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Transcendental Mathematics into the Real Modern World group 3 by BENEDICTO, QEN PATRICK C DEL MUNDO, MARILYN NYLA M. NAVARRO, DOMINIC R. YANSON, VIANA LEIGH M.

ABOUT US QEN PATRICK C. BENEDICTO Mabuhay! I am Qen, 19, and I reside in San Juan City. I'm actually afraid of mathematics due to its complexity. But as the saying goes, we should conquer our fears. That's one of the reasons why I am taking BS Statistics right now. As time passed, I realized mathematics's importance in my daily life. Mathematics is already part of our lives and is always there wherever you go. I hope I can show this to you as you explore this magazine. Enjoy reading! MARILYN NYLA M. DEL MUNDO Hello, I’m Nyla, pursuing BS-Statistics. When it comes to mathematics, I believe that one must be committed to continuous learning in the field. Because it can be observed and used to a variety of various situations in life, it necessitates far more than just basic math skills. I hope that through this mini magazine you’ll find a reason to like and learn mathematics. DOMINIC R. NAVARRO Hi! I am Mico from Ilocos Sur. Ever since I was younger, I have always been passionate about math. Frankly, I wouldn't be really interested in listening if the subject isn't math. But, I had to get good grades, so I somewhat ground. Anyhow, I am tenacious and I love challenges. Being surrounded with anything math makes me happy, and I would love to still be in my life later. So, I will immerse myself in it. Along with my groupmates, take the time to read our piece of work. You'll learn so much from it. VIANA LEIGH M. YANSON Hello everyone, I'm Viana! When I was younger, I've always been drawn to things that challenged me. I thought that if I could comprehend and fulfill these, my existence would be meaningful. So, as I went through life, I've gone through various paths that I don't think I'm even fit for. One of these things is pursuing a BS in Statistics, a very math-intensive field. Although maths isn't my forte, I've always thought that learning mathematics would enable me to understand the world better. It would give me the power to solve problems, be efficient, and be one with the universe. Mathematics changed my life and will continue to do so... and I hope it will change yours too! So, delve into this mini-magazine and learn few of the many real-life applications of mathematics in the world we live in today. 1

TABLE OF CONTENTS ABOUT US ................................................... 1 THE IMPORTANCE OF FUZZY LOGIC IN THE MEDICAL FIELD ...................................... 3 THINKING LIKE A LAWYER: LOGIC IN LEGAL ARGUMENTS ....................................... 5 THE RENAISSANCE MAN: MATHEMATICS AND DA VINCI ................................ 7 THE GREAT PI ............................................... 10 FRACTALS: A RECURSIVE SELF- SIMILAR BEAUT IN NATURE ................................. 12 LOOK, IT'S THE FIBONACCI SEQUENCE .................................................. 13 THE GOLDEN RATIO EXISTS IN TRADING?! .................................................. 17 DON'T JUST SIT THERE! START LEARNING ABOUT QUANTITATIVE INVESTMENT STRATEGIES................................... 18 IF YOU DON’T KNOW BUSINESS ANALYTICS NOW, YOU’LL HATE YOURSELF LATER ........................................... 19 ENERGY EFFICIENCY ........................................ 20 ACTIVITY: CROSSWORD PUZZLE ............................. 21 2

Mathematical logic is commonly regarded as the fundamental language of mathematics. Furthermore, logic is involved in evaluating arguments to find the universal truth. We encounter several debates in our everyday lives via reading books and newspapers or just speaking with people. Mathematical reasoning also helps us construct standards for judging the arguments of others. Then, using mathematical logic as a guide, we develop our ideas. Furthermore, there are irregularities and mistakes in the medical diagnosing process. One example is when different people with the same ailment exhibit other disease behaviors. Also, there are times when different types of disorders show comparable symptoms, complicating the treatment of such conditions. Not every proposition can be assigned a truth value of true or false; consequently, Boolean logic cannot always be used. The harshness of what a patient experiences, for example, cannot be ascribed to a binary truth value. Patients often rate their discomfort on a scalar scale. As a result, fuzzy logic is employed. Fuzzy logic has shown to be a beneficial decision- making tool, and some medical specialists commonly employ it because most medical ideas are not always based on binary conclusions and reasoning. 3

