Pythagoras or Pythagoras of Samos (c. 570 – 480 BC) was a Greek philosopher, mathematician, and scientist. Little is known about his personal life, but he is famous for founding the Pythagorean school, which introduced numbers and mathematics as the fundamental principles for understanding the world.
Due to the unknown details of his personal life, Pythagoras is often regarded as a mythical figure in Greek culture. He spent a considerable amount of time on educational travels, during which he became familiar with various schools of thought, such as the school of philosophers in Miletus and the school of Italian philosophers. He also traveled to Egypt and Babylon, where he received instruction from the great scholars and scientists of those regions. In addition to his philosophical and religious studies, he was interested in researching and studying mathematics and natural sciences. He was particularly interested in investigating whole numbers and their relationships, and he sought to discover the hidden mathematical laws governing the natural world.
The Pythagorean school, with its emphasis on the importance of numbers and mathematics for understanding the world and existence, had a significant influence on the history of philosophy and mathematics. Some of Pythagoras’ accomplishments include discovering the Pythagorean theorem, discovering the mathematical relationship between the lengths of the sides of a triangle, conducting research on large numbers, and discovering mathematical laws governing the movement of planets and stars. He passed away at approximately 80 years of age in Metapontum, in southern Italy. He is known as one of the prominent scholars of history and had a significant impact on human mathematics and philosophy. In fact, Pythagoras is the same person as Pythagoras. His name is mentioned in some sources as Pythagoras and in others as Pythagoras. The difference in naming is due to differences in pronunciation and spelling of his name in different languages. Pythagoras had a very diverse and extensive philosophy. He was looking for a complete and comprehensive explanation of the world and existence, and was seeking a deeper understanding of reality.
In general, Pythagoras believed that everything in the world is based on numbers and mathematics, and these numbers and mathematical relationships exist in nature and everything around us. Based on this belief, he believed that mathematical methods should be used to understand the world and existence.
Pythagoras also attached great importance to ethics and the effort to achieve authenticity and justice. He believed that to achieve authenticity and justice, humans must help themselves and their community and adhere to ethical principles in all their actions. He also placed great importance on the relationship between music and mathematics and believed that music could help better understand the world. He found formulas for the relationship between music and mathematics and taught them to those around him.
Pythagoras was seeking a complete explanation of the world and existence, and believed that mathematics and numbers could help humans achieve this goal. As one of the greatest ancient mathematicians and philosophers, he had various opinions about science and its concept. He believed that science and mathematics should be based on experience and rational thinking, and should not be based on unscientific or religious perspectives. He believed that to find the truth and better understanding of the world, mathematical and logical methods should be used. He was also interested in topics such as the theory of harmony, the Pythagorean theorem, number theory, and relationships between shapes.
Pythagoras placed great importance on scientific experimentation and experience, and therefore emphasized precise and rigorous experimentation to achieve true knowledge of the world. As a philosopher and mathematician, he was seeking a complete and logical explanation of the world, and believed that science and mathematics should be based on experience and rational thinking.
Pythagoras was very interested in the science of numbers and mathematics, and used them as tools to better understand the world. He valued the number “one” highly and considered it as the foundation for other numbers.
Based on this belief, Pythagoras also attached great importance to the numbers “two” and “three”, and introduced them as the main numbers in number theory. He believed that all natural numbers are derived from the numbers “two” and “three”. He was also interested in the relationships between numbers and shapes, and studied them. He believed that different relative numbers could be associated with specific geometric shapes. For example, triangles are associated with specific geometric shapes, and this relationship between numbers and shapes is known as the theory of harmony.
Pythagoras placed great importance on the science of numbers and mathematics, and was seeking relationships between numbers and shapes and theories to describe these relationships. The theory of harmony or “harmony of numbers” was one of Pythagoras’ fundamental philosophical principles, referring to the existence of a relationship between numbers and shapes in the world. This theory is based on the idea that everything in the world takes shape with scales and proportions of numbers and shapes that can be harmonized like music. Pythagoras believed that the relationship between numbers and shapes could be compared to music. For example, he believed that each musical note is associated with a specific number, and different musical notes are related to different relative numbers.
