provide tools for calculations ❖ provide new questions to think about CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.3: Importance of Mathematics  Why is Mathematics Important to Learn? ❖ It puts order in disorder. ❖ It helps make a world a better place to live in. ❖ It helps us become better persons. CHAPTER 1. THE UNIT 1. Mathematics NATURE in Our World / MTH101OF MATHEMATICS Lesson 1.3: Importance of Mathematics  END OF DISCUSSION… UNIT 1. Mathematics in Our World / MTH101