TUKLAS GROUP 8 MAGAZINE-DRAFT

TUKLAS DISCOVER MATHEMATICS AROUND THE WORLD ARTICLE TITLE ARTICLE ARTICLE TITLE TITLE Breathtaking view away Surprising retreats & from the city | p. 14 Top secret hideaways local favorites | p. 112 and exotic escapes | p. 35

TUKLAS: ABOUT \"Tuklas\" is the Filipino word for \"Discover\" which THE means to travel in or through in order to TITLE familiarize. Words by: Trinity Bancoro Being human beings who are on the constant Photographs by Mark Halberg lookout for something new, we are always GEMATW GROUP # yearning to see or do something better: to live through different experiences & learn about different qualities that make people distinct from one another. Tuklas is an ode to these: to every force that has driven us to escape our familial range of comfort: to go out there into the world & to realize how small we are in this otherwise infinite universe, and to know what it means to live. In this magazine, you will be comforted by the learning and understanding of new and familiar mathematical concepts. You will be amazed by how mathematics can be seen in the smallest objects, and you will wonder how many more things make more sense with it. Amidst all of these, I hope you are compelled to deviate from living life as you know it, and to employ complex mathematical concepts in living your best lives. Discover life. Discover you. Join us as we go Around the World. This iNsOTMuAkDlaI Cs. | 2 4

TUKLAS Table of Contents JOURNEY WITH US 2   AROUND THE WORLD Editor's Note 7   New Releases 20     8 Young Emerging Writers This year's promising young writers are about to shine  23     INDIE INSIDER: Hidden Bookshops Hole in the wall bookshops are popping all over the Metro 30     NEW BLOOD: Christina Adams Explore Christina's world of magical realism 32     REVIEW: Flesh and Blood This year's most-awaited thriller 40   SHORT STORY: The Buried Key by Alexander Wyeth 43     POETRY: Sweet Serenity by Samantha Adams 52     COMICS CORNER:  Incidental Ideas TUKLAS

BY: DANIELLE ILAGAN UNRAVEL your travel charges A travel plan isn’t complete without the travel funds. But what if you’re short in cash? Will you give up on a possible memorable and life-changing travel experience or will you get a loan to fund that travel plan you’ve always wanted? In this article, we’ll learn how to unravel the totality of your travel charges by calculating the interest you owe when you borrow funds for your traveling expenses so that you can prepare for immediate payments right after your travels. After all, you can’t enjoy your journey around the world when you’re constantly thinking about making the right amount of payments. What is interest? Interest is the monetary charge of a loan balance or deposit paid to the lender periodically for the privilege of using their money. When borrowing money, the borrower needs to compensate the lender for the risk of lending monetary funds to them and the opportunity cost. In short, the borrower will pay the borrowed amount with additional interest. When lending money, the lender may lend it to a borrower. Another way that a lender may use is to deposit the funds in a savings account, letting the bank lend it out or invest funds in exchange for earning interest (Brock & Pritchard, 2020). The amount you pay or earn in interest depends on the following (Brock & Pritchard, 2020): The interest rate The amount of the loan Length of payment There are two main types of interest that can be applied to loans, simple and compound, and they are typically expressed as a percentage (Chen, 2020; Khartit & Nickolas, 2021). Simple interest is an interest that does not compound and is calculated on the principal amount of a loan or a deposit (Khartit & Nickolas, 2021). It is calculated using the formula in the next page --->

unravel Examples of simple interest and compound interest In contrast, compound interest is the addition of interest to the principal sum of a loan or deposit or, SIMPLE INTEREST WHEN in short, interest on the interest (Khartit & BORROWING MONEY Nickolas, 2021). It is calculated by using either of the formulas given: Andrea wants to go on a vacation to Paris, France for three days. However, she is quite short on funds especially when it comes to providing her necessities when she’s on the trip. After several calculations, she concludes that she needs to borrow an amount of Php 40,000 to secure her dream vacation in the City of Love. She decides to ask her mother to lend her money, and she agrees to it as a four-month, non-compounding loan with a 3% annual interest rate. What is Andrea’s total interest expense? Andrea, therefore, has a total interest expense of Php 2,400 to her mother.

SIMPLE INTEREST WHEN LENDING MONEY Shirley was asked by Barry to lend him some money to use for his 7-day trip to Boracay. The amount that Barry was asking her was a three year, non-compounding loan of Php 50,000 with an annual interest rate of 4%. Shirley disagreed with the suggested annual interest rate and she told him to multiply it by two, to which Barry reluctantly agreed since he needed the money. Based on the situation, how much interest will Shirley earn in this transaction? Shirley will earn an interest of Php 12,000 in this transaction with Barry.