Also, Fuzzy logic is frequently employed in an illness diagnosis. Most illnesses are largely unexplored, making it difficult for doctors to establish a diagnosis. Fuzzy logic is a superior approach to the probability that aids in discovering medical diagnoses based on actual or false statements with an acceptable degree of fuzzification. Fuzzy logic has been used in the majority of medical problems. However, a few still need to be investigated further because so many instances have identical symptoms. An example of the process involving Fuzzy logic can be seen below: Aside from determining if a patient has a medical condition or illness, doctors may also prescribe medicine to treat certain disorders or diseases. On the other hand, doctors are human and prone to mistakes. Although they have the requisite skill and understanding in their different disciplines of human health, it is conceivable that they will make mistakes in judgment, such as failing to consider considerations or miscalculating supposed dose prescriptions. As a result, fuzzy logic can help provide appropriate pharmaceuticals to treat such conditions. 4

thinking like a lawyer: logic in legal arguments by Viana Leigh M. Yanson The ability to form a logical argument is at the core of being a great lawyer. It is definitely common knowledge that lawyers maximize the use of logic in their practice such as in creating legal documents, researching evidence, and arguing cases in court. What makes up a compelling argument is its level of adherence to logic and facts. In countries where a jury system is employed, emotions play a role in the fortunes of cases. However, in some countries like the Philippines where the jury system is not adopted, the verdicts of cases rely more heavily on legal reasoning and presentation of facts. In Logic for Law Students: How to Think be removed from office on Like a Lawyer, one of the most used impeachment. The major premise in this materials in teaching logic to law example is the legal basis from the 1987 students in the U.S., Federal Judge Constitution, the minor premise is the Ruggero Aldisert highly suggested the verification of member’s X acts of use of categorical syllogism in bribery, and the conclusion is the presenting one’s side. Categorical consequence stated in the major syllogism has three components: the premise which also applies to the case major premise, the minor premise, and at hand. Clear and well-constructed the conclusion. The major premise must presentations can reduce truth be a statute or a law-based fact, the arguments and call to action at once, minor premise is the facts of the case at this enables the judges to get a grasp of concern, and the conclusion is drawn by the case better. Although this integrating how the statute or common formulation of legal reasoning may look law applies to the facts of the case. As too unnecessary to be noted, this an example in the context of the knowledge actually helps lawyers in the Philippines, as stated in Article XI, Section long run and on a larger scale. In reality, 2 of the 1987 Philippine Constitution, the not all parts of a syllogism are explicitly members of the Supreme Court may be stated and it is the duty of a good lawyer removed from office on impeachment to pick apart a statement or an for committing bribery; an SC member X argument for it to make absolute sense. is proved to have been involved in acts These implicit arguments are actually of bribery; therefore, SC member X may known as the legal jargon, “enthymeme”. 5

spotting fallacious arguments Another major advantage of having examined. The usual form of circular extensive knowledge of logic is being reasoning is when the conclusion is able to quickly point out fallacious synonymous with the premise e.g. “I am statements. A syllogism is definitely one definitely telling the truth because I’m of the most prevalent forms of logic not lying.” In this sentence, the premise is found in the field of law. Further, there similar to the conclusion and there is no are arguments that look like syllogisms premise that can prove the truth value of but are actually fallacies in disguise. A either. common form of an impending fallacy usually starts with a misused existential Coming from the words of Lee quantifier such as “all,” “some,” “every,” Lovevinger, a member of the SCOTUS etc. For instance, some politicians Bar, most men will admit that they are acquire money legitimately; person X is not good-looking, many will concede a politician; thus, she acquired her they are not strong, but no one will money legitimately. This is a general acknowledge that they are not logical. example of the fallacy “affirming the Law is one of the many fields where logic consequent” while misinterpreting the is widely and explicitly employed. existential quantifier “some” at the same Without the use of logic in law, it would time. In this type of fallacy, the only be impossible to create arguments that statement proved to be true is the can justify anything. Moreover, it is a consequent and shall not necessarily crucial component of the legal system. imply that the antecedent is also true. Because of this, the term “think like a lawyer” is even often used to tell During cross-examination in a court trial, someone to spot issues, question all circular reasoning may be one of the sides, and use logic; it is the foundation most often resorts of entities being of reason. ////// circular reasoning in the courtroom 6

