When it comes to ancient human mathematics, it is impossible not to mention book of ancient Greek mathematician Euclid "Elements of Geometry". It has had a great impact on modern science and cannot be overestimated. Many people think with admiration that human knowledge originated in ancient Greece, and ancient Greece is cradle of scientific spirit.
However, from early ancient Greek mathematicians Thales, Pythagoras to Euclid, in just over 300 years, Ancient Greece suddenly heralded pinnacle of ancient geometry - "Elements of Geometry", which never existed. A long process of accumulation and development, at least not found in ancient Greek archeology, is such a sudden development that violates law unthinkable? Although Western scholars regard ancient Greece as a "special civilization" or "Greek particularism," a special phenomenon in history of human civilization, this is nevertheless inevitably questionable.
As underground cultural relics continue to emerge, truth about origins of ancient Greek geometry is gradually coming to surface. At least based on current evidence, geometry and many of achievements of ancient Greek civilization did not originate in ancient Greece.
It is impossible to verify when geometry of ancient Greece was born, but it is said that in 7th century BC Thales traveled to ancient Egypt and introduced geometric materials such as points, lines, surfaces and circles to ancient Greece. Regarding deeds of Thales, Aristotle has only 2 sentences left.
About 6th century AD, a "great mathematician" appeared in Ancient Greece. His name was Pythagoras. Grass' theorem." Pythagoras left no scriptures, no words. Decades later, Herodotus, author of "History", said: "He once went to Ancient Egypt to study, and taught about immortality of ancient Egyptian soul, reincarnation, etc. Teachings brought back in Greece and established religious groupings in Greek colonies in southern Italy It should be noted that at that time no one said that he was a mathematician, and no one said that he knew geometry, but after his death a branch of sect he founded preached that " everything is number." From these descriptions, it is not difficult to conclude that Pythagoras must have learned algebra and geometry from Ancient Egypt and introduced them into Ancient Greece.
About 500 B.C. BC, after Pythagoras, Ennopid of Ancient Greece was very knowledgeable in astronomy and geometry. According to Diodorus Siculus, historian of 1st century BC. BC, Ennopid learned astronomy and geometry from ancient Egyptian priests. Ennopidus had a student named Hippocrates, who is said to have written earliest version of Elements.
After Hippocrates, most prominent master of geometry in ancient Greece was Eudoxa (408-355 BC), from whom main content of volume "Stereo Measurement" is derived. However, according to literary records, Eudoxus was born on west coast of Asia Minor. As a young man, he went to Italy to study at Pythagorean school, then went to Athens to study, but finally went to Ancient Egypt to study astronomy. and mathematics. Among them, it is said that he studied very hard in Athens and lived a very difficult life. Having collected enough funds for journey, he went to Ancient Egypt to study for 16 months. If knowledge of astronomy and mathematics in Ancient Greece is most advanced, then does Eudoxus need to go to Ancient Egypt and study for 16 months? Later, Eudoxus returned to Asia Minor, which already belonged to Persia, visited Athens along way, and then returned to his native city until his death.
Plato was a contemporary of Eudoxus, and most famous after him were Euclid, Aristotle and Archimedes, who moved earth. Among them, Archimedes also went to Egypt to study. After our era, mathematicians Hero, Papus, Ptolemy, Diophantus and Hypatia, by coincidence, also studied in Egypt.
As "father of geometry", Euclid, where did his knowledge of geometry come from? Textbooks tell us that Euclid was a Ptolemaic scientist in Hellenistic era and lived in Alexandria, Egypt in 3rd century BC. Although he lived in Egypt, Euclid was a real Greek. It was Euclid who summarized geometric achievements of ancient Greek sages, organized and supplemented them.
According to Proclus, an Eastern Roman, about a thousand years later, Euclid traveled across ocean as a young man, came to Athens from Alexandria, and studied at Plato's Academy with a strong mathematical atmosphere. it was written that "those who do not understand geometry are not admitted." Therefore, at Academy of Plato, Euclid drew richest geometric knowledge, returning to Alexandria, dismantled and supplemented this knowledge and finally formed "Elements of Geometry". If this description is correct, then it can prove to some extent that geometrical principles familiar to us are mainly borrowed from Ancient Greece, but problem is that Proclus is an Eastern Roman, and there is an interval of thousands of years from Euclid. And there is no other literature in the middle that can confirm Euclid's learning experience.
There is even more unfavorable evidence for this description. After Plato (427 BC-347 BC), third generation head of academy, Xenocrates, there is no document showing what else remained in Academy of Plato at that time. time Mathematical tradition, and from fourth generation of Palemon to Rome, to contribute to Athens, Plato of Academy did not leave any mathematical works, not even individual fragments, not even title of book. At same time, after Aristotle (384 BC-322 BC), there were no worthy mathematical achievements in all of Athens. That is, according to modern literary records, Euclid (330 BC-275 BC) finds it difficult to learn anything in Athens, so legend that he studied geometry at Plato's Academy, most likely invented.