COMPOUND INTEREST WHEN LOANING Continuing with the given example in Simple Interest when lending money, Barry needs to borrow an additional Php 70,000 for three years. Unfortunately, Shirley refused since she needed her money at the time. Barry then decided on taking a loan from the bank at an interest rate of 6% per year compounded annually, with the full loan amount and interest payable after three years. What would be the total interest paid by Barry? The total interest to be paid by Barry in the bank is Php 9,550.80. COMPOUND INTEREST WHEN DEPOSITING Josh decided on depositing his travel funds of Php 100,000 instead of using it. It was deposited at an annual interest rate of 5% and is compounded monthly. What will be the value of the investment after 7 years? The value of Josh’s investment after 7 years will be Php 70, 901.80.

Museu do Amanhã, Gustavo Xavier BY: DANIELLE ILAGAN Mathematics is evident around us. It can be seen in Also known as symmetrical balance, this is achieved the structure of a building, in a visual artwork, or by the arrangement of elements on both sides of the basically in any objects we create. It is also present centerline, meaning the work of art is the same on in the nature and landscapes that surround us. Let’s one side as the other, formed through horizontal or have a look in the online exhibit entitled “The vertical division. Though symmetrical balance is most Hidden Beauty of Mathematics” created by Museu often used by artists, most of them look towards the do Amanhã located in Rio de Janeiro where the slight shifts in asymmetry, biaxial symmetry, inverted concept of symmetry is elegantly expressed in symmetry, near symmetry, and radial symmetry to different kinds of art forms and in nature itself. have a focus on one particular element or part within Here, we’ll understand and appreciate the a composition. symmetrical patterns evident in everything that we see and create, and the beauty of the fusion of Symmetry in Arts mathematics, nature, and arts in our lives. Symmetry is evident in different kinds of art forms What is symmetry? including architecture. Multiple aspects of architecture present the concept of symmetry, one of Let us first have a brief understanding of a principle which is the external views of the structure of of design called Balance. Balance is the arrangement buildings. An example of this is the structure of of elements to create an equal distribution of visual Museu do Amanhã itself. Spanish architect Santiago weight throughout a composition, making its Calatrava has a unique way of playing with lines, individual parts appear equally important (Issaquah curves, and open spaces, and Museu do Amanhã is Schools Foundation, n.d.). Symmetry commonly one of his projects which is evident of his style refers to a sense of harmonious and appealing (Writers, 2017). The museum, taking up 135,625 proportion and balance. In art, however, it is a square feet of space, has a cantilevering roof evident formal type of balance consisting of a mirroring of of symmetry. The large mobile wings and facade portions of an image (Mittman, n.d.). structure of the roof extend almost to the full length of the pier, emphasizing the extension into the Guanabara bay while minimizing the building’s width (Architect Magazine, 2016).

Another example would be an image entitled “Modern architecture” taken by an anonymous photographer presented in the online exhibit of Museu do Amanhã entitled “The Hidden Beauty of Mathematics.” Symmetry is also evident in the designs of building elements such as tile mosaics or the arabesque patterns (Pantelić, 2016). Two examples of such is presented in the aforementioned online exhibit, one is a photograph of the ceiling of the Lotfollah mosque in Isfahan, Iran taken by Phillip Maiwald and another is a photo of the interior of the mosque presenting several rooms with diverse symmetrical motifs taken by Masih khosravi Dehkordi. When there is “harmony in proportions,” meaning the balance of height, length, and width, then an artwork or object is deemed symmetrical. In Ancient Greece, the word or concept of “symmetry” did not exist Greek vocabulary in the days of Plato, however, it was already developing. The Greek noun “summetria,” which means “of the same size” in the English language, was being utilized to refer to \"proportion.” Proportion is fundamental in the aesthetic of art, guiding composition, design, and form. In Mathematics, it is the observance of ratios. Ratios connect parts of a design as a whole whether these be canons of human proportion, architectural design, or symbols and letter fonts (Schattschneider, 2003). Symmetry in Nature The art world has felt the influence of the Golden Ratio for centuries and it has been equated with the human’s √perception of beauty. Also known as the Golden Section or the Divine Proportion, this mathematical principle is the irrational number (1 + 5/2) which is approximately equal to 1.618 and often denoted by the Greek letter “ϕ” or “τ” (Carlson, 2019). There is a special relationship between this and Fibonacci Numbers. When we take any two successive Fibonacci Numbers, their ratio is very close to the Golden Ratio “ϕ” (phi). The larger the numbers in the Fibonacci sequence, the closer the ratio is to the golden ratio (Palmer, 2015). The Fibonacci sequence is often visualized in a graph, and each of the squares illustrates the area of the next number in the sequence. The Fibonacci spiral is then drawn inside the squares by connecting the corners of the boxes. The Fibonacci spiral uses “ϕ” as its basis, and this spiral can be spotted in Art as well as in Nature (Velasquez, 2017).

