PATTERNS-AND-NUMBERS-IN.pdf

Application of mathematics  Predicting the sun’s behavior  Predicting natural phenomenon/calamity  Controlling overpopulation  Controlling a pandemic  PATTERNS AND NUMBERS IN NATURE AND THE WORLD  WHAT DOES MATHEMATICS HAVE TO DO WITH NATURE?  The nat...

Application of mathematics  Predicting the sun’s behavior  Predicting natural phenomenon/calamity  Controlling overpopulation  Controlling a pandemic  PATTERNS AND NUMBERS IN NATURE AND THE WORLD  WHAT DOES MATHEMATICS HAVE TO DO WITH NATURE?  The natural world is full of beauty and amazing shapes and patterns. In his book, Nature by Numbers, Ian Stewart mentioned that we live in a universe of patterns. If you observe our nature diligently, you can prove that our nature bounds in mystical colors and intricate shapes and patterns that can be described mathematically  PATTERN  Patterns are things that are repetitive, which can be found in nature as color, shape, action, or some other sequences that are almost everywhere. Mathematics expresses patterns. These sequences that repeat, follows a rule or rules. A rule is a way to calculate or solve a problem.  TYPES OF PATTERN IN NATURE 1. Symmetry  According to the American Heritage Dictionary, symmetry is an exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis. It indicates that you can draw an imaginary line across an object and the resulting parts are mirror images of each other.  TYPES OF SAYMMETRY a. Reflection Symmetry  It is also called mirror symmetry or line symmetry. It is made with a line going through an object which divides it into two pieces which are mirror images of each other. This is often termed as bilateral symmetry as it divides the object into two (“bi “ means two) mirror images.  TYPES OF SAYMMETRY b. Rotational Symmetry  It is also called radial symmetry. In Biology, this kind of symmetry is exhibited by objects when their similar parts are regularly arranged around a central axis and the pattern looks the same after a certain amount of rotation. Note that if you rotate the given images below by several degrees, you can still achieve the same appearance as the original position  TYPES OF SAYMMETRY c. Translational Symmetry  This kind of symmetry is exhibited by objects which do not change its size and shape even if it moved to another location.  TYPES OF PATTERN IN NATURE 2. Fractals  These are never-ending patterns that are self-similar across different scales. The image just reappears over and over again no matter how many times the object is magnified.  TYPES OF PATTERN IN NATURE 2. Spiral pattern  A circular pattern beginning at the center point and circling around the center point as the pattern moves outward.  TYPES OF PATTERN IN NATURE 4. Spots and stripes Patterns are also exhibited in the external appearances of animals.  TYPES OF PATTERN IN NATURE 5. Flower Petals  Flowers are easily considered as things of beauty. Their vibrant colors and fragrant odors make them very appealing as gifts or decorations. The flowers below have different number of petals. Flowers with 5 petals are said to be the most common. Notice that these numbers are all Fibonacci numbers.  TYPES OF PATTERN IN NATURE 5. Flower Petals FLOWERS NUMBER OF PETALS Lilies 3 Buttercups 5 Delphiniums 8 Marigolds 13 Asters 21 Daisies 34, 55, 89  TYPES OF PATTERN IN NATURE 6. Number Patterns and Sequences  Consider the pattern below.  Are you familiar with this number pattern in a triangle? What do you think will be the next layer of the numbers in the triangle? common. Notice that these numbers are all Fibonacci numbers.  FIBONACCI SEQUENCE  The Fibonacci numbers are a series of number that often occur in nature. This number sequence was developed in the Middle Ages, and it was named after Leonardo Pisano Bigollo, a famous Italian mathematician who also happened to discover Fibonacci. He is the greatest European mathematician of the middle ages. He was born in 1170 and died in 1240. He introduced the Arabic number system in Europe.  Fibonacci is a short term for the latin filius bonacci, which means “the son of Bonacci”. Think of this! At the beginning of a month, you are given a pair of newborn rabbits. After a month the rabbits have produced no offspring; however, every month thereafter, the pair of rabbits produces another pair of rabbits. The offspring reproduce in exactly the same manner. If none of the rabbits dies, how many pairs of rabbits will there be at the start of each succeeding month?  At the start of 4th month, how many pairs of rabbits will there be?  How about at the start of the 5th and 6th months?