This relationship between numbers and music is known as the theory of harmony.
The theory of harmony states that everything in the world takes shape with a synchronization and relationship between numbers and shapes. This theory has been of great importance in the history of mathematics and philosophy and has had a significant impact on later thinking in the fields of mathematics and philosophy. The theory of harmony also has applications in philosophy. It expresses that everything in the world takes shape with a synchronization and relationship between numbers and shapes. In philosophy, this theory is used as a fundamental principle for a better understanding of the world and the relationship between all existing things.
For example, some philosophers believe that everything in the world takes shape with a synchronization and balance, and that none of them can exist independently of the other. This theory is based on the idea that only by considering the synchronization and relationship between the different components of the world can we gain a better understanding of the world. The theory of harmony is used in philosophy as a fundamental principle for understanding and interpreting the world and the relationship between all existing things. This theory has been very important in the history of philosophy and has been considered as one of the basic principles in the philosophical thinking of many philosophers over the past centuries.
The theory of harmony is also used as a fundamental principle in many other fields. For example, in natural sciences, the principle of synchronization and the relationship between different components of systems is used as a fundamental principle for explaining the behavior of natural systems. In mathematics, this theory is used as a fundamental principle for describing the relationships between numbers and shapes, as well as in the study of the relationships between numbers and values found in nature. For example, in mathematics, the concept of “equilibrium” in explaining the behavior of dynamic and coordinated systems is used with the help of the principle of the theory of harmony.
The theory of harmony is used as a fundamental principle in philosophy and other sciences and is very valuable as a basic principle for understanding the relationships between different components of systems and interpreting their behavior. One can also use the theory of harmony as a fundamental principle in social sciences. For example, in sociology, the theory of harmony is used as a principle for describing and interpreting the relationships between different components of society. The theory of harmony can be used as a principle for describing and interpreting the relationships between members of a group or organization. In this case, the principle of the theory of harmony means that the members of a group or organization will be more successful in their collaborative activities with coordination and cohesion.
Absolutely, the theory of harmony can also be used to examine the relationships between different social strata in society. For example, this theory can be used as a principle for describing and interpreting the relationships between different social strata. In this case, the principle of the theory of harmony means that with coordination and collaboration between members of different strata, society as a whole will have greater superiority and progress. The theory of harmony can be used as a fundamental principle in social sciences and can be used in describing and interpreting the relationships between different components of society and interpreting the behavior of society. The theory of harmony is used in examining the behavior of society and interpreting it. This theory suggests that all components of a system are interdependent and the behavior of each component of the system can be influenced by the behavior of others. In the case of society, this theory means that individual and group behavior in society is influenced by the behavior of others. For example, an individual’s behavior in society may be influenced by the behavior of others in that society. If the behavior of individuals in society is interdependent and there is coordination and cohesion among them, this can lead to an increase in the harmony of society and a decrease in conflicts and contradictions.
As another example, in the face of social issues such as poverty, unemployment, and crime, individuals and groups within society may work together and coordinate with each other to find solutions to these problems. In this regard, the theory of cohesion can be used as a fundamental principle in describing and interpreting society’s response to social issues. The theory of cohesion is used to examine society’s behavior and its role in creating coordination, solidarity, and reducing conflicts. The theory of cohesion can be used as a fundamental principle in society. For example, in societies where individuals are coordinated with each other and require cooperation, this theory is used as a principle in describing and interpreting society’s response to social issues.
One example of the application of this theory in society can be cooperation and collaboration. In societies where individuals cooperate and collaborate with each other, the likelihood of creating positive relationships between individual’s increases, and as a result, social cohesion increases. For example, in a small town, individuals may work together and cooperate with each other to solve problems such as water and electricity supply, city cleanliness, and other issues. In this regard, the theory of cohesion can be used as a principle in describing and interpreting society’s response to social issues and the role of cooperation and collaboration in increasing social cohesion. The theory of cohesion can be used as a fundamental principle in society and can be employed in describing and interpreting society’s response to social issues and the role of cooperation and collaboration in increasing social cohesion.
