Topic 1: Patterns in Nature and the Regularities in the World PDF

Topic 1: Patterns in Nature and the Regularities in the World Patterns and counting are correlative. Counting happens when there is pattern. When there is counting, there is logic. Consequently, pattern in nature goes with logic or logical set-up. There are reasons behind a certain pattern. That's...

Topic 1: Patterns in Nature and the Regularities in the World Patterns and counting are correlative. Counting happens when there is pattern. When there is counting, there is logic. Consequently, pattern in nature goes with logic or logical set-up. There are reasons behind a certain pattern. That's why, oftentimes, some people develop an understanding of patterns, relationships, and functions and use them to represent and explain real-world phenomena. Most people say that mathematics is the science behind patterns. Mathematics exists everywhere as patterns do in nature. Not only do patterns take many forms within the range of school mathematics, they are also a unifying mechanism. Number patterns-such as 2, 4, 6, 8-are familiar to us since they are among the patterns first learned in our younger years. As we advance, we experience number patterns again through the huge concept of functions in mathematics inside and outside school. But patterns are much broader and common anywhere anytime. Patterns can be sequential, spatial, temporal, and even linguistic. The most basic pattern is the sequence of the dates in the calendar such as 1 to 30 being used month after month; the seven (7) days in a week i.e. Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday; the twelve (12) months i.e. January, February, March, April, May, June, July, August, September, October, November, December, and the regular holidays in a year i.e. New Year's Day, Valentine's Day, Holy Week, Labor Day, Independence Day, National Heroes Day, Ramadan, All Saints Day, Bonifacio Day, Christmas Day and Rizal Day. These are celebrated in the same sequence every year. All these phenomena create a repetition of names or events called regularity. In this world, a regularity (Collins, 2018), is the fact that the same thing always happens in the same circumstances. While a pattern is a discernible regularity in the world or in a man-made design. As such, the elements of a pattern repeat in a predictable manner. Patterns in nature (wikipedia) 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. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design. In Algebra, there are two common categories of patterns, the repeating pattern and the growing pattern. Regularity in the world states the fact that the same thing always happens in the same circumstances. According to Ian Stewart (1995), we live in a universe of patterns. Every night the stars move in circles across the sky. The seasons cycle at yearly intervals. No two snowflakes are ever exactly the same, but they all have six-fold symmetry. Tigers and zebras are covered in patterns of stripes, leopards and hyenas are covered in patterns of spots. Intricate trains of waves march across the ocean; very similar trains of sand dunes march across the desert. Colored arcs of light adorn the sky in the form of rainbows, and a bright circular halo sometimes surrounds the moon on winter nights. Spherical drops of water fall from clouds. Human mind and culture have developed a formal system of thought for recognizing, classifying, and exploiting patterns. We call it mathematics. By using mathematics to organize and systematize our ideas about patterns, we have discovered a great secret: nature's patterns are not just there to be admired, they are vital clues to the rules that govern natural processes. Some Examples of Patterns in Nature Symmetry (wikipedia) means agreement in dimensions, due proportion and arrangement. In everyday language, it refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" means that an object is invariant to any of various transformations including reflection, rotation or scaling. A spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Cutaway of a nautilus shell shows the chambers arranged in an approximately logarithmic spiral A meander is one of a series of regular sinuous curves, bends, loops, turns, windings in the channel of a river, stream, or other watercourse. It is produced by a stream or river swinging from side to side as it flows across its floodplain or shifts its channel within a valley. A meander is produced by a stream or river as it erodes the sediments concave bank (cut comprising an outer, bank) and deposits this and other sediment downstream on an inner, convex bank which is typically a point bar. A wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport. Waves consist of oscillations or vibrations of a physical medium or a field, around relatively fixed locations. Surface waves in water show water ripples. Foam is a substance formed by trapping pockets of gas in a liquid or solid. A bath sponge and the head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin films of liquid or solid separating the regions of gas. Soap foams are also known as suds. A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries. A fracture or crack is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular. to the surface of displacement, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially to the surface of displacement, it is called a shear crack, slip band, or dislocation. Stripes are made by a series of bands or strips, often of the same width and color along the length. A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems the pictures of chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Affine Transformations - These are the processes of rotation, reflection and scaling. Many plant forms utilize these processes to generate their structure. In the case of Broccoli and Cauliflower heads, it can readily be seen that there is a type of pattern, which also shows some spiraling in the case of Broccoli. What is happening in Cauliflower head is perhaps not so obvious but in the case of a fern the rotating pattern is very evident. Each branch appears to be a smaller version of the main plant and so on, at smaller scales. Fibonacci Sequence Another one in this world that involves pattern is the Fibonacci number (Grist, 2011). These numbers are nature's numbering system. They appear everywhere in nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees and even all of mankind. In Mathematics, (wikipedia), the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones: 1,1,2,3,5,8,13,21,34,55,89, 144,... The sequence F of Fibonacci numbers is defined by the recurrence relation: Fn = Fn−1 + Fn−2 with seed values F1 = 1, F2 = 1 F1 = 1, F3 = 2 The first 6 Fibonacci numbers F, for n = 0, 1, 2,..., 6 are F0 F1 F2 F3 F4 F5 F6 0112358 George Dvorsky (2013) highlighted that the famous Fibonacci sequence has captivated mathematicians, artists, designers, and scientists for centuries. Also known as the Golden Ratio, its ubiquity and astounding functionality in nature suggests its importance as a fundamental characteristic of the universe. Leonardo Fibonacci came up with the sequence when calculating the ideal expansion pairs of rabbits over the course of one year. Today, its emergent patterns and ratios (phi = 1.61803...) can be seen from the microscale to the macroscale, and right through to biological systems and inanimate objects. While the Golden Ratio doesn't account for every structure or pattern in the universe, it's certainly a major player. Here are some examples: 1. Seed heads The head of a flower is also subject to Fibonaccian processes. Typically, seeds are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns. 2. Pine cones Similarly, the seed pods on a pinecone are arranged in a spiral pattern. Each cone consists of a pair of spirals, each one spiraling upwards in opposing directions. The number of steps will almost always match a pair of consecutive Fibonacci numbers. For example, a 3-5 cone is a cone which meets at the back after three steps along the left spiral, and five steps along the right. 3. Tree branches The Fibonacci sequence can also be seen in the way tree branches form or split. A main trunk will grow until it produces a branch, which creates two the growth points. Then, one of the new stems branches into two, while other one lies dormant. This pattern of branching is repeated for each of the new stems. A good example is the sneezewort. Root systems and even algae exhibit this pattern. 4. Shells The unique properties of the Golden Rectangle provide another example. This shape, a rectangle in which the ratio of the sides a/b is equal to the golden mean (phi), can result in a nesting process that can be repeated into infinity and which takes on the form of a spiral. It's called the logarithmic spiral, and it abounds in nature. 5. Spiral Galaxies and Hurricane Not surprisingly, spiral galaxies also follow the familiar Fibonacci pattern. The Milky Way has several spiral arms, each of them a logarithmic spiral of about 12 degrees. As an interesting aside, spiral galaxies appear to defy Newtonian physics. As early as 1925, astronomers realized that, since the angular speed of rotation of the galactic disk varies with distance from the center, the radial arms should become curved as galaxies rotate. Subsequently, after a few rotations, spiral arms should start to wind around a galaxy. But they don't – hence the so-called winding problem. The stars on the outside, it would seem, move at a velocity higher than expected -- a unique trait of the cosmos that helps preserve its shape. “Pure mathematics is, in its way, the poetry of logical ideas." – Albert Einstein Importance of Mathematics in Life According to Katie Kim (2015), Math is a subject that makes students either jump for joy or rip their hair out. However, math is inescapable as you become an adult in the real world. From calculating complicated algorithms to counting down the days till the next Game of Thrones episode, math is versatile and important, no matter how hard it is to admit. Before you decide to doze off in math class, consider this list of reasons why learning math is important to you and the world. 1. Restaurant Tipping After you have finished eating at a restaurant, it is common courtesy to pay your waiter a generous tip. You need to have the most basic math skills to calculate how much a 15% or 20% tip would be. Tipping your waiter shows your appreciation for his service and ultimately benefits the restaurant, too. 2. Netflix film viewing Let's say you have approximately one hour until you have to leave to go somewhere very important, like your job or your grandmother's birthday party. You really want to fit in a couple Netflix episodes before you leave, but you don't know how many you will be able to watch. You need math to figure that out! For example, an episode of Friends on Netflix is about 20 minutes... so you would be able to fit 3 episodes in that hour. As simple as it is, math just made your hour 100 times better. 