Full transcript of “Mathematics in our World: Mathematics in the modern world (Patterns and Sequence) - Tagalized”. Click a timestamp to open the video at that moment. Need another video? Use the YouTube transcript generator.
0:00 Saan, kailan, at paano ginagamit ang math? I have no idea. Pabubuhay ba tayo ng walang math? No. Kailangan ba talaga natin ito? Saan lupalog ba ito nang galing? Um, I don't know. Ang sabi nga nila, ang math daw, ay mental abuse to human. Hindi po totoo yan. Ang sabi naman ni Papa P, merienda, almusal, kanghalian, at kapunan. Ede wow! Anyway, on this video, we will try to answer this query. On this video, we will try to answer this query and discuss some topics pertaining to patterns like the Pibonacci Sequence, the Golden Ratio, Pesalition, and Fractals. Alamin natin kung anong kinalaman nito sa kapaligiran at sa pang -araw -araw nating
0:45 pamumuhay. Kaya, programales! Ayon sa isang sikat na science writer na si William John Navin Sullivan, Mathematics, as much as music or any other art, is... one of the means by which we rise to a self -consciousness. The significance of mathematics resides precisely in the fact that it is an art. By informing us of the nature of our own minds, it informs us of much that defends on our minds. True to what Sullivan said, ang math ay nasa gitna ng kasaysayan at pag -unlad ng isang kultura. ng kasaysayan at pag
1:32 -unlad ng isang kultura. Makikita natin ito sa mga sinaunang arts, Egyptian architecture and music. Actually, si Papa Pinga, Pitagoras, and na -discovery ang numerical reasons in musical harmony. So strict, di ba? Actually, sa pang -araw -araw na buhay, kasama natin ang man. Akala mo lang wala! Pero meron, meron, meron! Oh! Akala mo lang wala, pero meron. May tinatawag na tayong body clock. Yung usual na oras ng gising. Kain mo, tulog mo, at pag... O tulog mo kapag inagaman niya. Na kung saan, our body reacted to the usual routine. Mathematically. Kapag nagwawaldas ka ng pera. Lalo na kapag pinakirapan, sarap, sarap, sarap. Ang programang ito
2:18 ay rated LPG. Kapag mabili ka sa tindahan, nagpapabayad ka ng pamasahe. Nagpabayad ka ng pamasahe. Kapag matiprediksi pag -aasan ng bagyo. O weather forecast. Kapag pinag -aaralan ng life cycle ng mga animal. Whether for us, kapag pinag -aaralan ng life cycle ng mga animal, animals, ng mga tao, sa mga building construction, magmula sa paghahalo ng semento hanggang sa pinakamalalaki at pinakamabibigat, lahat ng ito ginagamitin ng math. Ang space exploration lalo na, hindi pwedeng siyang balang. Every detail of the plan should be completed accurately and precisely. Otherwise, a slight discalculation sometimes will result to a disaster. Ang cellphone na gamit mo, walang parte niyan ang hindi ginamitan ng... Pag -disaster, ang cellphone na gamit mo, walang parte
3:06 niyan ang hindi ginamita ng math. Ginagawa pa lang tayo, I mean, pagsilang pa lang natin, hanggang mag -atiyowa, mag -asawa, at hanggang makasama na natin si Lord. Through our journey in life, kaakibat natin ang math. Tinutulungan tayo ng math to develop our reasons and logical thinking, analytical thinking, and critical thinking. Ginagamit natin ito to describe patterns and explain phenomenon. Kahit nga sa sports, solving crime, medicine, psychology, social science, political science, etc. Right, medicine, psychology, social science, political science, etc. Ginagamit na rin ng math. Anyway, ang math ay galing sa Greek word na mathema, which, in the ancient Greek language, means that which I learned or lesson in the modern Greek. Ang Tagalog na pala nito, sipnayan. Hango sa salitang, sana yan ng isip.
