The Pythagorean theorem is a dazzling pearl in geometry, known as the "cornerstone of geometry", and has a very wide range of applications in today's advanced mathematics and other disciplines. The physical data that have been unearthed prove that the splendid Babylonian civilization had already put forward the answer to this question as early as 3000-4000 years ago. In addition, several other ancient civilizations in the world, such as ancient Egypt, China and ancient Greece, have each discovered and proposed the theoretical prototype of the Pythagorean theorem.
China is one of the oldest countries to discover and study this theorem. In China, ancient Chinese mathematicians called a right-angled triangle a Pythagorean shape, the shorter right-angled side is called a hook, the other right-angled side is called a strand, and the hypotenuse is called a chord. The famous mathematics book "Zhou Bi Suanjing", which was written around the 2nd to the 1st century BC, once recorded a dialogue between the mathematician Shang Gao and Zhou Gong in the early years of the Zhou Dynasty. Shang Gao (about 1120 B.C.E.) replied to Duke Zhou, "...Therefore, break the moment, go three wide, repair four, and repair four corners." Shang Gao's sentence means: when the two right angles of a right-angled triangle are When the sides are 3 (short side) and 4 (long side), the radius corner (that is, the chord) is 5. In the future, people simplified this fact into "three strands, four strings and five". This is the famous Pythagorean Theorem in China, also known as the "Shang Gao Theorem".
Although the pioneering discovery of this theorem in the ancient East was much earlier than that in the West, why was this theorem known as the "Pythagorean Theorem"? It turns out that in the 6th to 5th centuries BC, ancient The famous Greek mathematician Pythagoras discovered this theorem and first used deductive method to prove that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two right angles. After that, when Euclid, another Greek mathematician in the 3rd century BC, wrote the book "Elements of Geometry", he believed that this theorem was invented by Pythagoras and called it the "Pythagorean Theorem". . The name also spread. According to the historian Plutarch, in order to celebrate this groundbreaking discovery, the Pythagoreans sacrificed a hundred oxen to pay tribute to the gods, so this theorem is also known as the "Hundred Ox Theorem".
So how did Pythagoras, who lived 2,500 years ago, discover this wonderful mathematical relationship contained in the right triangle?
Russell, a famous western philosopher, once commented on Pythagoras: "In terms of his intelligence or in terms of his unintelligence, Pythagoras is the most important thought in terms of his life. One of the characters." The ancient Greek who was born on the island of Samos in the Aegean Sea (today's eastern Greek island) is a well-deserved thinker in mathematics and philosophy. Throughout his life, he has always believed that there is a law of numbers behind everything at work. "Whether it is to explain the external material world or describe the internal spiritual world, we cannot do without mathematics!"
Pythagoras, a wealthy, intelligent and eager to learn since childhood, studied geometry, natural science and philosophy under famous teachers. When he grew up, he longed for the wisdom of the East, and traveled through thousands of rivers and mountains to study and travel in Babylon, India and Egypt, and extensively absorbed the essence of ancient eastern civilization. Around 530 BC, he returned to Samos. Later, he moved to Croton in southern Italy and founded the well-known Pythagorean school, engaged in education and mathematics research at the same time.
One day, Pythagoras was invited to a dinner party for a wealthy dignitary. The owner's luxurious palatial dining room has a delightful square marble floor. As the sumptuous feast was delayed, some hungry VIPs were quite critical, but only Pythagoras was slightly different. The observant and exploratory mathematician is gazing intently and thoughtfully at the neatly arranged, ornate square tiles beneath his feet. However, it was not just the pleasure of appreciating the beautiful tiles that attracted Pythagoras, but the wonderful relationship between the combination of the tiles and the "number" that attracted his attention. I saw that Pythagoras quickly picked up the paintbrush, squatted on the ground, selected a tile, and drew a square with its diagonal AB as the side. He found that the area of this square was exactly equal to the sum of the areas of the two tiles. . This discovery made him even more curious... So when he made another square from the diagonal of the rectangle made of two tiles, he found that the area of the new square was exactly equal to the area of 5 tiles, which is two The strands are the sum of the areas of the squares with sides. So far, Pythagoras, who has been seriously verified, has made a bold assumption: For any right-angled triangle, the square of the hypotenuse is exactly equal to the sum of the squares of the other two sides. During a meal, the ancient Greek mathematician's eyes never left the ground...
A fundamental theorem of geometry was born in a meal in this way. As a result, there is the scene of killing a hundred cattle in the previous article to celebrate. Sadly, Pythagoras' method of proof has long been lost. But the Pythagorean theorem, as one of the "ten most important mathematical formulas" in the world, has been attractive for thousands of years. Proofs of it are eagerly awaited, including notable scientists, dignitaries, and dignitaries. The 18-year-old Albert Einstein and former US President Garfield both actively explored the proof of this theorem. Hippassos, a student of Pythagoras, further discovered another important concept in mathematics through this theorem - irrational numbers. Although this discovery broke the Pythagorean belief that everything in the universe is a ratio of whole numbers to whole numbers, and led to the tragic death of Hippasus, the discovery of irrational numbers directly triggered the first crisis in the history of mathematics.
The world-famous Pythagorean Theorem was born out of a long overdue feast and a beautiful combination of marble tiles. The extremely extensive and important application of this theorem in later generations seems to reflect the absurdity of its background. However, the beating pulse of history is not random, and the path of scientific discovery is not dictated by the goddess of luck. The success of Pythagoras is not only a coincidence of fate and historical chance, but more importantly, as a wise man, he has a pair of eyes that are good at discovering and an enterprising spirit that always thinks bravely. The Pythagorean theorem is a silent confirmation of the old adage of wisdom: Science will not abandon those who truly love it.
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