L O D I P u b l i c a t i o n s INARTSANDNATURE NOVEMBER 2022 Mathematics

LODI P HP U B L I S H I N G H O U S E NOVEMBER 202 2 n o v e m b e r E d i t i o n | 2 0 2 2 pa g e 1 LODI NOVEMBER 202 2

L O D I JOHN CHESTER MARTINEZ EDITOR-IN-CHIEF ISABELLE REFUGIA LAYOUT ARTIST JAY BASONG ROMAR CUSTODIO JOHN ALEXANDER DIMAANO RAFAEL MAALA L O D I P U B L I S H I N G H O U S E AUTHORS AND CONTRIBUTORS november Edition | 2022 page 2 NOVEMBER 202 2

L O D I L O D I P U B L I S H I N G H O U S E NOVEMBER 202 2 TABLE OF CONTENTS november Edition | 2022 page 3 GEOMETRICAL SHAPES BY JAY BASONG SYMMETRY BY JOHN DIMAANO FUN FEATURES PT. 1: WHAT TO FIND IN THE NATIONAL MUSEUM OF FINE ARTS? BY ISABELLE REFUGIA FIBONACCI SEQUENCE BY JAY BASONG GOLDEN RATIO BY ROMAR CUSTODIO FUN FEATURES PT. 2 FRACTALS BY RAFAEL MAALA REFERENCES P. 4-5 P. 6-7 P. 8 P. 9-10 P. 11-12 P. 13 P. 14-15 P. 16

By jAY bASONG GEOMETICAL SHAPES Geometric and mathematical shapes can be found everywhere. Almost everything is made up of geometrical shapes in two and three dimensions (3D). According to splash learn, geometric shapes are closed objects made of points, line segments, circles, and curves; a regular shape has equal sides on all sides. For example, a square or a regular hexagon. Side lengths differ between irregular forms. As an example, consider a scalene triangle. These shapes can be found all around us. As the image shows, it has numerous angles and shapes. It can undoubtedly display beauty on both sides due to the light and the size of the pattern. It depicts the allure of a work of art that will entice viewers to look at it again and again. It will provide them with information not only about specific types of art or shapes but also about our daily lives, including geometric shapes. Another image is the museum floor, which is a representation of the traditional floor from previous generations. LODI Monthly Magazine november Edition | 2022 page 4

It has strong ties to geometric shapes; each shape has angles, and we learned that one of the qualities of a shape is a brighter line that conveys meaning to it. The use of mathematical equations shows how the patterns and lines are used in the shapes that result in geometrical shapes. There are many plane geometry shapes in nature, including the shapes of each human. in this image, the geometrical shapes are many plane geometry shapes in nature, including starfish, circles in tree trunks, and hexagons The hexagon is both the most prevalent shape in nature and the one that consistently baffles mathematicians. Hexagons are six-sided polygons that are found in a variety of natural structures, including beehives, bug eyes, and snowflakes. The geometric sequence is a product of nature, just like in the image. Shapes can be found everywhere and come in a variety of shapes. Shapes might be 2-D or 3-D, as was already mentioned. 3-D shapes are a subset of spatial geometry, whereas 2-D shapes belong to the category of plane geometry. Why do you need to learn the connection of mathematics with our nature? LODI Monthly Magazine november Edition | 2022 page 5

BY jOHN DIMAANO SYMMETRY We encounter math every day. We learn that nature can be quantitatively characterized when we learn more and more about our surroundings and the world around us. Even the rocks on which we walk can display nature's sense of symmetry, as can the beauty of a flower, the height of a tree, or both. We have picked representations within objects in our frame of vision that demonstrate a variety of symmetry types, while there are other instances in crystals and even at the microscopic level of nature. LODI Monthly Magazine november Edition | 2022 page 6 We are surrounded by symmetry. All life on earth and in the universe is symmetrical, including people, animals, and plants. Nature's masterpiece of harmony and balance is symmetry. All geometrical natural objects exhibit some degree of symmetry. If something is symmetrical in its design, it looks good. Bilateral symmetry is seen in the majority of species, and some also have radial symmetry. We, humans, find symmetrical things pleasant in our eyes.