3:57 Yan ang Tagalog ng mathematics, sipnayan. If you are looking for the exact and concise definition of mathematics, sorry to say, pero wala pa, wala pa. size definition of mathematics sorry to say pero wala pa wala pa although numerous definitions can be found from different texts one of the closest is given by the encyclopedia britannica that is evident in the modern world today according to this mathematics is the science of structure order and relations that has evolved from elemental practices of counting measuring and describing the shapes and characteristics of objects these are the characteristics of mathematics that object. These are the characteristics of mathematics that can be found and explained on this book. By can I man? Because mathematics plays such a central
4:45 role in modern culture, some basic understanding of the nature of mathematics is a requisite for synthetic literacy in the modern world. This figure shows the nature of mathematics. Ngayon naman, magtungo tayo sa mga patterns. The characterization of mathematics as the study of patterns had been first made by British mathematician of patterns had been first made by British mathematician Godfrey Harold Hardy. Sabi niya, a mathematician, like a painter or a poet, is a master of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. Actually, a pattern is a visible regularity in the world or in a man -made design. As such, the element of a pattern repeat in a predictable manner. Let us start with the
5:34 famous Fibonacci sequence. All manner. Let us start with the famous Pibonacci sequence. Nakilala ito sa book ni Leonardo Pesano or Leonardo Otisa, nicknamed Pibonacci, noong 1202. Actually, according to Dr. Kate Devlin, who is also a British mathematician or math historian, the said sequence was established 1 ,000 years before Pibonacci, that is around 200 BC. It was introduced by Pingala of India. Anyway, si Pibonacci naman ang unang shoutout kaya sa kanya ang credit. Ganun talaga. Bonacci naman ang unang shoutout kaya sa kanya ang credit. Ganun talaga. Parang ang Pythagorean theorem kasi Pythagoras ang nauna. Moving on, this sequence was introduced in the book called Liber Abachi, means the book of calculation, where he introduced the Hindu -Arabic numeral system sa mga merchants
6:25 sa Europe noon. Hihirap nga naman mag -compete noon kasi ang gamit pa nila is Roman number system. Just imagine, 2 plus 3 equals 5 sa Hindu -Arabic. Pero sa Roman numeral, 2 plus 3 is this one. Medyo okay rin pa ito kasi maliit. Pero sa Roman numeral, 2 plus 3 is this 1. Medyo karyo pa ito kasi maliit. Eh, paano na kapag medyo malaki na, tsaka multiplication. Example, 15 times 11, 155. Pero kapag ka Roman numeral, kayo na bahala. Itong nasabing sequence na ito ay isa sa mga problem sa library abachi ni Fibonacci. Ito yung rabbit problem. And it goes like this. A man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits On all sides by a wall. How many pairs of rabbits are produced from
7:13 that pair in a year if it is supposed that every month, each pair produces a new pair which from the second month onwards becomes productive? At the start, we have a pair of young rabbits, male and female. After a month, when they are fully grown up, they are capable of yabbing -yabbing. Again, pagkatapos iling isang buwan, manganak yung old rabbits at the same time, lalaki na yung dalawang rabbits Manganganak yung old rabbit at the same time, lalaki na yung dalawang rabbit at Again, again, again, after a month, lalaki na yung dalawang pair of rabbits at manganak na rin ng another set of pair of rabbits. So, lima na silang lahat. Similarly, as months goes by, ganito lagi ang kwento. Lalaki, digdugan, mga nganak.
