Patterns and Numbers in Nature and the World LESSON 2 M AT H E M AT I C S I N O U R W O R L D After going through this lesson, you are expected to 1. What is patterns? 2. Identify patterns in nature and regularities in the world. 3. Classify objects according to symmetry. 4. Explain Fibonacci numbers and their origin. 5. Illustrate how the Fibonacci sequence is expressed in nature. What is Patterns? ➢ A patterns are regular, repeated or recurring forms or designs. Example: layout of floor tiles, design of buildings. ➢ It also shows what may have come before and it organizes information to bring order where there is disorder. ➢ Mathematics is the study of patterns . Hence, those who use patterns to analyze and solve problems often find success compared with those who cannot. The importance of Patterns ➢ Patterns helps us to find logical connections as well to form generations. Predictions and even identifying relations ➢ Patterns help us organize thoughts and establish order to our lives. As we begin to connect patterns in nature and life, they bring a sense of harmony to our minds. Patterns lead to and build math, vocabulary and cognitive concepts. Patterns are excellent in helping us establish priorities. ➢ Everything in our life has only patterns. PATTERNS AND NUMBERS IN NATURE AND THE WORLD Patterns in nature are visible regularities of form found in the natural world and can also be seen in the universe. Examples of some of these patterns and you may be able to spot a few the next time you go for a walk. 1. Patterns can be observed even in stars which move in circles across the sky each day. PATTERNS AND NUMBERS IN NATURE AND THE WORLD 2. The weather season cycle each year. All snowflakes contain sixfold symmetry which no two are exactly the same. How are snowflakes form? A snowflake begins to form when an extremely cold water droplet freezes onto a pollen or dust particle in the sky. This creates an ice crystal. As the ice crystal falls to the ground, water vapor freezes onto the primary crystal, building new crystals – the six arms of the snowflake. PATTERNS AND NUMBERS IN NATURE AND THE WORLD 3. Patterns can be seen in fish patterns like spotted trunkfish, spotted puffer, blue spotted stingray, spotted moral eel, coral grouper, red lion fish, yellow boxfish and angel fish. These animals and fish stripes and spots attest to mathematical regularities in biological growth and form. PATTERNS AND NUMBERS IN NATURE AND THE WORLD 4. Zebras, tigers, cats and snakes are covered in patterns of stripes; leopards and hyenas are covered in pattern of spots and giraffes are covered in pattern of blotches. PATTERNS AND NUMBERS IN NATURE AND THE WORLD 5. Natural patterns like the intricate waves across the oceans; sand dunes on deserts; formation of typhoon; water drop with ripple and others. These serves as clues to the rules that govern the flow of water, sand and air. PATTERNS AND NUMBERS IN NATURE AND THE WORLD 6. Other patterns in nature can also be seen in the ball of mackerel, the v -formation of geese in the sky and the tornado formation of starlings. PATTERNS AND R E G U L A R I T I E S Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. TYPES OF PATTERNS SYMMETRY – a sense of harmonious and beautiful proportion of balance or an object is invariant to any various transformations (reflection, rotation or scaling.) TYPES OF PATTERNS a.) Bilateral Symmetry: a symmetry in which the left and right sides of the organism can be divided into approximately mirror image of each other along the midline. Symmetry exists in living things such as in insects, animals, plants, flowers and others. Animals have mainly bilateral or vertical symmetry, even leaves of plants and some flowers such as orchids. TYPES OF PATTERNS b.) Radial Symmetry ( or rotational symmetry ): a symmetry around a fixed point known as the center and it can be classified as either cyclic or dihedral. Plants often have radial or rotational symmetry, as to flowers and some group of animals. A five-fold symmetry is found in the echinoderms, the group in which includes starfish, sea urchins and sea lilies. Radial symmetry suits organism like sea anemones whose adults do not move and jellyfish(dihedral-D4 symmetry). Radial symmetry is also evident in different kinds of flowers. TYPES OF PATTERNS 2. FRACTALS – a curve or geometric figure, each part of which has the same statistical character as the whole. A fractal is a never-ending pattern found in nature. The exact same shape is replicated in a process called “self similarity.” The pattern repeats itself over and over again at different scales. For example, a tree grows by repetitive branching. This same kind of branching can be seen in lightning bolts and the veins in your body. Examine a single fern or an aerial view of an entire river system and you’ll see fractal patterns. TYPES OF PATTERNS 3. SPIRALS - A logarithmic spiral or growth spiral is a selfsimilar spiral curve which often appears in nature. It was first describe by Rene Descartes and was later investigated by Jacob Bernoulli. A spiral is a curved pattern that focuses on a center point and a series of circular shapes that revolve around it. Examples of spirals are pine cones, pineapples, hurricanes. The reason for why plants use a spiral form is because they are constantly trying to grow but stay secure. EXAMINING PATTERNS Studying patterns helps students identify relationships and find logical connections to form generalizations and make predictions. (Aufmann, et al. 2018) A. LOGIC PATTERNS: It is the ability to discover meaningful patterns in strange and unpredictable situations. Example 1: 1. What should be the next figure in this sequence? A. LOGIC PATTERNS: 2. What will be the next figure in this sequence?