希腊早期的数学与天文学

希腊早期的数学与天文学 The documents I have carefully collated are from the web I only collect the collation If there are any mistakes Still ask oneself to check! Greece's early mathematics and astronomy What I'm talking about in this chapter is math It's not because of the math itself It's because of the Greek philosophy There is a relationship -- a very close relationship, especially in Plato's mind Greek excellent watch Now the math and astronomy It's more obvious than anything else The greeks were in art, literature and Philosophical achievements Whether it's good or bad can be judged by the taste of the individual; But they did it geometrically There is no doubt about it They got something from Egypt From Babylon there was very little; And they From these sources The main part of mathematics is rough experience In astronomy, it's not A long history of observations The proof of mathematics Almost entirely from Greece There are a lot of very interesting stories -- perhaps no historical veracity -- that can be shown What are the real problems It stimulated the study of mathematics The earliest and simplest story is about thales Legend has it that he was king in Egypt Ask him to find the height of a pyramid He waited until the sun shone the length of his shadow equal to his height hou To measure the shadow of the pyramid; This shadow is, of course, the height of the pyramid It is said that the law of perspective was originally The geometer, agathuus, studied the scenery of ischius's plays Legend has it that it was thales Study the question of finding a ship at sea It was done correctly at a very early stage Greece a few One of the big issues that he CARES about That is to double the cube of a cube It is said to have originated somewhere in the temple The priests; "The oracle told them A statue of god is twice as large as their original one Initially they were just Think of doubling the size of the original image But then they realized that it was eight times bigger than the original This is more than god It's much more expensive to ask for So they sent an envoy to see Plato Is there anyone in his school garden Can solve the problem The geometricians accepted the problem For centuries And it came with the property A lot of amazing results The problem is, of course, the cube root of 2 The square root of 2 is the first irrational number to be discovered This irrational number is known by the early pythagoreans Word of the And there's a lot of clever ways to approximate it The best way to do this is to assume two columns digital Let's call it a column and b column; Each column starts at 1 Each of the next steps is the final one that has been obtained A and b add up; The next b is made up of two times the former a plus the previous b This is the beginning of this The number is (1) 1) (2 3) (5 7) (12 17) (29 41) (70 99). In each pair of Numbers 2a2 minus b2 is either 1 or minus 1 So b/a is going to be the square root of 2 And every next The steps are getting closer For example, Readers will be happy to see them 99B70 squared is very close to 2 equal Procruz described Pythagoras -- the man who was always a rather dim figure -- but the first one Geometry is regarded as a kind of learning person Many pundits Including Sir Thomas heath They all believe in Nevada Russ may have seen the theorem named after him; The theorem says in a right triangle string Squared is equal to the sum of the two sides squared No matter how This is a theorem that was sent by the pythagoreans at an early age Know the They also know that the sum of the inner angles of a triangle is equal to two right angles Except the square root of 2 Other irrational Numbers have also been used in special cases by Socrates' contemporary dio Dorros studied it And, in a more general way, it was done in the same way that Plato had earlier studied Demurrey wrote a treatise on irrational Numbers But we don't know much about the content Plato This topic is deeply interested; He mentioned theodoros in the conversation that he named after "; tyad. Tiarted works In the law He said that the ignorant ignorance of the subject is very disgraceful And it also suggests that he himself began to know that it was too late It's certainly true of the Pythagorean philosophy Important relationships One of the most important consequences of seeing irrational Numbers is the invention of the yodokso (about 408 to 355 B.C.) The geometric theory of proportion Before he Only the theory of the proportions According to this theory If a passenger d etc. In b by c A is equal to c over d The nature of In the absence of the geometric theory of irrational Numbers Can only be For rational However, the New Territories, which are not subject to such restrictions, are said by the New Territories The way they are constructed implies close Generations of analytical methods This theory was developed in Euclid's book And it has great logical beauty And that's what he invented or he did the "exhaustive" It was later used successfully by a few meters This approach is a prediction of integration Such as We can take the area of the circle as an example You can take it inside A circle makes a positive hexagon Or a positive twelve-sided shape Or a multilateral that is a thousand sided or a million The shape This is a polygon No matter how many edges it has The area is proportional to the square of the diameter of the circle More than this The edges are more and more And the closer it is to the same as