The Nature of Mathematics PDF

The Nature of Mathematics At the end of this Chapter, the students must be able to: Identify patterns in nature and regularities in the world; Articulate the importance of mathematics in one’s life; Argue about the nature of mathemat...

The Nature of Mathematics At the end of this Chapter, the students must be able to: Identify patterns in nature and regularities in the world; Articulate the importance of mathematics in one’s life; Argue about the nature of mathematics, what it is, how it is expressed, represented and used; Discuss the roles of mathematics in some disciplines; and Express appreciation for mathematics as human endeavor Introduction Mathematics is a valuable tool for exploring nature and our surroundings. The study of patterns in nature and the environment is a natural extension of mathematics. Mathematics may be observed in almost every situation and is used to explain the most frequent phenomena. The history and usefulness of patterns and numbers can be traced back to the origins of mathematics. It is concerned with human-created thoughts and ideas that were transformed into products. They were created to connect the meaning of a pattern to the perception of counting, sequence, and regularities. Lesson 1: Patterns in Nature There is a link between patterns and counting. When there is a pattern, counting occurs. There is reasoning when there is counting. As a result, in nature, pattern corresponds to logic or logical arrangement. A specific pattern has its own set of characteristics. The most people believe that mathematics is the study of patterns. Mathematics, like patterns in nature, may be found everywhere. Patterns come in a variety of shapes and sizes. Number patterns, such as 2, 4, 6, and 8, are recognizable to us since they are among the first patterns we learn when we are young. We gain experience both within and outside of school as we progress. Patterns, on the other hand, are more wider and more prevalent wherever and at any time. Patterns can be sequential, spatial, temporal, and even linguistic. All these phenomena create a repetition of names or events is called regularity. Dates in the Calendar Days in a Calendar Months in a Year Regular Holidays Regularity - same things happen in the same circumstances. Pattern - regularity in the world or man-made design. Pattern in Nature or Natural Pattern - visible regularities found in the natural world. Some examples of Patterns in Nature Patterns are the repeated design or recurring sequence. It is also an ordered set of numbers, shapes or other mathematical objects that arranged according to a rule. One of the most intriguing things we see in nature is patterns. We tend to think of patterns as sequences or designs that are orderly and that are repeat object. For example, we recognize the spots on a giraffe as a pattern, but they are not regular nor are any of the spots the same size or shape. Types of Patterns Symmetry - it refers to a sense of harmonious and beautiful proportion and balance. Spiral - a curve which emanates from a point, moving farther away as it revolves around the point. Meander - one of a series of regular sinuous curves, bends, loops, turns, or winding in the channel of rivers, streams, or other water course. Waves or Riffles - a disturbance that transfer energy through matter or space, with little or no mass transport. Foams or Bubbles - a substance formed by trapping pockets of gas in a liquid or solid. Tessellation - tilling of plane using one or more geometric shapes, called the tiles, with no overlaps and no gaps. Tessellations are patterns that are formed by repeated cubes or tiles. Fractures or Cracks - separations of an object or material into two or more pieces under the action of stress. Stripes and Spots - series of bands or strips and spots, often of the same width and color along the length. Fractals - a never-ending pattern. Infinitely complex pattern that are self-similar across different scales. Uses of Mathematics Technology: navigation, prediction Engineering: construction, robotics Media: music, movie, election Medicine and Health: pharmacy, surgery Finance and Business: banking, gambling Fibonacci – introduced in “Book if Counting”, begins with 0 and 1, adding the last two numbers: 0, 1, 2, 3 … (petals). Golden Ratio – The Golden ratio (or Golden Part, or Golden Proportion, or Divine Proportion) is generally denoted by the Greek letter Phi (φ), in lower case, which represents an irrational number 1.6180339887..., It is said that Phi is the initial letters of Phidias’ name adopted to designate the golden ratio. Sequence – set of all numbers in special orders. Terms – number of a sequence. Series – sum of terms. Finite Sequence – has first and last terms. Infinite Sequence – has first term but no last term. Arithmetic sequence – term is obtained by adding d to the next term.