The mathematical beauty

The direct connection between design and mathematics

“What will I do with this life?”
For almost every high school student or student in the Faculty of Exact Sciences, this thought crossed his mind. For every student who has experienced frustration at mathematics studies at school and for every student who has had to break his teeth in order to pass the various math tests, this question has been questioned. So true, dealing with numbers can be boring, not fun and something that does not seem to come with pleasure. But that’s how it is in every field, even a book can be boring, even a movie can be frustrating and a football game can be a big disappointment. The main thing is that mathematics is an area that we are all influenced by, whether we like it or not. Everything in the universe is cataloged quantitatively and in cosmological aspects, things that are extraterrestrial are also mathematically related and affected.

In mathematics, it is very important to approach the correct pedagogical teaching and teaching, because it is all about how the messages are transmitted. The teacher is the emissary and, by virtue of his position, he is required to translate and make available the material in the most appropriate way. In recent years the Ministry of Education has embarked on an important reform known as “Giving Five” ( Which was led by Minister of Education Naftali Bennett, through the establishment of a mathematics council in which senior members of the Ministry of Education, mathematics teachers and other figures such as the author of the textbooks Yoel Geva, the 2005 Nobel laureate in game theory and economics Prof. Israel Aumann, together with former President Shimon Peres and heads of high-tech companies in the State of Israel, aimed at doubling the number of students taking the matriculation exam at the level of 5 credits in mathematics within four years to about 18,000 students per year Bennett reached an agreement with the heads of the universities to increase the bonus by enrolling students with 5 units in adulthood to 30. The cost of the reform was NIS 75 million and was one of the five goals set by Minister of Education Bennett at the Ministry of Education, Who is in charge of Druze and Circassian education, will see the fruits of this move in a few years’ time, which will increase in the various technological industries, since most of the manpower lacking in this field is engineering and the high-tech industry needs quality manpower.


Even if some of us have no affinity for formulas, vectors or logarithms, we are all influenced by this, whether it is in the various uses we make of electronic devices or whether it is in the philosophical plane, which is the plane through which Gd speaks to the universe. In both senses, our entire reality is necessarily influenced by numbers.

All the electronics and digital industries known as hi-tech and lutek have accumulated a great deal of mathematical knowledge over the course of thousands of years, which is becoming increasingly sophisticated over time, utilizing the physical forces and laws that characterize them.

Therefore, there is much to do with mathematics in life and the important task is to learn to love it, even in the practical aspect, that is, to implement it in products of value and aesthetics, that is, in the visual appearance of things.

Aesthetics is a branch found in the field of philosophy and deals with the question of beauty and its characterization. The goal of aesthetics is to examine the role of beauty in the creation of art and what are the ways to create beauty. Discussions about aesthetics can be found in antiquity in Plato’s writings, but the field of academia only entered the 19th century, which only then became a defined discipline.

The understanding of the term “aesthetic” is seemingly simple, but contains quite a few obstacles in the way, since in the present era a number of boundaries have been breached. The definition of what is beautiful or not is perceived as an individual experience and thus loses the chance to define beauty as a universal thing, since not every individual really understands the mathematical nuances that are influenced by aesthetics and without a clear mathematical distinction.


In the study of art history, a distinction is made between the realm of aesthetics and the realm of art theory by discussing the beauty of artistic work in isolation from the social and environmental reality that surrounds it and which has influenced it. In addition, there is a distinction between the esthetician’s occupation from the stage of creation itself to the stage of its absorption by man, as if it were a pure object that is cut off from the environment and devoid of any social or environmental connections. There are different views that link aesthetics to the philosophy of morality that share this approach, while the field of hermeneutics, which began in the 15th century, developed as a methodology for the study and correct analysis of the Bible. At the same time, the Hermeneutics also developed in various fields, such as in the field of law and in the field of classical writings that can be found in literature, ancient philosophy, philosophy and more.

One who conceived Hermeneutics as a field of general knowledge was the philosopher and religious thinker and German Friedrich Schliermacher, who showed that the analysis and interpretation of texts, of any field, required a different and unique way of thinking. In his approach, the purpose of each interpretation is to reconstruct the writer’s experience, so that the interpreter aspires to re-experience his world through the text that mediates with him. After Schleiermacher’s time, the field of hermeneutics expanded from dealing with texts to dealing with a variety of human behaviors and their research, including art and multimedia.

Those who support Schliermacher’s approach argue that by interpreting the texts and the people who wrote them, it is possible to reveal things about the social contexts and backgrounds in which they were created, as well as the experiences of the writers. However, it is important to emphasize that this is a subjective view, and it is impossible to scientifically prove the various interpretations, there is no basis for this, and everything is based solely on personal interpretation and conjecture.


So how is the realm of hermeneutics related to aesthetics?
Aesthetics is a philosophical discipline close to the philosophy of art and philosophic foundations dealing with beauty and related to the senses of man. The basic feature of aesthetics is what is called “beautiful” and its definition is anything that is widely absorbed by the senses. The aesthetic experience that makes enjoyment by looking at art or nature is an interest that comes from its visual elements, without deconstructing the work on its various causes, its function, its essence and the various functions it serves.

Alexander Gottlieb Baumgarten was a German philosopher and created the term aesthetics, as a science of absorbing the senses. Baumgarten called aesthetics as the science of sensory recognition, which is characterized by a cognitive mechanism called unifying art, or even unifying ability, in contrast to the separative capacity of science called analysis, and its function to intuitively translate complex complex sensations into a simple, uniform image. In this process of esthetic separation we find an image that has a kind of simple perfection, which is intuitively perceived by our senses rather than by our intellect, that is, we feel it.

