Leonardo da Vinci
Leonardo da Vinci and Mathematics
The historic figure of Leonardo da Vinci is impossible to underestimate. His genius comprises of a great variety of talents which show his incredible expertise in such areas of human knowledge and activity as painting, biology, chemistry, physics, philosophy, and mathematics. The phenomenon of Leonardo da Vinci was out of the blue for the time he lived and still it is the most versatile and profound figure for the contemporary people.
Leonardo da Vinci is known to live in the epoch of Renaissance. He was born in Ankiano in 1452, near the village which was called Vinci. His father was a notary. In 1469 he moved to Florence. The first teacher of Leonardo was Andrea Verrocchio. However, the tendency in art and in outlooks which had been proper to his teacher were not inherited by da Vinci. The figure of the angel in the painting "Baptism" already clearly demonstrates the difference in the perception of the world artists of the past and a new era of pores: no frontal flatness of Verrocchio, the finest cut-off and volume and unusual way of spirituality.
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In accordance with Leonardo, the art has always been a science. Performing any sort of art meant to make scientific calculations, observations and experiments. The connection the art has with optics and physics, anatomy and mathematics used to force and contributed to a great extent to the fact that Leonardo once decided to become a scientist. In his case, often, a scientist pushes the artist.
In terms of mathematics, da Vinci especially highly valued this science. He believed that there is purely no reliability in those sciences where it is not possible to apply any mathematical disciplines. Mathematical sciences possess, in his words, the highest reliability. Mathematics for Leonardo served as an empirical discipline. It is a well known fact that Leonardo da Vinci was an inventor of many devices designed for solving mathematical problems (proportional compass, the device for drawing the parabola, the instrument for the construction of a parabolic mirror, etc.).
Mathematics which Leonardo da Vinci has contributed to was a constant. Regardless of the fact that it, certainly, could not master the complex problems of motion. The simplicity of the mathematical apparatus and complexity of the tasks for which he undertook in physics and technology, in some cases, forced him to replace the mathematics observations by measurements. This used to lead to the invention of the numerous devices devices.
Da Vinci adored mathematics and regarded it as the only science which contains its own proof. The matter of mathematics comprised of, primarily the geometry and the laws of proportion, as he believed. It attracted only what can be seen; abstraction associated with the modern analysis and mathematics did not represent any interest for him.
In his mathematical experiments, Leonardo da Vinci made a number of successful attempts in order to define the sliding friction factors. In addition to this, he used to investigate the nature and conditions of the resistance of materials, and observed the hydraulics modeling. Other areas of science which represented an incredible interest for Leonardo da Vinci were acoustics, anatomy, astronomy, cartography, botany, geology, hydraulics, aeronautics, optics, mechanics, construction of weapons, civil and military construction and urban planning.
Through the prism of mathematical knowledge, Leonardo obtained a better perspective of paintings and could understand the world in a more profound way. Mathematics has been a loyal and reliable helper throughout of the period of his life. It helped him to reach such heights of art and science, which ordinary people of that time only can dream of. Combining science and creativity, having both logical and artistic thinking, Leonardo spent his life for scholar researches uniting them tightly with the fine arts.
At the courtyard of Milan, Leonardo used to work as an artist, scientist, technician, inventor, mathematician and anatomist. In accordance with Leonardo, art and science existed inseparably. Performing any form of art, he did scientific research, experiments, and observations. By the fact of close interconnection of art and mathematics, he could come across in the field of optics and physics, while the problems of proportions helped him succeed in anatomy.
One of the biggest innovations of da Vinci which has penetrated the world of mathematics was the introduction of two important signs: plus (+) and minus (-). This scientific results had led to a number of the further developments and discoveries. This fact was determined by the tight connection between mathematics and other science. Thus, it helped physics and chemistry develop into the the magnificent level we are currently can observe.
Being an incredible specialist in mathematics and mechanics, he was the first who expounded the theory of the forces acting on the lever in an indirect way. The numerous investigations in the field of astronomy and the great discoveries of Columbus brought Leonardo to the idea of rotating nature of the planet.
Being passioned about mathematics and measurements, Leonardo da Vinci invented the camera obscura, conducted hydraulic tests, brought the law of falling bodies and the motion on an inclined plane. Already some of these achievements would have been enough to consider Leonardo da Vinci is a remarkable historic figure.
Leonardo da Vinci was known to have enriched the world of the Renaissance period by the idea of the value of science: mathematics and science. The aesthetic interests as well as art and any other area of life, in his opinion had to be subordinate to the research and mathematics.
Mathematics had always been at the center of his scientific structures. He used to apply mathematics into various science, such as, for instance, biology and anatomy. He had a conviction that no human study can claim the title of true science if it does not use mathematical proofs. Da Vinci believed that there was no authenticity, where the application of one of the mathematical sciences is produced, or where the science, not related to math, is applied. While his active work, he used to have his notebooks filled with mathematical formulas and calculations. The role he played in mathematics throughout the centuries can be thought to triumph even the mathematical methods in the works of Galileo.
Thus, Leonardo da Vinci's extraordinary and multi-talented skills caused amazement and admiration of his contemporaries, who found him as a living embodiment of the ideal and harmoniously developed man. In all his endeavors, he was an explorer and a discoverer, and it had had a direct impact upon his art. He left a few works, but each of them was a milestone in the history of culture. The scientist had been also known as a versatile scholar. The scale and the unique talent of Leonardo da Vinci's drawings allow us judging his place and significance for the history, where he occupies one of the places of honor.
The drawings of Leonardo da Vinci, his sketches and diagrams are inextricably linked not only with the exact sciences. Leonardo da Vinci had made a contribution to the numerous discoveries appearance, projects and experimental research in mathematics, mechanics, and other sciences. The art of Leonardo da Vinci, his scientific and theoretical researches, the uniqueness of his personality went through the whole history of the world of culture and science, having produced a huge impact over it.
Relativity in Mathematics
All the possible differences between the two numbers, or two units, are identified only by comparing these two numbers, or two units. All the results of comparison are perceived to be relative, since they are dependable on each of the two elements which have been taken as a basis for the comparison. The results of the comparison display various types of symmetries. If symmetry is taken as a basis point of 'zero', the result is the mirror symmetry. If symmetry is taken as a basis point of the 'unit,' it has a tendency to result in a reverse symmetry. To measure the units of corners, the reverse symmetry is transformed into a perpendicular symmetry, which has values of trigonometric functions.
Comparing any of two numbers is not possible without a common base, which acts as a unit of measurement. In order to locate any of the numbers in ascending order in modern mathematics it is usual to use such notations as binary, ternary, octal, decimal, hexadecimal, and others. Comparing the two numbers with different bases is not possible without bringing them to a common base. It is also necessary to mention that the comparison of the two numbers in the different units becomes possible when using a third unit which is one of the number system, for example, decimal.
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