THE RENAISSANCE MAN MATHEMATICS AND DA VINCI BY VIANA LEIGH M. YANSON In the 15th century, Florence, Italy was the third-largest city in Europe and easily became the continent’s financial and economic hub. Wealthy people in Florence supported artists and intellectuals as a way to flaunt their money and power. Through this financial support, Florence quickly became the cultural center of Europe a nd the birthplace of the Italian Renaissance. Renaissance scholars, such as artists, writers, and philosophers were allowed access to ancient ruins and able to rediscover Greek and Roman texts. These texts which contained classical knowledge and philosophies enabled the people of the Italian Renaissance to revitalize their culture. They developed and reinterpreted them, generating their own art styles, philosophical interpretations, and scientific inquiries. Thus, the Italian Renaissance gained a reputation for its major contributions to art, architecture, literature, music, philosophy, science, and technology. Born in the village of Vinci in Florence, Leonardo is presently renowned as the artist who created the Mona Lisa and The Last Supper. He was a scientist, mathematician, inventor, artist, architect, botanist, musician, and writer. Leonardo has been frequently described as the epitome of a \"Renaissance man\", a person whose proficiency traverses a wide array of fields. He is regarded as one of history’s finest artists and arguably one of the most diversely talented individuals to have ever lived. Mona Lisa Salvator Mundi The Last Supper 7

Vitruvian Man One of the ancient problems given new life during the Renaissance is squaring the circle which has been frustrating mathematecians since the days of Pythagoras. As we might know, the area of a circle is equal to r^2 while the area of a square is equal to s^2. The geometric problem, squaring the circle, aims to form a square with the area of a circle. However, it was not until 1882 when Lindemann was able to prove that is transcendental, thus, squaring a circle is impossible. In Da Vinci’s Vitruvian Man (c. 1490), he places the man at the center of both a circle and a square which was regarded as his attempt toofsoDlvae the controversial problem. Roman architect Vitruvius, who was one Vinci’s greatest influences, claimed that if a compass’s fixed point is placed on a human’s navel, a circle can be perfectly drawn around the body with outstretched arms and legs. Further, he also claimed that arm span and height have a nearly similar measure, thus a square can be drawn around the body as well. Da Vinci tried to sketch Vitruvius’s idea of solving the problem of squaring a circle as the Vitruvian man we know today. Another assumption drawn from this sketch, is that the ratio of the radius of the circle to the side length of the square (the height and arm span of a man) is given by the golden ratio r= (1+sqrt(5))/2=1.6180.... During the Renaissance period in Italy, a movement called Neoplatonism was revived; it was based on Plato and Aristotle’s teachings. This belief claims that the universe has a chain-like hierarchy than begins with God, goes through the angels, mankind, plants and ends with demons. Early in neoplatonism, it was claimed that mankind is exactly in the middle of the chain because we have both a mortal body and an immortal soul. Around Leonardo’s time, a Neoplatonist who was one of the men responsible for Renaissance Neoplatonism, Giovanni Pico della Mirandola asserted that humans can take any position in the chain; they can take whatever form he pleases. This rising Neoplatonist idea had also allegedly influenced Leonardo as well. From the Vitruvian man, we can see that man can fill both the unresolvable areas of circle and square; he can fill whatever shape, mathematically and philosophically. Satellite Map of Imola Cesare Borgia, a military commander and the infamously ambitious son of Pope Alexander VI, seized the city of Imola in 1499. Three years later, he brought Da Vinci into the city as a military engineer. One of Da Vinci’s first tasks was to help Borgia learn the territory. Back then, territorial maps were commonly from a hillside point of view; in this perspective, some taller buildings blocked the view of others. Some maps were inaccurate in scale, usually to exaggerate a city’s landmark. Further, some maps had mythical creatures such as dragons or angels all over the place. 8