The realm of aesthetics raises another question: Does this object look beautiful or taste that feels delicious is subjective, depends on a subject, or is it objective, depending on an object? There are those who claim that the origin of the aesthetic experience is in the consciousness of the individual who experiences it and we experience it through the eyes and therefore it is an experience of the individual person. But there are those who claim that the source of the aesthetic experience lies in the object itself, that is, it has a well-defined aesthetic characteristics in which the individual is able to discern.

If so, there is much to do with mathematics in life and especially in aesthetics, since it is possible to study the properties of the work and quantify it. But in order to learn to love it, there is a need not only for usability, which means that it will be accessible and adaptable in our lives, but also an aesthetic value.
Of course, it is not enough just to present an aesthetic presentation and to design formulas that are perceived as experiential to the viewer, but much depends on how the audience is presented. As evidence, there is a new book called Mathematics and Art: A Cultural History by historian Lynn Gammwell, who explores the use of mathematics by various artists to create their own works. “Throughout history scientists have discovered mathematical patterns in nature and creative minds of inventors have made these patterns useful, While creative minds of artists have seen the beauty hidden in these patterns and translated them into aesthetic works.”


Mathematics has an abstract nature and therefore it is not easy to recognize its beauty wherever it hides. To visually understand the beauty of the mathematics and its aesthetic context, I collected three videos that translate and access mathematical information from three different angles and how this beauty appears in our lives:

1) Beauty in three dimensions –
In the first video ( you can see the math appear on three planes at the same time, when a trivial phenomenon appears on the right side of the screen, in the middle is a graphic animation that describes the phenomenon and on the left is the mathematical expression that describes the phenomenon. With this visual illustration, you can understand the forces that work on the wings while we sit in the plane, the rules of optics that allow the use of magnifying glass, the growth patterns of trees, the chemistry of coffee, the dice in the game of backgammon, the formation of snowflakes when They appear in the winter, the decibels of different noises that are created in different places and so on. This video gives the most beautiful answer to the question “What will I do with this in life?”.

2) Arabesque-
In the second video ( you can see the most important branch of mathematics and geometry. The science of geometry deals with shapes and spaces and constitutes one of the most important building blocks of the art field. Through this video you can understand how angles’ games become artworks and how symmetry becomes an engineering and aesthetic marvel. The video is presented so that each part begins with a mathematical representation of an angle and shape that takes shape and turns into beautiful arabesques and beautiful works of art.

3) The Pascal-
The third video ( shows a remarkable example of the natural formation of mathematics that appears in the Pascal triangle. The video presents a short animation from Ed-TED in which the secrets of the triangle are revealed, when it is actually an exemplary mathematical organization of numbers. The animation shows how the different lines meet the rules of mathematics and how the connection of the diagonals creates three-dimensional shapes. In addition, the animation presents the various uses of the triangle in everyday life and how one can calculate the chance of bringing a son or daughter to the world.
It is possible to scientifically prove the beauty of nature and the aesthetics that exist in it by means of numbers, that is, by means of mathematical expressions. Through geometry, which is the basis of all human engineering capabilities, the same works that have brought humanity to glorious achievements such as architectural works, spacecraft, nanotechnology and many other inventions can be understood as products of numbers and shapes. Throughout human history, attempts have been made to trace the first to discover geometry and to have different arguments. But when we go to the most elementary source of geometry, we discover that it existed before man, in nature.


Geometric relationships and mathematical series are exemplary in the animal, vegetative and inanimate worlds in countless forms and colors, and the prominent examples in which the filmmaker Cristóbal Vila ( became a short animated video called NATURE BY NUMBERS (

Villa presents in the video four geometric elements that are expressed in different places in nature: Fibonacci series, Golden Ratio, Trinity of Delony and the Voronoy diagram. This is a partial list of elements in nature that evolve according to the mathematical validity of some of these expressions, which include the branching of the branches in the tree, the arrangement of the leaves on a stalk, the pattern of the pineal scales, the flowering of the artichoke, the arrangement of the seeds in the sunflower flower and even the genealogy of bees. On his Web site (…/nbyn_htm/about_index.htm) Villa expands the explanations about the geometric relationships and mathematical series that are expressed in nature and superficially presents the theory behind the film.

In the beginning Villa presents how the series of numbers represents basic geometric shapes in a visual and simple way to understand, and then how rectangles and spirals are cast into patterns in nature such as shells, flowers, dragonfly wings and eyes. In every transition from one natural pattern to another we see the mathematical expression that describes the transition and shed light on the special relationship that exists between all the factors.

The video is a personal project of a villa aimed at providing an artistic interpretation of the legality that exists in nature as well as the contexts of the mathematical expressions that express it. For this reason, Villa does not claim scientific accuracy and points out that with a little creative freedom he acted in specific cases to complete the work in an artistic and accessible way to the audience. There is no doubt that his work represents an amazing phenomenon that exists in the universe and scientific proof in countless opportunities, since large parts of nature are based on symmetrical legality, which we humans attribute to it a considerable aesthetic value. In summary, mathematics and geometry are a large part of what makes nature so beautiful, and that is, in fact, the direct connection between design and mathematics.

What need to be proved (from geometry).


Credits: Eterea Estudios Kentucky Department of Education נפתלי בנט – Naftali Bennett משרד החינוך

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