8:01 So, after 5 months, 8 na yung pair of rabbits. Kapag tin -rate nyo to hanggang 12 months, 144 na silang lahat. 12 months, 144 na silang lahat na pair of rabbits. At mapapansin nyo, yung number of rabbits per month based on the assumption of the problem is 1, 1, 2, 3, 5, which is the Fibonacci sequence. Dahil dito, naging popular tong sequence na to. At, officially, ang nagpangalan ng Fibonacci sequence ay si François -Edouard Lucas, a French mathematician. Saan saan bang lupalop makikita to? Umpisahan natin sa sunflower at sa pineapple. Alam nyo ba, ng number Umpisahan natin sa sunflower at sa pineapple. Alam nyo ba na ang number of spiral ng sunflower ay mga Fibonacci numbers? Ganon din dito sa pineapple. Kapag
8:50 binilang natin yung mga mata nila, by following the spiral path, ay Fibonacci numbers din. Sa iba't ibang purutas, makikita din natin ito. Ang dami ng mga puto nila. Etcetera, makikita din natin itong Fibonacci numbers. Geometrically, in terms of square and a quarter circle, matitrace natin yung tinatawag na Fibonacci spiral. Ganito ay tura nun. Na kung saan, yung spiral na ito ay makikita natin sa iba't ibang bagay. mula sa pinakamaliliit hanggang sa pinakamalalaki. Furthermore, nagderive si Philip Binet ng formula for the Fibonacci sequence and he come up with this one. Na kung saan, mag -determine natin kahit gaano kalaki yung Fibonacci numbers. Kailangan lang natin yung n, kumpang ilan. Furthermore, if you get the ratio of the succeeding numbers
9:38 of the Fibonacci sequence, it approaches the golden ratio. Of the Fibonacci sequence, it approaches the golden ratio, 1 .61 etc. Denoted by P, like this one, the golden ratio. Actually, hindi lang naman ito yung pakunta ng golden ratio. Check the Lucas numbers. Eh, ano ba itong golden ratio na ito? Let us consider this line segment with length A plus B, where A is greater than B. Kung saan, yung ratio ng longer segment A sa smaller segment na B ay equal sa ratio ng sum ng A and B over A. The Z ratio is denoted by T. Since na si A and B are variables and dependent of each other, we may let one of these variables equals to
10:26 1. Say, T equals 1. Then substitute, we come up with this quadratic equation. And using the quadratic formula, we will get two possible results. Siyempre, yung positive mga kukuni natin, we will end up with this. Ito yung tinatawag natin na golden ratio. It is approximately 1 .618. That is also known as the which is approximately 1 .618 that is also known as the Divine Proportion. Sinasabing may kinalaman ang Golden Ratio at Tibonacci Numbers sa universe na ginagalawan natin. Makikita natin ito sa mga halaman, rutas, puno, hayop, tao, construction, biografiya, at kalawakan. Kahit nga sa ibang pelikula, ginagamit ito. Sa mga cinematography, hinihinala kasing maganda at kaaya -aya sa paningin ng tao kapag may kinalaman ang mga sukat sa Golden Ratio. sa
11:14 mga logo. Kapag may kinalaman ang mga sukat sa Golden Ratio sa mga logo, gaya ng National Geographic, Apple, Toyota, Pepsi, Google, Twitter, Chevron, ilan lang to sa gumagamit ng Golden Ratio. Kahit may ang katawan ng tao, sinasabing kaaya -aya sa paningin. Kumbaga, nagdagwapuhan at nagagandahan. Dila lang, kapag ang pagkakahulma ng muka at katawan ay approximately closer or equal to the Golden Ratio. Ang famous painting ni Da Vinci na Mona Lisa, sinasabing sukat ang bawat proportion sa Golden Ratio. na Mona Lisa, sinasabing sukat ang bawat proportion sa Golden Ratio. Since wala naman talaga tayong basihan ng maganda at it is most likely subjective, siguro one way to explain it is through the Golden Ratio. Kaya karamihan ng magaganda sa paningin ng tao ay ina -associate sa Golden Ratio. In addition, the proportion of man as described by
12:04 Da Vinci, based on the work of architect Vertubius, through the Betrubian man, Betrubius had shown a man in two superimposed positions, with his arms and legs apart and scribed. whose position, with his arms and legs apart, inscribed in the circle and square. Itong drawing na to is sometimes called the Canon of Proportion. Makikita to sa venice. In a nutshell, sinasabi dito na ang different parts of an ideal body should be or somehow proportion to the other parts of the body. Even in music, makikita natin ang Golden Ratio at Tibonacci Numbers. Ito yung tinatawag nilang five moments. Baka naman isipin nyo may kasamang calculator ng mga composer habang gumagawa ng kanta. I doubt it kung meron. Habang gumagawa ng kanta, I doubt it kung meron. Ito ay parang naka