These properties of the existing maps at that time made it harder to be used for tactical purposes. Borgia ordered Da Vinci to create an “ichnographic” map, an idea that was first coined by Vitruvius. This type of map aims to look as if you’re directly above whatever you’re mapping. However, at that time, there were not any modern tools such as satellites which would enable Da Vinci to map an entire city. According to Vox, studies claim that he had used a “bussola” or a disk that can mark the angles of streets with respect to a stable point. Further, he used a magnetic compass to record the orientation of the town’s perimeter at every turn. For the distance, it remains unsure if he tried to record it by foot or by using Vitruvius’s invention, a “hodometer”, now odometer. With these information and his exemplary imagination, he was able to create a considerably accurate map of Imola hundreds of years before satellite-generated maps were created and made available. The creation of the “Vitruvian Man” and a satellite map in 1502 are not even fully representative of Da Vinci’s plethora of achievements. Leonardo's imagination was evidently ahead of his time. Leonardo is recognized to be the first to write systematic explanations and illustrations of how machines work. Before even being invented, he had ideas for a helicopter, a tank, a concentrated solar power, a computer, and even a rough theory of plate tectonics. He has also demonstrated an advanced understanding of anatomy, civil engineering, optics, and fluid mechanics through his sketches and notebooks. Therefore, it is not exactly a surprise that he is considered as the embodiment of a Renaissance man. Lady with an Sketches of Ermine Fluid Mechanics Self-portrait 9

Nearly 4500 years ago, the Great Pyramid of Giza was completed. The Great Pyramid is, also known as the Pyramid of Khufu, located in Cairo, Egypt. The Great Pyramid is now considered one of the world's seven wonders, and it is the only one still standing. Because of its construction and historical relevance, the Great Pyramid has drawn the attention of numerous archaeologists and even mathematicians throughout history. Additionally, the mathematical constant pi value is thought to have been utilized in constructing the Great Pyramid. What is pi? Pi, the mathematical constant symbolized by the Greek letter ������, has a value of around 3.14. The number pi is said to be one of the easiest mathematical constants to grasp and is considered the most often used and studied mathematical constant today. About the Great Pyramid, there is a theory proposing that the height of the pyramid is similar to the circle's radius, whose circumference equals the perimeter of the pyramids' bases. This theory is known as the Pi theory. 10

The measurements of the Great Pyramid. Various publications on the Great Pyramid's measurements have appeared over the previous few hundred years. However, getting exact measurements of the pyramids is difficult today since certain parts have already been removed and ruined by other forces like theft and erosion. The royal cubit was the unit used by the Egyptians to measure the length of the pyramids. For you to imagine, a royal cubit is the distance between your elbow and the extended tip of your middle finger. Also, a royal cubit is supposed to be half a meter long. The pyramid is estimated to be 280 cubits, or around 146.64 meters tall. Next, the four sides of the pyramid's base range in length from 230.25 meters to 230.45 meters, or approximately 440 cubits. The measurements of the four sides of the Great Pyramid's foundation are reported to be 230.25, 230.36, 230.39, and 230.45 meters. If we take the perimeter of the Great Pyramid's base and divided it into two, we have, 230.25 + 230.36 + 230.39 + 230.45 = 921.45. 921.45/2= 460.725 m. If we divide 460.725 m by its height, we have, 460.725/146.64 = 3.1419. The result is very close to the value of pi. 11

