LAKBAY: Explore the World of Mathematics

mathematics in the modern world | May 2022 lakbay explore the world of mathematics HIDDEN GEMS OF NUMBERS USA $1.618 FREE TICKETS FOR A MATHEMATICAL JOURNEY DIVE INTO THE WORLD OF LOGIC A GOOD WAY TO UNDERSTAND THE WORLD

Table Of Content 2 SEARCH FOR PATTERNS Understanding of life begins with understanding of Patterns – Fritjoj Capra 7 TRAVEL FROM HOME Against logic there is no armor like ignorance – Laurence J. Peter 14 #BEAUTYSEARCHING: YOUR ITINERARY TO GOLDEN RATIO The golden ratio has inspired thinkers of disciplines like no other number in the history of mathematics. – Mario Livio

\"undeRSTANDING OF LIFE BEGINS WITH THE UNDERSTANDING OF PATTERNS.\" -Fritjoj Capra

Like us, patterns are everywhere. Even us! We are all pattern from our face to our organs. EVEN OUR JOURNEY, it is all patterned! Especially, our journey here in Math in the Modern World is a pattern as well. From topics, schedule, and to our learnings. For more information about patterns, let's go and learn in this mini magazine! FUN FACT 101 Filipino artistry and creativity are evident in various art forms but what makes the weaving culture distinct is its power to unite people as strong, resilient communities bound by living tradition and colourful textile patterns and motifs.

Patterns #1 Logic pattern It is a great day to start the sem with this topic! You have a new school, new friends, and a new lesson to learn. You show up the first day, and from the time you join the meeting, you are in a whole new world. You search for the familiar in everything that is new. Are there people you know or topics you’ve learned? How are people dressed and how do they interact? Who can you trust to know what’s up and to share it with you? Do you know the acronyms or the inside jokes? What about your professor and block mates? All day, you search for patterns, you try to make sense, and you do things to become a part of this strange new world. You are using Logic pattern. #2 NuMb3r P4Tt3rN 1,2,3,4 is used by singers to start their song, while dancers use 5,6,7,8 to continue their dance practice. These people know when to start even though the last number of their cue is not the real end. they just use this pattern traditionally and make a good cooperation with each other. With these example, we realize that numbers are used to have a pattern without us noticing it! FUN FACT 101 Number patterns are not restricted to a few types. They could be ascending, descending, multiples of a certain number, or series of even numbers, odd numbers etc.

#4 Geometric pattern Geometric patterns are a collection of shapes, repeating or altered to create a cohesive design. While you have the shape meanings down, you might not know where to start. As an architecture student, our hearts, mind, and soul are shaped to fully understand the perfection of such geometrical figures to make it symmetrical. asymmetrical, or balance it. #5 Word Pattern The English language is fascinating for so many reasons. On the one hand, it has many rules for spelling, pronunciation, and grammar; on the other hand, it breaks those rules. But it still follow the same pattern in English rules.

Euclidian isometry #1Translation Translation or slide moves a shape in a given direction by sliding it up, down, sideways or diagonally. #2 Reflection A reflection (or a flip) can be thought of a getting a mirror image. It has a line of reflection or mirror line where the distance between the image and the mirror line is the same as that between the original figure and the mirror line.

#3 Rotation Rotation (or a turn) has a point about which the rotation is made and an angle that says how far to rotate. #4 Dilation A dilation is a transformation which changes the size of an object. #5 Rigid Transformation A rigid transformation (or isometry) is a transformation that doesn't change the size or shape of a geometric figure. is a special kind of transformation that doesn't change the size or shape of a figure.

FRACTALS 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. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over. FUN FACT 101 Fractals are the backbone behind scientific concepts. They help give us a better idea of how bacteria grows, insight into how water freezes (snowflakes!), and even better comprehension of brain waves. The formulas are so intricate that studying them has led to numerous scientific breakthroughs.

Travel from home HAVE YOU EVER EXPERIENCE DRINKING A COFFEE IN THE MORNING AND THOUGHT OF THE ERA YOU ARE IN? Computers are all around us and we are currently in the information era where technology comes hand in hand with human. The pandemic has been a great way to know more about computers. It became so much easier for us to communicate to several people all at ones, discover new things, know the current news and we even had a way of learning during online classes. bcuotmhpuowtedrosewsork? There is a mathematical explanation for this and this is connected to LOGIC. Logic is the foundation for all mathematical and automated reasoning. GEORGE BOOLE The meaning of mathematical assertions is defined by logic rules. The AUGUSTUS DE MORGAN invention of logic is attributed to the Greek philosopher Aristotle (384- 322 BC). George Boole (1815-1864) wrote the Laws of Thought where logic was developed into an abstract mathematical system like algebra. He, together with Augustus de Morgan (1806 - 1871), founded symbolic logic. Logic principles give mathematical statements their proper meaning. Valid and incorrect mathematical arguments are distinguished using these standards. Logic has several applications in Computer Science, ranging from the design of digital circuits to the development of computer programs and the testing of program correctness.