EXCLUSIVE TOUR TIX BY: TRINITY BANCORO Art is meant to be seen. More than that, it is meant to be engraved to the minds of the people it encounters. With the constant bickering between art on its technical best and art as a mere escape, it still captures the essence of disturbing the comfortable and comforting the disturbed. Indeed, art may be a blessing or a curse. In this article, we are going to discover the mathematical concepts behind brilliant pieces of art that have been either celebrated by generations or have just been recently introduced to the modern eye.

ATTIC   |   JANUARY 2016 18 Bienvenue to presentoir numeró one! Golden ratio is the proportion given by the numerical value: r = (1 + 51/2) / 2 = 1.6180··· , or (1 / r) = (51/2 − 1) / 2 = 0.6180···. It is frequently believed that in the \"Vitruvian Man\", the ratio of the radius of the circle to the side length of the square which is illustrated by the tallness of the man is given by the golden ratio. In this standardized picture in which the range of the circle has been assessed, improvised by a slight change, where the figure supposed to be a square by da Vinci was acclimated to produce a shape that is similar to square by directly planning the picture with Adobe Photoshop with the necessary linear mapping (History Staff, 2019). The ratio was estimated at 0.606 ∼ 0.609, which is significantly smaller than the golden ratio 0.618.

18 ATTIC   |   JANUARY 2016 IN KANDINSKY'S EYES

ATTIC   |   JANUARY 2016 18 KINETIC ART IN TOWNLEY'S EYES The author's final message: Life is constantly evolving. This process allows people to adapt as human beings and this occurrence defines the past, the present, and the future. Change is necessary not only to improve existing practices and disprove misconceptions, it is also a pathway into discovering brand new awe-inspiring methods of life and living in it. I hope you had fun touring Musee d’Art Moderne de Paris and learning about the fusion of art and mathematics. Never stop learning and exploring. AU REVOIR!

18 ATTIC   |   JANUARY 2016 #SeoulSearching: Your Itinerary in Korea BY: CHARY VILLANUEVA Crash Landing on You, Goblin, Descendants of the Sun, and many more K-dramas. These Korean Novelas might have inspired you to go to Korea and witness in person the filming locations of your favorites! In order to have a fruitful journey, it is essential to plan an itinerary or book a tour before travelling. However, it is undeniable that in travelling, it is hard to plan one’s itinerary. It requires rigorous searching and asking given that you are not familiar to the place.

Suppose, you are bound to travel in After calculating the costs, your trip to South Korea and you want to know Seoul costs $400 which comprises 5 how much would it cost if you go to tourist spots and 2 restaurants. On the Seoul and Jeju Island whilst knowing other hand, your trip to Jeju costs $300 how many days you must allot for which comprises 6 tourists spots and 2 your travel in Seoul and Jeju Island restaurants. Given a minimum of 12 separately. Moving forward, since tourist spots and 5 restaurants which you want to become an independent you can go to according to a website traveler who has control over time, you searched on, let us calculate, graph, places to eat, and other factors, you and discover the cost and number of refused to book a tour and planned days of your travel! the itinerary by yourself. Decision variables: x = # of days in Seoul y = # of day in Jeju Island Cost = 400x + 300y Constraints: 5x + 2y >= 12 6x + 2y >= 5 x >= 0 y >= 0

BY: AALIYAH CAIG HAVE YOU EVER QUESTIONED HOW YOU CAN APPLY MATH LESSONS IN YOUR EVERYDAY LIFE? Sometimes, I wonder where numbers are incorporated besides money and engineering. However, it is not common knowledge that everything around us is guided by Mathematical concepts. So, how far does Math go? Growing up, I have always been so fascinated by living the Island Girl life. It must be exhilarating to wake up to the sound of the beach waves, feel the island breeze, and watch breathtaking sceneries. To fulfill that longtime dream of mine, traveling to Hawaii is included in my bucket list! According to Keoni (2017), Hawaii is a beautiful tropical vacation hot spot unlike any other in the world because there are vast reasons for travelers to enjoy such as its glamorous white sandy beaches, its majestic mountains and steep valleys, and its city life. In my case, I long to journey through the majestic seashores of the picturesque beaches in Hawaii and appreciate its scattered seashells.