Fractals: A Recursive Self- Similar Beaut in Nature Dominic R. Navarro Complexly simple yet sublime. That’s how fractals are described. These are infinitely self-repeating figures that create a seemingly chaotic pattern. You may not know, but they are found everywhere. I mean, everywhere. Beyond the surfaces of our skin, we have organ systems. Did you know these organs such as the kidney and lungs have a network of blood vessels and they are formed in a recursive fractal manner? Some scientists argue that through natural selection, our bodies have evolved in a way that our genes code these blood vessels that are oriented to optimize blood and food transport throughout the body. In the environment, we can see fractals in trees, snowflakes, and the weather. Trees have a trunk that eventually branches out. These branches also branch out, but in a similar fashion. They then form a fractal pattern that expand until its leaves. Snowflakes, on the other hand, are fractal objects themselves. Magnifying one part of a snowflake yields a more or less identical figure. In weathers, specifically in clouds, fractal structures exist. A wide range of, for instance, stratocumulus clouds demonstrates a self-similar form. Just like snowflakes, focusing one section of the range of clouds, you will get an almost the same scenario. It is compelling that on plain paper, although from afar with our eyes, these ordered appearingly mayhem look finite, but they are actually not. Starting from a point, it extends in an infinite length as they are infinitely repeated patterns since as you zoom in more and more, you would see the same pattern but in a smaller scale infintely. Fractals are not just mere Wooden Nose How long does the journey noble patterns in nature. They are created to I start with one take optimize whatever their function may be. One I start with one face Not until the end of time may overlook them, but the beauty and efficiency Oh, I’m carbon copied Confused and in crisis of fractals harmonize. To another place Waiting and identifying A similar face Or probably an exact face To not be deceived A part of me that looks like me I am it Be warned when it happens But also not When Pinocchio isn’t his A part of me that isn’t me normal phase 12

Mathematics is considered to hold the solutions to the majority of the universe's mysteries. Also, mathematics is said to be found everywhere. The Fibonacci Sequence is one great example. For hundreds of years, mathematicians, physicists, and painters have been captivated by this renowned sequence. The Fibonacci sequence can be found anywhere here on earth, and even across the universe. This sequence can be seen from the smallest to the largest detail in nature. But what is the Fibonacci sequence? The Fibonacci sequence is said to be a series in which each number is the sum of the two preceding numbers. The Fibonacci sequence usually starts from 0 and 1. The said sequence is given by 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. Each number in the sequence is called the Fibonacci number. Now, let's look at how abundant the Fibonacci sequence is in nature. Here are a few examples: 13

The numbers 3, 5, 8, 13, 21, 34, or 55 are the usual number of flower petals. Here, it can be seen that the lily, buttercups, chicory, and daisy have 3, 5, 21, and 34 petals, respectively. 14

If we look closely at the seed pods on a pinecone, we will see that it is arranged in a spiral pattern. For every cone, there is a pair of spirals in which each one is running in the opposite direction. The number of spirals will always match the Fibonacci numbers. The Fibonacci sequence is also found in the formation of tree branches. The branching pattern is continuously repeated for each new stem. As a result, a Fibonacci sequence is formed. 15

The Fibonacci sequence is used to explain some natural forms, such as the logarithmic spirals. Snail and nautilus shells, for example, follow the logarithmic spiral. Just like in snail and nautilus shells, galaxies, such as the Milky Way, follow the Fibonacci pattern. 16

The Golden Ratio Exists in Trading?! Dominic R. Navarro To start with, the Fibonacci Have you been thinking about the bearish scenario that has been going on in the crypto world lately? You must be retracement levels feeling not too good not having pulled out your long positions before everything went south. Nonetheless, let’s learn about one of the most fundamental trading strategies for technical analysis—the Fibonacci Retracement. Interestingly, you cannot only observe the golden ratio in nature but also within the blockchain and trade our favorite stocks and coins. commonly include 23.6%, 38.2%, 50%, 61.8%, and 78.6% although 50% isn’t really a Fibonacci ratio. Whether it be for day trading or long-term, it provides traders indicators of support and resistance levels as reference. For instance, if a stock went down by 38.2%, they may use this strategy to buy at a good price. Fibonacci Retracement is easy to use; you just have to plot the absolute highs and lows on the chart, then it will automatically show you the retracement levels. That’s it! If you haven’t done this strategy, go ahead and try it for yourself on charting platforms. As always, manage your risks well and trade responsibly. 17