Rotational symmetry can be seen in the oval that decorates a wall. Even though the positions have changed, rotating this shape one-fifth of a turn has no effect on the object, its patterns, or its appearance. In other words, even when rotated, the pattern remains the same. It is essential for us to learn the connection of mathematics with our nature. The knowledge we gathered can be a potential research concept. Mathematics and Nature is a crucial parts of a study. The most vital part of learning is contextualizing it in our daily lives. It was discovered that mathematics played the biggest part in helping people understand nature and mankind (Bayug, 2022). We can easily identify the things in our surroundings and we explicitly see the aesthetic side of it. The human body is an excellent example of a reflection axis because it can be divided into two identical halves in just one plane. The other example is an animal, which I chose to be a monkey because, like humans, if that monkey is divided into two halves, the other half remains similar. Rotational symmetry BIlateral symmetry LODI Monthly Magazine november Edition | 2022 page 7

Third Floor: The Senate Floor. The President Manuel L. Quezon Foyer, Exhibition Galleries XIII to XXIV, The Senate Session Hall (Main Level), The Senator Claro M. Recto Function Hall Fourth Floor: The Executive Floor. The Senator Benigno S. Aquino Jr. Foyer, Exhibition of Galleries XXV to XXIX, The Senate Session Hall (Mezzanine Level), The President Jose P. Laurel Function Hall, Management Offices by Isabelle Refugia WHATTO FIND IN THE NATIONAL MUSEUM OF FINE ARTS ? First Floor: The Judiciary Floor. The Government William H. Taft Entrance, The Architect Juan M. Arellano Foyer, The Sandiganbayan Reception Hall, Seminar Rooms, The National Fine Arts Repository, The National Archaeological Repository, Auditorium (North Annex), Administrative Offices (South Annex) Second Floor: The House of Representatives Floor. The Padre Jose Burgos Entrance, The President Manuel Roxas Foyer, The Spoliarium Hall, Exhibition Galleries I to XII, The President Sergio Osmena Function Hall The National Museum of Fine Arts is home to 29 galleries and hallway exhibitions. The building itself is remarkable. Constructed in the early 1920s. The most prominent masterpiece is Juan Luna’s Spoliarium, which was awarded a gold medal by the Exposición Nacional de Bellas Artes in 1884 in Madrid, Spain. LODI Monthly Magazine TRIVIA TIME page 8 november Edition | 2022

by jay basong The Fibonacci numbers are a series of integers that start with zero, then one, another one, and a series of numbers that climb gradually. According to Sheldon (2020), the sum of the two numbers before it is the same for every number in the series. The Fibonacci sequence is a design principle that can be used in art, architecture, and graphic design to produce visually appealing proportions. Our subconscious mind is drawn to the harmony created by the proportions, sizes, and arrangement of different elements with one another. Artists realized that the Fibonacci spiral is an expression of the rule of thirds, an artistic principle. This is used to balance the features in a picture's composition. Rather than exactly centering them, dividing the elements of the image by thirds creates a more aesthetically attractive flow. FIBONACCI SEQUENCE The monument depicts an unclothed woman who is fiercely self-assured and unconcerned with others' opinions. It also serves as a symbol of women's empowerment and the equality of all people in this world. The statue expresses various ideas since the golden ratio or Fibonacci is the main focus of it. LODI Monthly Magazine november Edition | 2022 page 9