preposition true false true false true false true fa true false true false true false true fa The fundamental building block of true false true false true false true fa logic is the proposition. It is described true false true false true false true fa as a declarative phrase that can only true false true false true false true fa be True or False. true false true false true false true fa true false true false true false The Truth Value of a proposition is True (denoted as T) if it is a true statement, and S ome sentences that do not have a False (denoted as F) if it is a false truth value or may have more than statement. For Example, one truth value are not propositions. 1. The sun rises in the East and sets in the West. For Example, 2. 1 + 1 = 2 3. 'b' is a vowel. 1. What time is it? 2. Go out and play. 3. x + 1 = 2. To represent propositions, propositional variables are used. By Convention, these variables are represented by small alphabets such as p, q, r, s TRUTH TABLE We analyze all potential combinations of propositions that are brought together by Logical Connectives to construct the given compound proposition since we need to know the truth value of a proposition in all feasible circumstances. A truth table is a collection of all potential circumstances in a tabular style. There are 5 common types of logical operators: NEGATION CONJUNCTION DISJUNCTION CONDITIONAL BICONDITIONAL

LLEOTGSICDAILVEOPIENRTAOTTOHRES negation dive in to logic If p is a proposition, then the negation of p is denoted by ¬p, which when translated to simple English means- “It is not the case that p” or simply “not p“ The truth table of p p ¬p with their T F corresponding ¬p is F T seen on the right. conjunction For any two propositions p and q, their conjunction is denoted by , which means “p and q“. ∧p q p q THE CONJUCTION IS TRUE TTT WHEN BOTH P AND Q ARE T F F TRUE, OTHERWISE FALSE F T F FFF disjunction For any two propositions p and q, their disjunction is denoted by , which means “p or q“. ∨p q p q T T T WHTEHNEOETDHIITSEHJREUWRCITPSIEOONFRA,QLISSIEST.RTRUUEE, T F T F T T FFF

conditional For any two propositions p and q, the statement “if p then q” is called an implication and it is denoted by p → q. In the implication , p is called the hypothesis or antecedent or premise and q is called the conclusion or consequence. p q p→q TTT FATWLHSHEEEINMOTPPHLIEISCRATWRTIIUSOEENAIITNSIDSFAQTLRISSUEE TFF FTT FFT biconditional STUDY f ↔ ↔or any two propositions p and q, the statement “p if and only if (iff) q” is called a biconditional and it is denoted by p q. The statement p q is also called a bi- implication. ↔p q p q T T T THE IMPLICATION IS TRUE WHEN P AND Q HAVE SAME T F F TRUTH VALUES, AND IS FTF FALSE OTHERWISE FFT

#BEAUTYSEARCHING: YOUR ITINERARY TO GOLDEN RATIO We observe that many of the natural things follow the Fibonacci sequence. It appears in biological settings such as branching in trees, phyllotaxis (the arrangement of leaves on a stem), the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bracts etc. At present Fibonacci numbers plays a very important role in coding theory. Fibonacci numbers in different forms are widely applied in constructing security coding. The Golden Ratio is also frequently seen in natural architecture also (Internet access, 18). It can be found in the great pyramid in Egypt. Perimeter of the pyramid, divided by twice its vertical height is the value of phi. Golden section (Gend, 2014) appears in many of the proportions of the Parthenon in Greece. Front elevation is built on the golden section (0.618 times as wide as it is tall). DID YOU KNOW Fibonacci was an Italian number theorist who lived from 1170 to 1240 or 1250. He popularized such diverse mathematical notions as the Arabic numbering system, the concept of square roots, number sequencing, and even math word puzzles. LEONARDO PISANO BIGOLLO

Why is Leonardo Pisa refeFrirbeodntaoccais? Leonardo of Pisa is today known as Fibonacci, which is short for Filius Bonacci. There are two possibilities for the meaning of Fibonacci: Fibonacci is a contraction of the Latin \"filius Bonacci,\" which is used in the title of his work Libar Abaci (more on that later), which means \"the son of Bonaccio.\" The Fibonacci Sequence is the series of numbers: The next number is found by adding up the two numbers before it: the 2 is found by adding the two numbers before it (1+1), the 3 is found by adding the two numbers before it (1+2), the 5 is (2+3), and so on! Golden RatioExample: the next number in the sequence above is 21+34 = 55 Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618. FUN FACT 101 Faces, both human and nonhuman, abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can been seen from the side, and even the eye and ear itself (which follows along a spiral).

euclid Euclid, in The Elements, says that the line ABAB is divided in extreme and mean ratio by CC if AB:AC = AC:CBAB:AC=AC:CB. TAHLETTHEORUMG, WH EEUSCHLAIDLLDC OAELSLNTOHTISUTSHEE GOLDEN RATIO. The definition appears in Book VI but there is a construction given in Book II, Theorem 11, concerning areas which is solved by dividing a line in the golden ratio. As well as constructions to divide a line in the golden ratio, Euclid gives applications such as the construction of a regular pentagon, an icosahedron and a dodecahedron. Here is how the golden ratio comes into the construction of a pentagon.

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