When textbook introduced Archimedes (287 B.C.-212 B.C.), it was said that ancient Greek civilization had declined at that time, and center of culture and economy had moved to Alexandria, Egypt, so Archimedes went to Alexandria in 267 BC. He left Alexandria and studied under disciples of Euclid Eratosthenes and Canonikos. However, difference between teaching Euclid in Athens and teaching Archimedes in Egypt is less than 50 years. If Athens is center of geometry in ancient Greece, with a long tradition and a strong academic atmosphere, then in absence of war under circumstances, in just 50 years it will fall into decay and he won't even have decent achievements? Obviously unlikely.
Therefore, most logical truth is that Euclid may have been in Athens, but his knowledge mainly came from Egyptians in Alexandria. There are some ancient Greeks and results of his research.
It can be said that ancient Greek scholars who greatly appreciated geometry (Plato went to Ancient Egypt) or who achieved great success in mathematics, including many mathematicians of Roman era, almost all had experience of studying in Egypt. And ancient Greek scientists who studied in Egypt often have some important results of geometric research, why is that? Before answering this question, let's take a look at archaeological finds.
Since modern times, archeology has discovered that both ancient Babylon and ancient Egypt had a deep knowledge of geometry, and in some aspects not weaker or even stronger than ancient Greece. An ancient Babylonian stone slab has been discovered in Mesopotamian archeology, which was made between about 1900 B.C. and 1600 BC, and it clearly records that ratio pi = 25/8 = 3.125. In ancient Egyptian archeology, ancient Egyptian cultural relics discovered around same time as stone tablet also show that ratio of pi is equal to square of a fraction of 16/9, which is approximately equal to 3.1605. It wasn't until 3rd century BC that Archimedes calculated that pi was between 223/71 and 22/7 and took their average of 3.141851.
Especially in Ancient Egypt, there are still magic pyramids, and in pyramid of Khufu there are countless "unsolved mysteries", such as: length of side of square at base of pyramid * 2 ÷ height of pyramid, which is exactly 3.14; weight of pyramid × 10 × 10 to 15th power = weight of earth; square of height of pyramid = area of the triangle on side of pyramid; pyramid height × 10 × 10 to 9th power ≈ 150 million kilometers = distance from earth to sun, etc. wait. It is believed that these data are not random phenomena, but a manifestation of outstanding achievements of ancient Egyptians in astronomy and mathematics. In addition, some knowledge of physics is required to make such a huge pyramid.
Judging by knowledge of mathematics, physics and astronomy embodied in pyramids, until end of ancient Greece, depth of research may not be as deep as that of ancient Egyptians.
Until now, origin of ancient Greek geometry has mostly been revealed to world.
About 3100 B.C. e. The first dynasty in human history was founded in ancient Egypt. During development of Ancient Egypt, due to ebb and flow of Nile River and unique geographical environment, ancient Egyptians needed to develop geometry to solve practical problems; at same time, due to worship of sun god, geometry and astronomy may have been developed. In addition, ancient Egyptians also developed a certain amount of physics for practical needs of building pyramids. After more than 2300 years of development, ancient Egyptians accumulated a profound knowledge of astronomy, mathematics and physics.
About 2800 years ago, ancient Greek civilization began to revive, getting rid of barbarism. According to law of social development, Ancient Greece at this time should be very backward compared to Ancient Egypt, so group after group of ancient Greeks came to Ancient Egypt to study mathematics, physics, astronomy, etc. and spread knowledge in Ancient Greece. , as a result of which social direction of thought in ancient Greece changed dramatically. During this process, early Greek scholars were basically supposed to "take teachings" and write down results of ancient Egyptian research in Greek. Even remarkable logical method of proof-deduction in "Elements of Geometry" was most likely developed not by ancient Greeks, but by ancient Egyptian civilization, because methods of proof-deduction were already in early ancient Greek works on mathematics and astronomy, but Ancient Greeks Early mathematics and astronomy undoubtedly belong to ancient Egypt.
In fact, it may not only be that much of geometry of Ancient Greece originated from Ancient Egypt, but also achievements of Ancient Greece in astronomy, philosophy and physics. In addition to Pythagoras, Ennopids, Plato, Eudoxus and others, there are Thales, so-called "father of Western philosophy", Herodotus, "father of history", and Athenian reformer Solon, both of whom studied in ancient Egypt or Hellenistic Egypt.
Prosperity of any civilization requires a process of continuous accumulation and development, and it is impossible to suddenly make a triple jump without a reason. Therefore, at least most of achievements of ancient Greek civilization must have come from ancient Egypt, and ancient Greece is heir to part of its knowledge.
Ancient Egyptian civilization was brilliant for thousands of years. She was a representative of human civilization in her era, but now only a blurry back remains. The crystallization of civilization over millennia is now called "achievements of Ancient Greek civilization", has become food for other civilizations and a stepping stone to obscurity, how sad!
By analogy with ancient Egypt, many of achievements of ancient China are far ahead of West, but “Zui principle” in West is called “Cavalieri principle”, and “Yanhui triangle” is called “Pascal triangle”. In West, China has long had dialectical philosophies such as "you and wu" and "yin and yang", but now dialectical philosophy is considered contribution of Germans, and so on.
Therefore, brilliant achievements of so-called "ancient Greek civilization" are most likely a lie. The truth is that ancient Greek sages basically copied or retelled some of achievements of ancient Egyptian civilization.