The Commonwealth of the Philippines is visible in the photograph. It is based on true events, and historical context, as well as specific details of individuals who actively supported the Commonwealth in its conflict with their city. The image is thought to be related to the Fibonacci series because of the statue's harmonious qualities, which have an appealing flow, and the number sequence that exemplifies how this image is tied to the Fibonacci sequence. According to Cleveland (2020), the Commonwealth shows the main character, which has a ratio and features on it. Fibonacci is found in the artwork. As said by Basirjafari (2020). The renowned mathematical model that defines the shape/ratio of several events that we are unaware exist in nature may be seen in the Fibonacci sequence. In nature, there are an endless amount of Fibonacci numbers; these numbers can be found all over the place. Our lives are made more ordered and less chaotic by mathematics. Power of reasoning, inventiveness, abstract or spatial thinking, critical thinking, problem-solving abilities, and even excellent communication skills are some of the attributes that mathematics naturally fosters. In a nutshell, it's a part of who we are. Cruz (2018) claims that there are numerous patterns and events in nature, our planet, and our lives that make life easier. "Why do you need to learn the connection of mathematics with our nature? LODI Monthly Magazine november Edition | 2022 page 10

By romar custodio GOLDEN RATIO Golden Ratio is famous in the world because people believe a golden ratio is a divine number or design myth. People that have different professions are fascinated by the golden ratio, and for many centuries has ended people still use the golden ratio. It has also been considered to be “The Perfect Illustration of Beauty.” The golden ratio is also called the Golden mean, Golden section, or the Divine proportion, it is one of the famous irrational numbers. The Greek letter phi is usually used as the name for the golden ratio. This is the artwork of Agustin Goy the music, artistic crafts, and wondrously boundless imagination, the Philippine Center New York Core Collection of 1974 paved a way for visitors to rediscover age-old artworks. The painting showed the subject in full size. It means the painter calculates that his/ her subject will occupy the entire space. It shows a golden section/ divine proportion. Every figure starts from a cube, a square, a rectangle, or even a circle to create a good balance figure. The painting was created by Vicente Manansala. Levering the Golden Ratio can help you design a visually appealing UI that draws the user’s attention to what matters the most. The artist made his painting like that highlights can follow the Golden Ratio and help you decide where to put the most important content. LODI Monthly Magazine november Edition | 2022 page 11

The Artwork is called the Ilocos Caravan (1974) by Hugo Yonzon Jr., from the Philippine Center New York Collection (PCNY). In nature the golden ratio is often used for arrangements of leaves or flowers like in the painting, these use the golden angle of approximately 137.5 degrees. Leaves or flowers arranged at that angle best use sunlight, in addition, the distance between the center of a person’s body and the floor and the distance between the crown of the heart and the base of the spine are both in accordance with the golden ratio. LODI Monthly Magazine november edition | 2022 page 12 "Why do you need to learn the connection of mathematics with our nature? Mathematics is important in many ways and assists us in our daily lives. It is widely held that mathematics can be used to understand nature; many scientists have discovered mathematical concepts and patterns in nature, ranging from sunflowers to snowflakes to hurricanes and galaxies (Internal, 2020). Mathematics can be found everywhere, even in nature. For example, statistics and probability can be used to count death tolls from natural death, calamities, and other natural disasters that have occurred. Life is full of unexpected phenomena that we did not anticipate, for example, the water you drink from a well, can be contaminated, but if we apply algebra, it helps us to determine whether it is contaminated or not, that is why mathematics is important not to solve mathematical equations but to help us in our day-to-day problems.

Guess whether Geometrical, Symmetry, Fibonacci, Golden Ratio, or Fractals. Fill in the blanks! 1. According to splash learn, geometric shapes are _______________, line segments, circles, and curves 2. Almost everything is made up of geometrical shapes in _________________. 3. All life on earth and in the universe is symmetrical, _________________________. 4. Fibonacci numbers are a series of integers that start with ___________, then one, another one, and a series of numbers that climb gradually. 5. Fractals are _______________ patterns that resemble one another at all scales. LODI Monthly Magazine NOVEMBER EDITION | 2022 PAGE 13 1._____________ 2. _____________ 3. _____________