3. Calculating Bills If you aren't already, we will all be home-owners and car-owners one day. With ownership comes the major responsibility of staying on top of mandatory payments like taxes, mortgage, and insurance. Math is required to calculate these payments and subtract them from your savings. 4. Computing Test Scores It is towards the end of May, and for all high school students, the school year is coming to an end very soon. That also means final report cards will be coming out. In order to finish with an A in that tough class, you need to know what to get on the next test to keep your average up. You need math to calculate that test score (and maybe even to ace the test) to know what your final grade can be. 5. Tracking Career Math is needed for almost every single profession in the world. If you want to be a CEO, a real estate agent, a biologist, or even a rocket scientist, it is without a doubt that numbers will be utilized. Basically, you will NEVER be able to escape math and you might as well accept it and have fun learning it while your career does not depend on it. 6. Doing Exercise Getting in shape and staying fit means achieving your health goals! Maybe you want to meet a personal goal by the end of the month. You need math to know how many more reps to curl, or how many seconds to cut off your mile time, or how many more pounds to lose to achieve that goal. 7. Handling Money Another aspect of growing up into a young adult is opening and managing a bank account. It is important to be accurate in math to care for your precious savings, making sure there are no mistakes. 8. Making Countdowns For many, this will be the most important reason on this list to know math: so you can countdown the days until school is over and summer starts! 9. Baking and Cooking Baking and cooking are hobbies enjoyed by many. In order to prevent unexpected results, you have to know the difference between a quarter of a cup from a quarter of a teaspoon. Baking + cooking-fractions=math! 10. Surfing Internet Ultimately, without math, how would you be reading this article online at this exact moment? How would you be able to tweet to your friends or post an Instagram from last night? We have math to thank for establishing technology and the social media that consumes our lives. Nature of Mathematics It is important to further discuss the nature of mathematics, what it is, how it is expressed, represented and used. According to the American Association for the Advancement of Science (1990), Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and its intellectual challenge. 1. Patterns and Relationships Mathematics is the science of patterns and relationships. As a theoretical discipline, mathematics explores the possible relationships among abstractions without concern for whether those abstractions have counterparts in the real world. The abstractions can be anything from strings of numbers to geometric figures to sets of equations. 2. Mathematics, Science and Technology Mathematics is abstract. Its function goes along well with Science and Technology. Because of its abstractness, mathematics is universal in a sense that other fields of human thought are not. It finds useful applications in business, industry, music, historical scholarship, politics, sports, medicine, agriculture, engineering, and the social and natural sciences. 3. Mathematical Inquiry Normally, people are confronted with problems. In order to live at peace, these problems must be solved. Using mathematics to express ideas or to solve problems involves at least three phases: (1) representing some aspects of things abstractly, (2) manipulating the abstractions by rules of logic to find new relationships between them, and (3) seeing whether the new relationships say something useful about the original things. 4. Abstraction and Symbolic Representation Mathematical thinking often begins with the process of abstraction-that is, noticing a similarity between two or more objects or events. Aspects that they have in common, whether concrete or hypothetical, can be represented by symbols such as numbers, letters, other marks, diagrams, geometrical constructions, or even words. Whole numbers are abstractions that represent the size of sets of things and events or the order of things within a set. The circle as a concept is an abstraction derived from human faces, flowers, wheels, or spreading ripples; the letter A may be an abstraction for the surface area of objects of any shape, for the acceleration of all moving objects, or for all objects having some specified property; the symbol + represents a process of addition, whether one is adding apples or oranges, hours, or miles per hour. Abstractions are made not only from concrete objects or processes; they can also be made from other abstractions, such as kinds of numbers (the even numbers, for instance). 5. Manipulating Mathematical Statements After abstractions have been made and symbolic representations of them have been selected, those symbols can be combined and recombined in various ways according to precisely defined rules. Typically, strings of symbols are combined into statements that express ideas or propositions. 6. Mathematics and Economics The level of mathematical literacy required for personal and social activities is continually increasing. Mastery of the fundamental processes is necessary for clear thinking. The social sciences are also beginning to draw heavily upon mathematics. Mathematical language and methods are used frequently in describing economic phenomena. According to Marshall - "The direct application of mathematical reasoning to the discovery of economic truths has recently rendered great services in the hand of master mathematicians." Another important subject for economics is Game Theory. The who' economic situation is regarded as a game between consumers, distributor and producers, each group trying to optimize its profits. 