In human history, one imposing figure that has left an indelible mark is that of Pythagoras. He was an ancient Greek mathematician, philosopher, and mystic who was revered for his intellectual and spiritual teachings.

Not only the development of math but also the areas of metaphysics were great and influential contributions of Pythagoras.

Pythagoras was an Ionian Philosopher and a brilliant mathematician. He was born in the 6th Century BC on the Greek island of Samos. He had followers called Pythagoreans who were either the Mathematekoi learners or the Akousmatics listeners.

He was one of the most important mathematicians who believed that everything could be reduced to numbers that had their characteristics. Pythagoras contribution to mathematics cannot be ignored. He also considered Geometry to be the highest form of mathematical study because through Geometry he can explain the real world.

So let us now have a look at some of contribution of Pythagoras in mathematics:

1) He discovered that in music, by beating strings tones are produced which are in a certain ratio and can be represented in whole numbers. This observation was extended to other musical instruments and hence, he was the one to open the gate of the musical world to us.

2) The Angle Sum Property Of Triangle was discovered by Pythagoras only when he proved that the sum of all angles of a triangle is equal to 180.

3) He even contributed to the discovery of Tetractys which was a mathematical magic pyramid.

4) His contributions were not limited only to triangles rather he also contributed to the Polygon Angles where he stated that the sum of interior angles n is 2n- 4 right angles and the sum of exterior angles will be equal to 4 right angles, which means 4 right angles subtracted from 2n then adding exterior angles will be equivalent to four right angles or simply 360.

5) Lastly, the most famous contribution for which Pythagoras is popular worldwide is the discovery of the Pythagoras Theorem which applies to all Right Angled Triangle. In the theorem, he stated that the sum of the square of both Base and Height will be equal to the square of Hypotenuse of a Right Angle Triangle. This theory was a massive achievement in his career which even unlocked many treasures of mathematics out of which Trigonometry is the most prominent.

A Piece of Geometric Art: The Pythagorean Theorem

It was his breakthrough in geometry that became the foundation of Pythagoras' stock of fame. Certainly, one of the most unmistakably legendary mathematical discoveries is the Pythagorean theorem. It is a basic theorem that describes the relationship between the sides of a right triangle.

The most powerful example of the Pythagorean theorem is that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

This theorem is the foundation of contemporary math and has many applications in engineering, architecture, and even the design of simple objects.

Pythagoras contribution to mathematics has been the first step for anyone who wants to dig deeper into the amazing field of geometry because of its simplicity. 

Indeed, this theorem is quite significant; however, Pythagoras contribution to mathematics is a lot more than just this theorem.

He and his followers also gave life to the concept that all the numbers could not be represented as ratios of whole numbers by developing the theory of irrational numbers. With this revolutionary approach, we transcended not only the finite but the transmundane as well.

A View of the Cosmos from Pythagoras: Spheres among Harmony

Yet, the contribution of Pythagoras to mathematics was not the only achievement. Cosmology and the study of the heavens comprised the two areas in which his mystical and philosophical concepts had a profound effect on Western thought.

According to Pythagoras' view of the cosmos, the universal concept was the idea of the "harmony of the spheres.". It means that it was believed that the movements of the sun, moon, and planets were subject to the harmonic arrangement of numbers.

In his view, Pythagoras believed that the universe was built from celestial bodies' individual tones, or "music," whose combination produced a cosmic harmony.

Since the first philosophers and scientists emerged, people have been captivated by this deep idea of math rules, which at the same time has this harmonious and enchanting breath of song. Along with showing how the divine and profane worlds are connected, the narrative also suggested a deep and coherent link between them.

Myth, Spirituality, and the Pythagorean Brotherhood

Other than his achievements as a mathematician and astronomer, Pythagoras contribution influenced mysticism and spirituality.

The Pythagorean Brotherhood, the famous philosophical and religious group, consisted of men who went through a rigorous ethic code, worshipped numbers, and assumed reincarnation.

The small society of people who accepted to work in unity in their search of knowledge, love, and spiritual growth was more than just a great school of philosophers.

The fundamental point of the Pythagorean strict system of initiation, study, and lifestyle habits was to purify the soul and to comply with the cosmos, as Pythagorus defined it.

Remarkably, the Pythagorean teachings attributed the revealing powers of numbers to their efforts to uncover the world's true nature. The workers of Pythagoras and his faithful shared the divine principles that had a spiritual and mystical essence that went beyond the mathematical deduction principles.

They thought that nature was woven together from the numbers, and behind every number was some divine property of creation.

In their admiration for the mathematical underpinnings of the universe, the Pythagoreans made significant progress in astronomy, music, and the emerging science of acoustics.

In particular, the inherent mathematical links that govern the harmony of sound were discovered while analysing the mathematical structure of musical intervals.