by rafael maala FRACTALS According to Fractal Foundation, a fractal is a pattern that never ends. Fractals are infinitely intricate patterns that resemble one another at all scales. They are formed by continually repeating a simple technique in a never-ending feedback loop. Fractals are recursive representations of chaotic dynamical systems. The painting Kalabaw (water buffalo) in "The Philippine Village Life" by Vicente Silva Manansala depicts indigenous subjects in the farmlands, where the Kalabaw is also used as a plowing device in farming. In terms of fractals, the painting depicts a neverending pattern in the vertical line of the grass, followed by the wavy lines of the farmlands, and finally, the pattern of Kalabaw. LODI Monthly Magazine NOVEMBER Edition | 2022 page 14 Another work by Manansala is the Harana, which depicts the traditional form of courtship in which a man serenades a woman. The artwork is another example of fractals, there were patterns in the color palette that shows synthetic cubism, which is characterized by brighter colors, and transparent cubism, which also includes patterns of shapes imposed.

Fractals can be found in nature that we are unaware of, such as trees and leaves, and lightning in the clouds (Internal, 2020). In relation to Vicente Silva Manansala's artwork, it produced a pattern known as Fractals through the use of colors and painting tools. We need to learn the connection of mathematics with nature because as we know, math is everywhere in the things we see, in nature, through art, and in the objects that we create and use. According to Landow (2020), he discussed that sometimes the concepts, the outcomes, or the explanations are where the beauty and delight of arithmetic lies. Other times, it's the thoughts that turn your mind in pleasant directions, the feelings you experience, or simply going with the flow—like losing yourself in a good book. Why do you need to learn the connection of mathematics with our nature? LODI Monthly Magazine november Edition | 2022 page 15

L O D I L O D I P U B L I S H I N G H O U S E REFERENCES november Edition | 2022 page 16 NOVEMBER 202 2 Journals: BAYUG, J. (2022). The Impact of Mathematics in Shaping the Understanding of Nature and Humanity. International Journal of Arts, Sciences and Education, 3(2 June Issue), 165-178. https://www.ijase.org/index.php/ijase/article/view/134 Website: What are Fractals? – Fractal Foundation. (n.d.). https://fractalfoundation.org/resources/what-are-fractals/ What is a fractal? - the ultimate guide to understanding fractals. Iternal Technologies. (2020, September 24). https://iternal.us/what-is-a-fractal/ Fisher, L. (2022). Geometric Shapes in Nature. Study.com. https://study.com/learn/lesson/geomety-in-nature-shapes-types examples.html#:~:text=These%20shapes%20include%20circles%2C%20squar es,ears%2C%20noses%2C%20and%20teeth. Memije-Cruz, L. (2018, June 20). The Nature of Mathematics. Share and Discover Knowledge on SlideShare. https://www.slideshare.net/memijecruz/the-nature-of-mathematics102702376 Landow, S. (2020, May 20). The mystique of mathematics: 5 beautiful math phenomena. Phys.org. https://phys.org/news/2020-05-mystiquemathematics-beautiful-math-phenomena.html Cleveland, J. (2020, November 19). The nature of design: The Fibonacci sequence and the golden ratio. Cleveland Design. https://clevelanddesign.com/insights/the-nature-of-design-the-fibonaccisequence-and-the-golden-ratio/? fbclid=IwAR0tt5xfDWvlcAtLVNAhXQNCb08FzNJXzaH8CPRZKvwf_wNEC9P5- 7jqjI Sheldon, R. (2022, May 6). What is the Fibonacci sequence and how does it work? WhatIs.com. https://www.techtarget.com/whatis/definition/Fibonaccisequence? fbclid=IwAR2IGTiJ1h2Z58iAj7vkRI66D0otrHBHdir1vR9rdb3TtDkX_KSgBDm0U Shapes – definition with examples. SplashLearn. (2022, September 2). https://www.splashlearn.com/math-vocabulary/geometry/shape? fbclid=IwAR01F5g1Q4BLTQyqjHHsD7ja_p4pemlvOgJRp0W0ExBMvtg_7jqf7iSS G8

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