7. Mathematics and Psychology The great educationist Herbart said, "It is not only possible, but necessary that mathematics be applied to psychology". Now, experimental psychology has become highly mathematical due to its concern with such factors as intelligence quotient, standard deviation, mean, median, mode, correlation coefficients and probable errors. Statistical analysis is the only reliable method of attacking social and psychological phenomena. Until mathematicians entered into the field of psychology, it was nothing but a flight of imagination. 8. Mathematics and Actuarial Science, Insurance and Finance Actuaries use mathematics and statistics to make financial sense of the future. For example, if an organization embarks on a large project, an actuary may analyze the project, assess the financial risks involved, model the future financial outcomes and advise the organization on the decisions to be made. Much of their work is on pensions, ensuring funds stay solvent long into the future, when current workers have retired. They also work in insurance, setting premiums to match liabilities, areas of finance, from banking and trading on the stock market, to producing economic forecasts and making government policy. 9. Mathematics and Archaeology Archaeologists use a variety of mathematical and statistical techniques to present the data from archaeological surveys and try to distinguish patterns in their results that shed light on past human behavior. Statistical measures are used during excavation to monitor which pits are most successful and decide on further excavation. Finds are analyzed using statistical and numerical methods to spot patterns in the way the archaeological record changes over time, and geographically within a site and across the country. Archaeologists also use statistics to test the reliability of their interpretations. 10. Mathematics and Logic D' Alembert says, "Geometry is a practical logic, because in it, rules of reasoning are applied in the simplest and sensible manner". Pascal says, "Logic has borrowed the rules of geometry; the method of avoiding error is sought by everyone. The logicians profess to lead the way, the geometers alone reach it, and aside from their science there is no true demonstration". C.J.Keyser "Symbolic logic is mathematics, mathematics is symbolic logic". The symbols and methods used in the investigation of the foundation of mathematics can be transferred to the study of logic. They help in the development and formulation of logical laws. 11. Mathematics in Music Leibnitz, the great mathematician said, - "Music is a hidden exercise in arithmetic of a mind unconscious of dealing with numbers". Pythogoras said - "Where harmony is, there are numbers". Calculations are the root of all sorts of advancement in different disciplines. The rhythm that we find in all music notes is the result of innumerable permutations and combinations of SAPTSWAR. Music theorists often use mathematics to understand musical structure and communicate new ways of hearing music. This has led to musical applications of set theory, abstract algebra, and number theory. Music scholars have also used mathematics to understand musical scales, and some composers have incorporated the Golden ratio and Fibonacci numbers into their work. 12. Mathematics in Arts "Mathematics and art are just two different languages that can be used, to express the same ideas." It is considered that the universe is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures. The old Goethe Architecture was based on geometry. Even the Egyptian Pyramids, the greatest feat of human architecture and engineering, was based on mathematics. Artists who strive and seek to study nature must therefore first fully understand mathematics. Appreciation of rhythm, proportion, balance and symmetry postulates a mathematical mind. 13. Mathematics in Philosophy The function of mathematics in the development of philosophical thought has been very aptly put by the great educationist Herbart, in his words, "The real finisher of our education is Philosophy, but it is the office of mathematics to ward off the dangers of philosophy." Mathematics occupies a central place between natural philosophy and mental philosophy. It was in their search of distinction between fact and fiction that Plato and other thinkers came under the influence of mathematics. 14. Mathematics in Social Networks Graph theory, text analysis, multidimensional scaling and cluster analysis, and a variety of special models are some mathematical techniques used in analyzing data on a variety of social networks. 15. Mathematics in Political Science In Mathematical Political Science, we analyze past election results to see changes in voting patterns and the influence of various factors on voting behavior, on switching of votes among political parties and mathematics models for conflict resolution. Here we make use of Game Theory. 16. Mathematics in Linguistics The concepts of structure and transformation are as important for linguistic as they are for mathematics. Development of machine languages and comparison with natural and artificial language require a high degree of mathematical ability. Information theory, mathematical biology, mathematical psychology etc. are all needed in the study of Linguistics. Mathematics has had a great influence on research in literature. In deciding whether a given poem or essay could have been written by a particular poet or author, we can compare all the characteristics of the given composition with the characteristics of the poet or other works of the author with the help of a computer. 