FINANCE REVIEW ISSUE NO. 9 JULY MARILYN NYLA M. DEL FEATURES MUNDO ADVICE Sam Eisenstadt developed the first quantitative ranking system based on a stock's Don't Just Sit There! Start performance over the preceding six months Learning about Quantitative and found that the top stocks outperformed Investment Strategies the companies with the lowest rankings. In addition, he laid the groundwork for As the market continues to develop, an quantitative investing in the year 1965. In increasing requirement for advancement today's day and age, most investment would simplify the process. This must- communities use quantitative investing tactics. needed enhancement is what led to the They put these techniques to use to surpass discussion of quantitative investment the competition and boost their returns. strategies. Therefore, seen as a step Taking the approach of adopting investment forward in terms of technological techniques that evaluate historical quantitative development in the finance sector. These data is sometimes referred to as systematic emphasize implementation, leading to investing, which is another name for this improved decision-making and an approach. Quantitative investment can be increase in portfolio size. divided into two primary components: research and implementation. This is done to find stocks with a greater possibility of outperforming an index by using a wide variety of features. As a result, it is helpful for asset allocation, risk management, and tailoring investment portfolios to meet the requirements of individual customers. 18

DECISION SCIENCE IF YOU DON’T KNOW BUSINESS ANALYTICS NOW, YOU’LL HATE YOURSELF LATER MARILYN NYLA M. DEL MUNDO In the modern economy, business analytics Business Analytics gives a clear route has become a beneficial instrument. Across regarding relocating past the actual all sectors of the economy, companies functional to enable correct breakthrough produce enormous volumes of data, which along with pace as well as agility. Business has led to an increase in the demand for analytics presents quantitative methods to individuals who are data literate and who analyze information and make better can understand, evaluate, and apply the management decisions. The way is not from information they gather. Sixty percent of rote learning of equations or facts but companies worldwide are using data to concentrated on honing the understanding of improve the efficiency of their business critical concepts, managerial opinion, and the processes and costs; 57 percent are using ability to use course concepts for business data to drive strategy and change; 60 problems of consumer analytics. percent are using data to monitor and improve their financial performance (52 Business analytics describes and predicts percent). trends and consequences and makes wiser data-driven business decisions. Embracing In light of this development, acquiring a and applying Business Analytics is not comprehensive knowledge of business something the company can do overnight. analytics might be a method to progress But, if the company has some best practices your career and make more competent for Business Analytics, they can take the levels judgments while working. This is because of understanding they want and grow more business analytics is becoming increasingly aggressive and productive. Thus, incorporating important. An organization can be business analytics are likely to be the ones significantly influenced for the better by who can make most valuable contributions applying data analytics. Business analytics and have the most significant impacts for the aims to streamline decision-making by business. gleaning valuable insights from a company's data and presenting those findings in a comprehensible format. 19

MATHEMATICS JULY MARILYN NYLA M. DEL MUNDO EE N fE R GfY iciency The manifestation of creativity frequently takes the form of improvements in effectiveness. It is vital to improving energy efficiency to reduce energy consumption without abandoning the program. With increased energy efficiency, the target level of the program can be achieved at significantly reduced costs for the necessary energy. The industrial sector is not the only one that may benefit from innovations in energy efficiency. In addition to that, they are present with these completed products. Greater force efficiency in consumer items minimizes the amount of rivalry for resources that exists between demand and production. As a result, the supply threat that the system faces is also reduced. This last issue is vital to consider from a competitive standpoint. It has been a trend of discussion on renewable energy and its environmental and economic benefits in media and politics. There is increasing recognition of the need to improve energy efficiency to reduce cost and carbon footprint. Awareness of options emphasizes the ability to make conscious decisions about our role in the global effort to be environmentally friendly. As Mathematics can be seen in electricity through the cost of bulbs, lifetimes, and the price of electricity. Thus, discussing concepts on how we can utilize mathematics beneficially or effectively for efficient energy would be the answer to attaining sustainability and affordability for these needs—stating that mathematics helps calculate the fuel used, which is equal to what people would pay. In the end, the knowledge of mathematics would enable the world to conquer energy efficiency through technological advancement or innovation with alternatives to renewable energy. 20

CROSSWORD PUZZLE Quantitative Investment Strategy 21