The Beautiful Nature Of Mathematics
Beauty, as its definition given by Miriam Dictionary, is the quality or aggregate of qualities in a person or thing that gives pleasure to the senses or pleasurably exalts in the mind or spirit. In addition, as Cambridge Dictionary, is the quality of being pleasing, especially to look at, or someone or something that gives great pleasure, especially when you look at it. Lastly the Collins Dictionary, the quality attributed to whatever pleases or satisfies the senses or mind, as by line, color, form, texture, proportion, rhythmic motion, tone, etc., or by behavior, attitude, etc. Then let us go to the subject matter the “Mathematics” according to Britannica Encyclopedia, is the science of structures, order, and relation that have evolved from elemental practices of counting, measuring, and describing the shapes of objects. It also deals with the logical reasoning and quantitative calculation and its development has involved an increasing degree of realization and abstraction of its subject matter that has the substantive branches such as Algebra; Arithmetic; Combinatorics; Combinatorial Geometry; Game Theory; Number Theory; Numerical Analysis; Optimization. And the mathematical theory of Probability Theory; Set Theory; Statistics; and Trigonometry. Then how this two do collide and creates, let us find out.
Let us start with the idea of Fibonacci, Leonardo Fibonacci or also known as Leonardo of Pisa a well-known mathematician mainly because of Fibonacci’s Sequence of Number that derive from his book “Liber Abaci” (1202; Book of Abacus) this is intent to use to guess the reproduction outcome of a pair of rabbits after a year. Then resulting to these 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… respectively (Leonardo himself omitted the first term) in which each number is the sum of the two preceding numbers, is the first recursive number sequence. In addition, within the 19th century Edouard Lucas a France mathematician and scientist begun to discover such a sequence in the nature. Example, the spirals of the sunflower heads, in the pinecones, in the rectangular descent (generalogy) of the male bee, in the related logarithmic (equiangular) spiral in snail shells, in the arrangements of the leaf buds on the steam and even in the animal horns. And being considered as a perfect sequence because no one was able is find a flaws on Fibonacci sequence of number, it is said that anything that has an element of the said sequence is considered beautiful or attractive.
Another example an idea from mathematics that created beauty is the golden ratio. Golden Ratio is Also Known as the Golden Mean. Old Egypt said to use pi (π) to build their pyramids but also uses ( φ). Therefore, to be more specific Golden Ratio is approximately equal to 1.618. In addition, it does have connection with the Fibonacci’s sequence number, if you would notice the quotient of the two consecutive numbers from the sequence equals to the golden mean. Even though the last digits of the quotients are different, the first four digits will be the same. This said ratio used to say that add the attractiveness of an item that containing it. As example, Leonardo De Vinci known as one of the greatest artist of all times but the same time he considered as a great mathematician. His works “The Man in Action” and “Mona-Lisa” considered as one of his greatest works, but unknowingly there is mathematics applied on it. If you draw, lines to produce several rectangles in the figure of “The Man in Action” you were able to produce three golden rectangles below its torso, when we say golden rectangles, rectangles that has the golden ratio as the ratio of its sides. The same with the “Mona-Lisa”, this work of art made an uproar way back years ago because of the its confusing looks, has applied the same concept of golden rectangles to it.
Suerat’s “Bathers”, “Composition with Grey and Light Brown” and “Composition of Red, Yellow, and Blue” by Piet Mondrian also have the golden rectangles. This way mathematics creates beauty. Other than that in the way of architectures, the Ahmes Papyrus of Egypt that built 4700B.C. in Giza and used to classify as one of the Great Pyramid said to use “the secret ratio”. The Parthenon of Greece has applied the characteristic of the golden rectangle, Porch of Maidens, Acropolis, Athens and Chartres Cathedral used the same concept in the construction.
Mathematics creates beauty through arts and architecture, but mathematics is not for those things only it also applies in music. First, what is music? According to Jack David it is a sound that is organized in a meaningful way with a rhythm, which also has the melodies and lastly the harmony. Also according in Merriam Dictionary, it is the science or an art of sequencing the tones or the sounds in finalization and succession, in complementation in the temporal kind of relationships to produce a composition having both unity and continuity. Pythagoras (500B.C.E) it is said that music and mathematics shares an intimate kind of relationship. Mathematics has been a great use to understand the waves of music; tune in the musical tunes; that help the creation of proper and appropriate musical instruments, and to generate the novel music. Rhythms, there are more than 17 trillion different rhythms with 3 levels where in 16 distinct time locations every beat occurs. There are two mathematical principles to trick the small proportion of musical interest and these two is the mathematical principles- well-formness and perfect balance this allows to navigate two distinct rhythmic sub-spaces that are of musically interest. When we say well-formedness is the generalization of the three properties that is commonly found in the real world, the multilevel rhythms. The said rhythmic levels compromise only a small number of distinct beat lengths only one or two’s. Each should beat fairly and well-distributed spaces of time. Lastly, said rhythmic levels are in orders. Many geometrical shapes is associated to the production of music. However, in the end, well make music has followed many mathematical ways and that creates its beauty in music.
Beauty is everywhere and Mathematics is everywhere also that makes these two interconnected into each other.
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