Indeed, travelers often visit Hawaii for its phenomenal sceneries, splendid beaches, and unforgettable vibe. But, little did they know that as they discover the beauty of the island life and feel the aloha spirit, the sceneries they admire are surrounded by mathematical concepts. Let’s take seashells as an example. Did you know that along with the delicate and mysterious beauty of seashells come mathematical models within nature? To be specific, the shape of the nautilus and other spiraling shells follows a pattern called the Fibonacci sequence. Keiren (2020) explained that the Fibonacci sequence, introduced by Leonardo of Pisa, is recursive, generated by adding the two previous numbers in the sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987… Keiren further added that if you were to draw a line starting in the right bottom corner of a golden rectangle within the first square and then touch each succeeding multiple squares outside corners, you would create a Fibonacci spiral as seen in the illustration. As you can notice, the numbers in the spiral are those from the sequence mentioned above.

Truly, a nautilus seashell follows the Fibonacci sequence. It is amazing how Mathematics is seen in Nature and Arts given that it seems to be a strange pairing at first sight. Initially, we only view Mathematics as a concept that revolves around logical and comprehensive ideas but in reality, everything that surrounds us including the things we admire such as nature and the arts have integrations with it. With that, may we not grasp the idea that Mathematics is a boring and intimidating subject we learn at school because Mathematics offers artistry and delicacy beyond what our eyes can perceive and what our minds can comprehend.

At this point, I just can’t wait to travel to Hawaii and take a closer look at the seashells beautifully scattered in the seashores! The next time you travel, remember to observe your surroundings keenly because you never know when a Mathematics lesson pops up. Remember, just like how Moana worked hard to see her fullest potential, no one will know how far Mathematics goes until it is discovered.

GEMATW BY: CHARY VILLANUEVA To travel the whole world is one of my dreams in life. Even though I have acrophobia, it is surprising how this fear of mine instantaneously disappears whenever I ride a plane. Also, as an ambivert who is in between being introvert and extrovert, I am also becoming a hundred percent extrovert when I travel. I ask questions with enthusiasm, listen to tour guides, and understand the history behind the places with sincerity. In fact, my heart beats for eating new dishes, experiencing various cultures, and meeting diversified people in different countries and places. To track one’s progress of being a wanderlust, a checklist of places you have wandered seems to be always present. For me, my checklist is the 7 Wonders of the World 2021 which are elaborated by Millar, A. (2021):

THE NAZCA LINES, PERU WILDEBEEST MIGRATION, KENYA ARCHES NATIONAL PARK, UTAH MOUNT FUJI, JAPAN LAYOUT BY: T BANCORO HADRON COLLIDER, SWITZERLAND AMAZON RAINFOREST, BRAZIL CALLANISH STONES, SCOTLAND To integrate Mathematics in this area, I conducted a simple survey to obtain knowledge about other people’s preferences over these places. next page

I asked 15 respondents to rank the 7 Wonders based on what is the most beautiful place for them: 1 as the highest while 7 as the lowest. After tabulating all the responses, I have arrived at this preference table: Written by Chary Villanueva. Photos by Lee Min-Han. Using the plurality method: Using the Majority Voting Method: A = 0, B = 0 A = 0, B = 0 C = 0, D = 10 C = 0, D = 10 E = 0, F = 4 E = 0, F = 4 G=1 G=1 The plurality method winner is The majority method winner is Mount Mount Fuji, Japan, gaining 14 total Fuji, Japan, gaining 14 total first-place votes which is beyond 7.5, that is half first place votes. of the number of voters.

NNNNNN A = 8 + 0 + 2 + 3 = 13 B = 16 + 4 + 4 + 4 = 28 C = 24 + 12 + 0 + 2 = 38 D = 48 + 20 + 12 + 5 = 85 E = 0 + 8 + 6 + 0 = 14 F = 40 + 24 + 8 + 1 = 73 G = 32 + 16 + 10 + 6 = 64 Given this result, the Borda Count Winner is still Mount Fuji in Japan with a total of 85 points. With these computations, Mount Fuji in Japan seems like the Most Beautiful among the 7 Wonders based on the voters’ preferences. Surely, it is a must to travel to that place even alone, with friends, or family!