17. Mathematics in Management Mathematics in management is a great challenge to imaginative minds. It is not meant for the routine thinkers. Different mathematical models are being used to discuss management problems of hospitals, public health, pollution, educational planning and administration and similar other problems of social decisions. In order to apply mathematics to management, one must know the mathematical techniques and the conditions under which these techniques are applicable. 18. Mathematics in Computers An important area of applications of mathematics is in the development of formal mathematical theories related to the development of computer science. Now most applications of mathematics to science and technology today are via computers. The foundation of computer science is based only on mathematics. It includes, logic, relations, functions, basic set theory countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatory, discrete probability, recursion. recurrence relations, and number theory, computer-oriented numerical analysis, Operation Research techniques, modern management techniques like Simulation, Monte Carlo program, Evaluation Research Technique, Critical Path Method, Development of new Computer Languages, study of Artificial Intelligence, Development of Automata Theory etc. Cryptography is the practice and study of hiding information. In modern times cryptography is considered a branch of both mathematics and computer science and is affiliated closely with information theory, computer security and engineering. It is the mathematics behind cryptography that has enabled the e-commerce revolution and information age. Pattern Recognition is concerned with training computers to recognize pattern in noisy and complex situations. e.g. in recognizing signatures on bank cheques, in remote sensing etc. 19. Mathematics in Geography Geography is nothing but a scientific and mathematical description of our earth in its universe. The dimension and magnitude of earth, its situation and position in the universe the formation of days and nights, lunar and solar eclipses, latitude and longitude, maximum and minimum rainfall, etc. are some of the numerous learning areas of geography which need the application of mathematics. The surveying instruments in geography have to be mathematically accurate. There are changes in the fertility of the soil, changes in the distribution of forests, changes in ecology which have to be mathematically determined, in order to exercise desirable control over them. Indeed, mathematics exists everywhere in any program, course, or subject. It is something that we can never do away with. It is always a part of human endeavor. Mathematics is universal. Appreciating Mathematics as a Human Endeavor In order to appreciate mathematics much better, every person should have the thorough understanding of the discipline as a human endeavor. Mathematics brings impact to the life a learner, worker, or an ordinary man in society. The influences of mathematics affect anyone for a lifetime. Mathematics works in the life of all professionals. Mathematics is appreciated as human endeavor because all professionals and ordinary people apply its theories and concepts in the office, laboratory and marketplace. According to Mark Karadimos (2018), the following professions use Mathematics in their scope and field of work: Accountants assist businesses by working on their taxes and planning for upcoming years. They work with tax codes and forms, use formulas for calculating interest, and spend a considerable amount of energy organizing paperwork. Agriculturists determine the proper amounts of fertilizers, pesticides, and water to produce bountiful amounts of foods. They must be familiar with chemistry and mixture problems. Architects design buildings for structural integrity and beauty. They must know how to calculate loads for finding acceptable materials in design which involve calculus. Biologists study nature to act in concert with it since we are very closely tied to nature. They use proportions to count animals as well as use statistics/probability. Chemists find ways to use chemicals to assist people in purifying water, dealing with waste management, researching superconductors, analyzing crime scenes, making food products and in working with biologists to study the human body. Computer Programmers create complicated sets of instructions called programs/software to help us use computers to solve problems. They must have a strong sense of logic and have critical thinking and problem-solving skills. Engineers (Chemical, Civil, Electrical, like Industrial, Material) build automobiles, products / structures / systems buildings, computers, machines, and planes, to name just a few examples. They cannot escape the frequent use of a variety of calculus. Geologists use mathematical models to find oil and study earthquakes. Lawyers argue cases using complicated lines of reason. That skill is nurtured by high level math courses. They also spend a lot of time researching cases, which means learning relevant codes, laws and ordinances. Building cases demands a strong sense of language with specific emphasis on hypotheses and conclusions. Managers maintain schedules, regulate worker performance, and analyze productivity. Medical Doctors must understand the dynamic systems of the