Pythagoras was passionate about studying trigonometry, and his most famous theory about trigonometry is the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the sum of the squares of the shorter sides (legs) is equal to the square of the length of the hypotenuse (the longest side).
In other words: $a^2 + b^2 = c^2$
where the longest side (hypotenuse) and the shorter sides (legs) are the sides of the triangle.
This theorem has solved many important mathematical problems and has had a significant impact on the development of mathematics. For example, this theorem can be used in solving geometric problems such as calculating the diameter of a circle, calculating the area of a triangle, and even in physics to calculate some natural phenomena such as the existence of sound and light waves. Although Pythagoras is famous for discovering the Pythagorean theorem, it is likely that this theorem existed prior to him and had been discovered by other individuals as well. However, Pythagoras is known as one of the greatest mathematicians in history because he provided a rigorous proof for this theorem.
The Pythagorean theorem is still used in modern mathematics and is one of the fundamental and most commonly used theorems in mathematics. This theorem is used in many areas of mathematics, including geometry, analysis, physics, and engineering. For example, in geometry, the Pythagorean theorem is used to calculate the diameter of a circle, the area of a triangle, and even in modeling, such as determining the distance between two points in two-dimensional space.
In analysis, the Pythagorean theorem is used as one of the fundamental principles, for example, in calculating the distance between two points in three-dimensional space. Additionally, in physics, this theorem is used as one of the fundamental principles in interpreting and analyzing concepts such as distance, time, and speed. Considering that the Pythagorean theorem is one of the fundamental and most commonly used theorems in mathematics, it is still used and researched in many different fields, and remains an essential topic in mathematics education.
In engineering, the Pythagorean theorem is used as one of the fundamental principles. One practical example of the use of this theorem is in civil engineering and concrete structures. In construction, engineers use the Pythagorean theorem to determine the length of the diagonals of concrete walls and various structures. For example, in the design of various concrete structures such as bridges, towers, buildings, etc., calculations such as calculating the length of the diagonal of the bases and curved bases to determine the precise dimensions of the structure and its safety are done using the Pythagorean theorem.
For example, in the design of concrete foundations for bridges, the precise dimensions of the foundations are crucial. Using the Pythagorean theorem, engineers can calculate the length of the diagonal of the foundations and then use these dimensions to design the concrete foundations. Additionally, the Pythagorean theorem is also used in calculating the size of concrete blocks. The Pythagorean theorem is essential in engineering for calculating the length of the diagonal and precise dimensions of concrete and structural constructions.
Pythagoras had a strong interest in studying geometry and had various opinions in this field. He believed that geometry is one of the most important areas of mathematics and, philosophically speaking, is in harmony with the order and coordination of the heavens and the earth. In Pythagoras’ view, geometric shapes had philosophical and spiritual meanings. He looked at geometric shapes as symbols of philosophical, spiritual, and existential concepts. For example, the triangle as a symbol of the holy trinity, the square as a symbol of the frame of the earth and its harmony with the heavens, and the circle as a symbol of the infinity and the heavens, were highly regarded in the works of Pythagoras and Pythagorean scientists.
Moreover, Pythagoras was one of the first individuals who was deeply interested in numbers and counting. He is known as the father of proper mathematics, as the first person who could express the concept of whole numbers and higher numbers. Pythagoras’ opinions on geometry show that he looked at geometric shapes as symbols of philosophical concepts and gave them real value as a basis for the development of mathematics. Pythagoras believed that geometry is not only one of the important areas of mathematics but also geometric shapes can be used as symbols of philosophical and spiritual concepts.
Pythagoras looked at the triangle as a symbol of the holy trinity, the square as a symbol of the frame of the earth and its harmony with the heavens, and the circle as a symbol of infinity and the heavens. He believed that geometric shapes, in harmony with the order and coordination of the heavens and the earth, have a philosophical meaning. He looked at geometric shapes as symbols of philosophical concepts and gave them value as a basis for the development of mathematics.
In his time, Pythagoras did not pay much attention to economic and managerial issues, and his main focus was on mathematics and philosophy. Therefore, his opinions on economics are rarely found, and we do not know much about his views on this subject.