12:51 -embed na sa atin, naka -program. Parang it is written in our biology. Aside from the golden ratio and the Pibonacci numbers, makikita rin natin sa kapilgiran ang tinatawag nating fractals. Ano bang fractals? In mathematics, a fractal is a self -similar subset of Euclidean space whose fractal dimension exceeds its topological dimension. This fractal dimension exceeds its topological dimension. Kung baga, makikita natin yung kabuuan sa bawat party niya. Weird na no? Never -ending patterns. Para mas maintindihan natin ito, tingnan natin ang famous na Mandelbrot set. As you can see, even how many times we magnify this figure,
13:39 lagi lang natin makikita yung kabuuan. Kagaya ng Serfensky triangle, ganun din. Never -ending patterns. Parang may salamin sa harap mo at likod na kung saan Never Ending Patterns Parang may salamin sa harap mo at likod na kung saan nakikita mo yung sarili mo sa loob ng salamin ng paulit -ulit Fractal In nature, katulad ng Fibonacci numbers at golden ratio, makikita rin natin to kagaya ng fern Makikita natin dito na yung bawat dahon ay may maliliit na dahon na kawangis nung malalaki Ganon din tong Romanesco broccoli at marami pang iba sa kapaligiran Ang Cox snowflakes Pwede natin gawin to by drawing an equilateral triangle then create a triangle Hindi natin gawin ito by drawing an equilateral triangle, then create a triangle on each side,
14:27 and new triangle on each side, so on and so forth. Dito makikita natin na ang perimeter ay palaki ng palaki, approaching infinity. Pero ang area niya naman ay hindi. Kasi kapag nag -circumcribe tayo ng circle dito, with fixed area, pasok siya. Weird, no? Infinite perimeter with limited area. Parang load, unlimited text, pero one day lang. Actually, one of the first one day lang. Actually, one of the first application of fractals is sa wireless communication through antenna that has something to do with the repeated wavelengths of signal. Another pattern that is usually seen on nature and arts is the so -called tessellation or tiling.
15:14 Ito yung pag -a -arrange ng mga shapes or objects that is closely fitted together gaya ng sa pineapple. completed together, gaya ng sa pineapple, especially of polygons, in a repeated pattern without gaps or overlapping. Other patterns that can be found in nature are symmetry and radial symmetry. There are many patterns that exist in different platforms. Human mind are somewhat programmed to find, solve, and analyze these patterns. For instance, what is the next term in the sequence 2, 4 8 6 3 5? 10, 8, 4 Sige nga, 5 seconds, or pause mo na lang, or antay mo
16:01 na lang, sasagot ang ko rin naman to Kung napapansin nyo, hindi pa tapos yung 5 seconds Observe that, from 2, plus 2, we get 4 Times 2, we get 8 Minus 2, we get 6 Divided by 2, we get 3 Ngayon, ulitin lang natin Plus 2, we get 5 Times 2, we get 10 Minus 4, we get 8 2, we get 5, times 2, we get 10, minus 2, we get 8, divided by 2, we get 4. So again, plus 2, so obviously, we get 6. What should be the next term in this sequence? Pili lang kayo, A, B, C, or D. So if you observe, if we're going to retreat 8, mas maganda kung dito tayo mag -uupisa. Pabalik, then makikita natin, we get letter B. Kung gusto nyo mag -relax, mag -explore,
16:50 enjoy life to the fullest, find the rule on these patterns. Enjoy life to the fullest, find the rule on these patterns, and find what's next, okay? Salamat sa pagkatsaga at umabot kayo hanggang dito. Napala, shoutout sa Pogging Pogi kong Pamangki. Lamin na ako sinukamukhaan ko. At, sabay ako, nakonti na lang, kamukha ko na. Mahina, mahina, mahina! at sa mga nagagandahan at ang pagwapuhan kong mga estudyante mag -iingat kayo palagi and stay safe and please don't forget to subscribe and hit the notification bell para lagi
17:39 kong updated sa mga i -upload ko na video and once again thank you for watching if you have any questions, clarification, suggestion don't hesitate to comment I will respond to the best of my ability keep safe and God bless Mama Chukuk
