Patterns in Nature PDF

JOSE RIZAL MEMORIAL STATE UNIVERSITY The Premier University in the Province of Zamboanga del Norte Gov. Guading Adaza St., Sta. Cruz, Dapitan City Province o...

JOSE RIZAL MEMORIAL STATE UNIVERSITY The Premier University in the Province of Zamboanga del Norte Gov. Guading Adaza St., Sta. Cruz, Dapitan City Province of Zamboanga del Norte Mathematics in the Modern World Lesson 1: Patterns in Nature Pattern exist in different variety of forms. The petals of a flower, arrangement of leaves reveals a sequential pattern. Natures are bounded by different colors and shapes- the rainbow mosaic of a butterfly's wings, undulating ripples of a desert dune. But these miraculous creations not only delight the imagination, they also challenge our understanding. How do these patterns develop? What sorts of rules and guidelines, shape the patterns in the world around us? Some patterns are molded with a strict regularity. At least superficially, the origin of some regular patterns often seems easily to explain. Thousands of times over, the cells of the honeycomb repeat their hexagonal symmetry. The honeybee is a skilled and tireless artisan with an innate ability to measure the width and to gauge the thickness of the honeycomb attests to the honey bee’s remarkable architectural abilities. Objectives: At the end of the lesson, you will 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; and 3. Articulate the importance of mathematics in one’s life. Motivation: “4 Pics 1 Word” Activity Guess the word that represents by the given pictures. Discussion: Pattern is something which helps us anticipate what we might see or expected to happen next. It may also help us know what may have come before or what we are seeing currently. There are four types of patterns; 1) logic patterns, 2) number patterns, 3) geometric patterns and 4) word patterns. 1. Logic Pattern- is the ability to discover meaningful patterns in strange and unpredictable situations. When you enter a strange space, like a new job, you spontaneously search for patterns to influence how you think and act and speak in the new space. Example of logical pattern: 2. Number Pattern- is a sequence of number that are formed in accordance with a definite rule. We can often describe number patterns in more than one way. To illustrate this, consider the following sequence of numbers {1, 3, 5, 7, 9....}. Clearly, the first term of this number pattern is 1; and the terms after the first term are obtained by adding 2 to the previous term. We can also describe this number pattern as a set of odd numbers. Example of number pattern:  3. Geometric Pattern- is a pattern that represented by geometric figures such as polygons and isometric shapes. Example of geometric patterns: 4. Word Pattern- are represented by jumbled words and analyse the hidden logic in it. Example of word pattern. Patterns are part of our everyday life and are visible in shapes, colors, number, and object repetition. Below are some of the patterns in nature; 1. Symmetry Symmetry is pervasive in living things. Animals mainly have bilateral or mirror symmetry, as do the leaves of plants and some flowers such as orchids. Plants often have radial or rotational symmetry, as do many flowers and some groups of animals such as sea anemones. Five hold symmetry is found in the echinoderm the group that includes starfish, sea urchins, and sea lilies. Examples: 2. Trees and Fractals The branching pattern of trees was described in the Itallian Renaisance by Leonardo da Vinci. He stated that: All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk. Fractals are infinitely self-semilar, iterated mathematical constructs having fractal dimension. Infinite iteration is not possible in nature so all fractal patterns are only approximate. Examples: 3. Spirals Spirals are common in plants and in some animals, notably mollusks. For example, in the nautilus, a cephalopod mollusks, each chamber of its shell is an approximate copy of the next one, scaled by the constant factor and arranged in a logarithmic spiral. Given a modern understanding of fractals, a growth spiral can be seen as a special case of self-similarity. Examples: 4. Spots and Stripes Leopards and ladybirds are spotted; angelfish and zebras are stripped. These patterns have an evolutionary explanation; they have functions which increase the chances that the offspring of the patterned animal will survive to reproduce. One function of animal patterns is camouflage; for instance, a leopard that is harder to see catches more prey. Examples: 5. Waves and Dunes Waves are disturbances that carry energy as they move. Mechanical waves propagate through a medium-air or water, making it oscillate as they pass by. Wind waves are sea surface waves that create the characteristic chaotic pattern of any large body of water, though their statistical behavior can be predicted with wind wave models. As waves in water or wind pass over sand, they create patterns of ripples. When winds blow over large bodies of sand, they create dunes, sometimes in extensive dune fields as in the Taklamakan desert. Dunes may form a range of patterns including crescents, very long straight lines, stars, domes, parabolas, and longitudinal or self (sword) shapes. Examples: Application: Fact or Bluff Test your understanding. Each number has 2 icons, color the fact icon if the statement is correct, and the bluff icon if otherwise. (2 pts. Each number) Generalization: Reflect the use of it! In an essay no more than 100 words, how do you think learning mathematics and patterns in general are important in your daily lives?