However, some historians and later philosophers have referred to Pythagoras’ opinions on social organization and resource management. They believed that Pythagoras believed that for balance and harmony in society, a specific political and economic structure should be considered. For example, as the founder of one of the first philosophical communities on the island of Samos, Pythagoras tried to achieve balance and harmony among the members of the community by creating a community with specific principles and regulations.
Although Pythagoras did not directly focus on economic issues, as a philosopher and leader of society, he paid attention to the importance of organization and coordination in society. For example, in his philosophical community, he tried to achieve balance and harmony among the members of the community by creating a specific structure. Pythagoras had a great interest in political and social issues. He believed that for balance and harmony in society, a specific political and social structure should be considered. For example, as the founder of one of the first philosophical communities on the island of Samos, Pythagoras tried to achieve balance and harmony among the members of the community by creating a community with specific principles and regulations.
In general, Pythagoras emphasized the importance of organization and coordination in society. As a philosopher, Pythagoras was looking for solutions to improve the conditions of society. As a leader, he tried to achieve balance and harmony among the members of the community by creating a specific political and social structure. Pythagoras believed that politicians should adhere to their own principles and values in all their decisions and should not succumb to external pressures. He also emphasized the importance of ethical and higher values in politics and believed that politicians should work towards improving living conditions and social development as representatives of society. Therefore, he had a great interest in political and social issues and emphasized the importance of organization and coordination in society. He was looking for solutions to improve the conditions of society and emphasized the importance of ethical and higher values in politics.
In general, Pythagoras paid attention to the economic development of society, but due to the scarcity of resources during his time and the lack of quantitative and qualitative tools for economic analysis, his views on economics have not reached us in detail. As the founder of one of the first philosophical communities on the island of Samos, Pythagoras tried to achieve balance and harmony among the members of the community by creating a society with specific principles and regulations, known as the “Pythagorean community”. This community had principles based on balance and harmony in economic and social relationships. Due to the cultural and educational compatibility of its members, the Pythagorean community was successful in both economic and cultural development.
Pythagoras believed that moral and educational values could help improve the economic conditions of society. He was looking for solutions to improve the conditions of society and emphasized the importance of ethical and higher values in both politics and economics. Therefore, it can be concluded that Pythagoras paid attention to the economic development of society and emphasized the importance of moral and educational values in this field. Pythagoras had a great interest in philosophy and ethics. In general, his views on philosophy and ethics were based on the idea of harmony and balance in the world. One of the important concepts that Pythagoras focused on was the idea of harmony and balance. He believed that all existences, including humans, exist in a harmonious and balancing world. This idea in Pythagorean philosophy is known as “Harmonia”.
Pythagoras also emphasized the importance of ethics and education in life. He believed that ethics and education are very important for achieving harmony and balance in the world. For example, he paid attention to the importance of educating children and believed that proper education of children can improve the conditions of society. He also emphasized the concept of “philautia” or love of self and others. He believed that love for others can improve the social and spiritual conditions of society. Pythagoras emphasized harmony, balance, ethics, education, and love of self and others, and incorporated these concepts into his philosophy and ethics.
Pythagoras also paid attention to religious issues, and for him, religion and philosophy were intertwined. He believed that religion can provide clarity and guidance on the meaning of human existence and the world. One of the important concepts that Pythagoras focused on was the idea of the infinite world. He believed that the world is infinite and its stability is based on the order and law of God. Based on this belief, Pythagoras was looking for a mathematical model to understand the world and contributed to the formation of theories such as the theory of integers and geometry to describe and interpret the world.
Indeed, Pythagoras believed that religious beliefs and rituals can help elevate the human spirit and spirituality. He paid attention to the importance of religious ceremonies and rituals, such as sacrifice and Shamloo ceremonies, and believed that these rituals can help elevate spirituality and develop human perspectives.
It can be said that Pythagoras paid attention to religious issues and believed that religion and philosophy are intertwined. He believed that proper understanding of the world leads to proper understanding of God and religion. Therefore, Pythagoras believed that philosophy and religion complement each other and can help humans achieve a deeper understanding of the world and their place in it.