human body. They research illnesses, carefully administer the proper amounts of medicine, read charts/tables, and organize their workload and manage the duties nurses and technicians. Meteorologists forecast the weather for agriculturists, pilots, vacationers, and those who are marine-dependent. They read maps, work with computer models, and understand the mathematical laws of physics. Military Personnel carry out a variety of tasks ranging from aircraft maintenance to following detailed procedures. Tacticians utilize a branch of mathematics called linear programming. Nurses carry out the detailed instructions doctors given them. They adjust intravenous drip rates, take vitals, dispense medicine, and even assist in operations. Politicians help solve the social problems of our time by making complicated decisions within the confines of the law, public opinion, and (hopefully) budgetary restraints. Salespeople typically work on commission and operate under a buy low, sell high profit model. Their job requires good interpersonal skills and the ability to estimate basic math problems without the need of paper/pencil. Technicians repair and maintain the technical gadgets we depend on like computers, televisions, DVDs, cars, refrigerators. They always read measuring devices, referring to manuals, and diagnosing system problems. Tradesmen (carpenters, electricians, mechanics, and plumbers) estimate job costs and use technical math skills specific to their field. They deal with slopes, areas, volumes, distances and must have an excellent foundation in math. To realize the love for and interest in mathematics, Annenberg Learner shared the following notes that mathematics is everywhere and is always an integral part of human endeavor. How can math be so universal? According to Annenberg Learner (2017) First, human beings didn't invent math concepts; we discovered them. Math can help us to shop wisely, buy the right insurance, remodel a home within a budget, understand population growth, or even bet on the horse with the best chance of winning the race. When you put money in a savings account, the bank pays you interest according to what you deposit. In effect, the bank is paying you for the privilege of "borrowing" your money. The same is true for the interest you pay on a loan you take from the bank or the money you "borrow" from a credit card. With population growth, new members of the population eventually produce other new members of the population. Population increases exponentially as time passes. What does math have to do with home decorating? Most home decorators need to work within a budget. But in order to figure out what you'll spend, you first have to know what you need. Understanding some basic geometry can help you stick to your budget. Not all people are chefs, but we are all eaters. Most of us need to learn how to follow a recipe at some point. To create dishes with good flavor, consistency, and texture, the various ingredients must have a kind of relationship to one another. For instance, to make cookies that both look and taste like cookies, you need to make sure you use the right amount of each ingredient. Mathematics is the only language shared by all human beings regardless of culture, religion, or gender. Pi is still approximately 3.14159 regardless of what country you are in. Adding up the cost of a basket full of groceries involves the same math process regardless of whether the total is expressed in dollars, rubles, or yen. With this universal language, all of us, no matter what our unit of exchange, are likely to arrive at math results the same way". Being fast in mental arithmetic can save your money when you go to the market. Mathematics is all around us. With these, mathematics can be a great aid in all our activities in the world and deserves huge appreciation and therefore everyone realizes the following: 1. Mathematics helps organize patterns and regularities. 2. Mathematics helps predict the behavior of nature and phenomena in the world. 3. Mathematics helps control nature and occurrences in the world for our own ends. 4. Mathematics has numerous applications in the world making it indispensable. René Descartes Biography Academician, Philosopher, Mathematician, Scientist (1596-1650) Philosopher and mathematician René Descartes is regarded as the father of modern philosophy for defining a starting point for existence, "I think; therefore I am." Synopsis https://www.biography.com/people/ren-descartes-37613 René Descartes was born on March 31, 1596, in La Haye en Touraine, France. He was extensively educated, first at a Jesuit college at age 8, then earning a law degree at 22, but an influential teacher set him on a course to apply mathematics and logic to understanding the natural world. This approach incorporated the contemplation of the nature of existence and of knowledge itself, hence his most famous observation, "I think; therefore I am." Early Life Philosopher René Descartes was born on March 31, 1596, in La Haye en Touraine, a small town in central France, which has since been renamed after him to honor its most famous son. He was the youngest of three children, and his mother, Jeanne Brochard, died within his first year of life. His father, Joachim, a council member in the provincial parliament, sent the children to live with their maternal grandmother, where they remained even after he remarried a few years later. But he was very concerned with good education and sent René, at age 8, to boarding school at the Jesuit college of Henri IV in La Flèche, several miles to the north, for seven years.