The Importance of Pythagoras and His Influence on Western Philosophy

The Pythagoras contribution to Western philosophy and culture is enormous. The overwhelming majority of the most important painters, philosophers, and thinkers of all time got fired up by his teachings.

Pythagoras contributions to philosophy, namely the harmony of the spheres, the transmigration of souls, and the role of mathematics, have all remained significant. Well-known philosophers such as Plato and Aristotle employed a great many Pythagorean principles in their analyses of the cosmos and philosophical concepts.

Moreover, Western art and music highly regard the Pythagorean heritage. Countless musicians and composers have been mesmerised by the principle of spherical harmony and the deeper conviction that the cosmic order is reflected in music and numbers to strive for a higher harmonious spiritual satisfaction.

The influence of Pythagoras on science and the science community is tremendous. His contribution to modern knowledge may be traced back to his extraordinary insights into the natural world and the mathematical basis of the universe, as well as to his holistic concept of reality as a single and cohesive whole.

The Pythagorean ideas about the physical world have survived to this day, from the study of acoustics to the fundamental geometry foundations.

A Mathematical and Scientific Factor Of The Pythagorean Triangle

To say that Pythagoras contributed to mathematics and science would be an understatement. His work became the keystone for the majority of the core concepts and principles upon which our perception of the natural order is based.

Besides showing the famous Pythagorean Theorem, Pythagoras and his followers performed outstanding work in the theory of numbers. They were the first people to recognize the existence of irrational numbers, which are values that cannot be expressed as the ratio of two whole numbers. This revolutionary finding opened the door to the investigation of more intricate mathematical relationships by dashing the widespread belief in the existence of a formula for all numbers.

The Pythagoreans observed the Fibonacci series alongside other key number properties and patterns. Their endeavour was to serve as a basis for the scientific understanding of the natural world.

They, after the most laborious study of numerical correlations, laid the foundation for modern algebra, number theory, and the mathematical subdiscipline known by the name "sacred geometry."

Besides mathematics, he was seen as an influence on various fields. Long ago, before modern science, people had a way of thinking about nature called "philosophy of nature." They believed that everything in the universe was connected and worked together like a big system. They thought that this system followed certain rules, like math rules, to keep everything in harmony.

Astronomers and cosmologists now believe that they were influenced by Pythagoras, who was interested in planetary equilibrium. This subject captured and shaped their interest in the cosmos.

Later theorists, as well as more knowledgeable ones such as Galileo and Copernicus, have consequently added to these theories. They have provided us with a better understanding of lunar phases, planetary movements, and a heliocentric solar system.

The Pythagorean principle, too, led to discoveries that were revolutionary in the study of music. In particular, it brought out the mathematical basis for both music and acoustics.

The modern discipline of acoustics was rediscovered by Plato and his circle of students, who, by looking into the numerical congruity present in the musical intervals, revealed the physical quantities of sound waves.

The Influencing Effect of Philosophical and Spiritual Aspects

Last but not least, philosophy and spirituality are among the areas where Pythagoras's influence is everlasting. His doctrine of the soul, the soul's immortality, and the necessity to elevate oneself spiritually and morally will remain crucial for Western thinking and religion for a long time to come.

Contrary to popular Greek theories about the beyond, the Pythagoreans claimed that the soul could be reincarnated or travel to a different body after death.

Plato and other ancient Greek thinkers developed their philosophies in this light, and this later served as the basis for both the religious and spiritual developments of cultures in the East and West.

Pythagoras had a big impact on how people think about living a good life. His teachings emphasised being good and living in harmony with others. He believed that following certain rules could help people achieve inner peace, which he called nirvana.

Pythagoras and his followers believed in self-control and personal growth. They lived by strict rules that included not eating certain foods and avoiding actions like gambling and being sexually immoral.

Pythagoras had a big impact on how people think about the universe, the relationship between religion and science, and the quest to find ultimate truth. His ideas focused on numbers and math as the basis of existence. Other philosophers, like Plato, who was influenced by Pythagoras, also played a major role in shaping Western philosophy. They explored deep questions about the nature of reality and how we can understand it.

Why Pythagoras is Still Important Nowadays

As in our current time, when technology and science are leading the way, Pythagoras's timeless knowledge and views could not be more relevant. His ability to combine mathematics, philosophy, and spirituality to create the complete and consistent concept of reality represents how far mankind can learn and how powerful our minds are.

The relevance of mathematical and scientific examination, the pursuit of truth and growth in person, and the interconnectedness of each single thing in the universe are just some of the echoes in the teachings of Pythagoras. Pythagoras contribution to mathematics still guides us to the complexity of the present world.

By recognising the advanced studies of the ancient Greek scholar, we appreciate the knowledge of the past and prepare for the future when planetary harmony becomes not just an idea but a fundamental concept.

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