History – Euclidean geometry

History – Euclidean geometry

Euclidean geometry

In this article we will see: “Euclidean geometry”, history, the chronicle of human civilization, serves as a window to the past, illuminating the triumphs, struggles, and evolution of societies over millennia. Through the study of historical events, we unravel the complexities of our collective heritage and gain insight into the forces shaping our present and future.

Summary : History – Euclidean geometry

In the bustling city of Alexandria, amidst a fervent pursuit of practical knowledge, scholars and philosophers alike sought to unravel the mysteries of the universe. From Euclid’s geometric treatises to Archimedes’ ingenious discoveries, each contribution illuminated the boundless potential of human intellect.

As students pondered the cosmos, artisans crafted marvels, and explorers ventured into the unknown, a vibrant tapestry of innovation and curiosity adorned the ancient world. In this epoch of enlightenment, the quest for understanding transcended boundaries, paving the way for unprecedented advancements and shaping the course of history.

History – Euclidean geometry

In expanding Alexandria, people were intensely interested in practical matters such as weights and measures, currency, numbers, and shapes. Students at the Museum pondered over these even in their dreams. They were all young scholars in the making, practical boys whose teachers, through equally practical methods, sought answers to the most challenging questions. They wondered, for instance, “How big is the moon?” “What size is the smallest being in the world?” “What is the earth made of?”

Most of these issues had never been addressed before. The scholars were explorers clearing the mysteries of the surrounding universe. They had no maps to guide them, but Aristotle had left them a sort of vast sketch on which they could work. The philosopher had established sectors where everything had its place: animals, medicine, stars, and the rest. His students had learned to see, measure, and count. T

To Aristotle, nature was like a giant puzzle to be carefully pieced together. One of his disciples, Theophrastus, continued to live in Athens. He was passionate about studying the flowers and plants that Alexander had sent from Asia for his old master. Meanwhile, in Alexandria, other scholars were delving deeper into the realm of knowledge. Each had chosen a specialty.

With each new discovery, no matter how small, they rejoiced and worked with renewed vigor. However, each science seemed as complicated as the entire universe. Euclid, a disciple of Plato, taught at the Museum of Alexandria. His interest lay in the laws of geometry. An eminent teacher, he compiled in a book what he had discovered.

This book, “The Elements,” actually comprised fifteen substantial volumes that still serve as the basis for teaching geometry today. Other scholars, studying in different fields, often encountered great difficulties in reaching a result. The most sensational discoveries were usually made by pure chance.

So, on certain mornings as he prepared to bathe, Archimedes of Syracuse entered his bath and, sitting down, noticed the water level rising. He took out a foot: the level dropped slightly. He put his foot back in the water: the level rose again. Archimedes repeated his experiment several times, increasingly intrigued by what he observed.

Finally, enlightenment dawned on him, and he shouted at the top of his lungs, “Eureka!” which, as everyone knows, means “I have found it.” Terrified by his cries, his servants rushed in convinced that their good master was drowning and ready to assist him. To their great surprise, they found the scholar safe and sound, smiling at them from the depths of his bathtub.

And if he smiled thus, it was for a reason: he had just discovered how to calculate the weight of a ship. Let us recall his famous “principle”: “Any body immersed in a fluid experiences a buoyant force equal to the weight of the fluid displaced by the body.” As we can see, a bathtub could be as valuable as any measuring device in reaching the truth. It must be said that at that time, scholars had at their disposal neither microscopes nor telescopes, thermometers, nor precise equipment to assist them in their research.

They had to make do with what they had at hand: strings, pieces of wood, bits of bronze, etc. When Archimedes returned home to Syracuse, he astonished the king with his discoveries. Among other things, he devised a system of pulleys, or a crane, that could effortlessly pull a boat out of the water. Then he showed the amazed sovereign that where eight men failed to move an enormous rock by combining their strength, he could do it very simply using what he called a lever.

Another scholar, Eratosthenes, managed to approximately calculate the size of the earth by measuring the shadows cast by the sun in two places in Egypt located seven hundred miles apart. Not wanting to be left behind, Aristarchus of Samos worked tirelessly and discovered a way to measure the sizes and distances of the sun and moon. However, poor Aristarchus had little success. He was really too eccentric in his statements.

Did he not argue that the sun was the center of our universe and that the earth rotated? It was quite ludicrous. It took nearly 2,000 years to realize that he was right. Nonetheless, while more or less mocking unfortunate Aristarchus, everyone followed with great interest the research of the famous astronomer Claudius Ptolemy. Ptolemy was not at all related to the royal family of the same name. But he was almost as famous as them. He drew a map of the universe, with the earth at the center and the other planets and stars all around.

About a thousand stars were thus represented. Most had been discovered – without the aid of a telescope – by Hipparchus of Rhodes, an astronomer whom Ptolemy paid homage to and whose teaching was precious to him. Hipparchus made many discoveries. He was the first to determine the length of a year according to the sun. He invented the lines indicating latitude and longitude used by geographers to draw maps of the earth.

The maps of the time were quite large because explorers were going further and further afield. Sometimes, on returning from a long expedition, they recounted things so extraordinary that they seemed unbelievable. When Ptolemy drew a map of the terrestrial world to match his map of the universe, he indicated the Atlantic Ocean and the newly discovered British Isles. However, he refused to include a certain sea, covered with a crust of ice, which sailors returning from a long voyage to the north claimed to have seen.

A man who knew only the warm waters of the Mediterranean could not believe in the existence of a glacial ocean. While philosophers preferred to settle in Athens and scholars in Alexandria, Greek artists traveled from place to place, each trying to do his best in his specialty. Moreover, they were not idle, for they were in great demand.

Last word about : History – Euclidean geometry

In the annals of history, the era of Euclid’s geometry and Archimedes’ revelations stands as a testament to humanity’s relentless pursuit of knowledge. From the shores of Alexandria to the streets of Syracuse, the thirst for understanding propelled scholars to new heights of discovery. As their insights echoed through the corridors of time, they left an indelible mark on the fabric of civilization.

Today, we continue to draw inspiration from their achievements, embracing the spirit of inquiry and innovation that defines the human experience. In honoring their legacy, we reaffirm our commitment to the pursuit of truth and enlightenment.

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