the circle Can you prove that As long as you can make this polygon have feet Enough of the edge The difference between the area and the area of the circle is less than any pre-specified area Whatever that means in advance How small the area is For that purpose And it quotes the "a few meters of axioms" This is the axiom To simplify it, say: suppose there are two quantities Divide the larger one in half Half the half halves And so on And then you end up with a smaller number than the original two In other words If a greater than b So there's going to be some integer n that's going to make 2n times b greater than a A poor method can sometimes yield accurate results For example, the area of the paraboloid, which is done by a few meters; sometimes You can only get a constant approximation For example, when we try to find the area of the circle So let's do the area of the circle It's the ratio of the circle to the diameter This ratio is called PI; A few meters in the calculation USES a close of 22/7 As the value He did the inside and out of the 96 And that proves PI; It's less than 3 and 1/7 and it's greater than 3 and 10/71 This approach can proceed to any degree of approximation required And that's what any method is on this issue I can do everything I can Use in-line and ex-cut polygons for PI; The approximation of It should go back to Socrates The contemporary of antifeng Euclid - when I was young It is also the only textbook of geometry that is widely acknowledged as a textbook for schoolchildren Yuan before 300 It was a few years after the death of Alexander and Aristotle Living in Alexandria He's a few What was originally was not his creation But the order and the logical structure of propositions are mostly his The more a man studies geometry The more you can see how impressive they are He dealt with the famous conduct theorem The method of conduct With a double virtue; The deduction is powerful And it does not implicitly assume the dubious nature of the original hypothesis The theory of proportion is the inheritance of the one The method that it USES is essentially the same as that of westras introduced to nineteen The analytical mathematics of the century Thus, the difficulties of irrational Numbers are avoided And then Euclidean transition A geometric algebra And in volume 10 we looked at the problem of irrational Numbers After that, he goes on to talk about stereo what And the end of the question of being a regular polyhedron This problem was done by tyad, who was in Plato It's been mentioned in the timmyo Euclid's geometry is one of the greatest books of all time It is the end of Greek intelligence One of the monuments of beauty Of course, he also has a typical Greek limitation: his method is purely deductive And among them There is no way to verify the basic assumptions These assumptions were thought to be unproblematic But by 19 century Non-euclidean geometry indicates that some parts of them are available And only observation can determine it Are they wrong Euclid's geometry is contemptuous of practical values This has long been taught by Plato It is said that there was a After hearing a proof, the student asked What good is learning geometry So Euclid called in one The slave said, "go and give three cents to the young man Because he must benefit from what he has learned "However, It makes sense to be contemptuous of practical but pragmatic reasons No one in the Greek era imagined a conical curve It is of any use; Finally, in the seventeenth century, Galileo discovered that the projectile was moving along a parabola And open Plumb found that planets move in ellipses so The greeks did the work of pure love theory Just one It became a key to war and astronomy The Roman mind was too practical to appreciate Euclid; The first one to mention Euclid's Romans is the west The ROM. In his time Euclid probably had no Latin translation; And in boiseus (about 480 A.D.) before It is true that there is no record of any Latin translation. The arabs are more likely to appreciate Euclid. big In about 760 AD The Byzantine emperor once sent a Muslim khalifa a Euclid; About 800 AD when When halon al rashid was in office Euclid had a translation of Arabic Now the earliest Latin The translation was translated from Arabic in 1120 Since then The study of geometry The study was revived in the west; But it was not until the late Renaissance that important progress was made I'm going to talk about literature now The greeks' achievements in this regard are equally striking in terms of geometry In Greece before The babylonians and egyptians have laid a foundation for centuries of observation They recorded the The sight of the planet But they do not know that the morning star and the evening star are one Babylon undoubtedly And Egypt also may The cycle of erosion has been discovered This is a reliable predictor of eclipse But it does not predict eclipses; Because solar eclipses are not always visible in the same place Divide a right triangle into 90 degrees Divide the time into six very We also have to be with the babylonians; The babylonians liked the number of sixty There is even a sixth The decimal system of counting Greek people always like to put their first 穉 e character of the wisdom of all charges and traveled to Egypt The results of But before the greeks What people have accomplished is very few But thales's prediction eclipses It's an example of a foreign influence; There is no reason to suppose that he was learning from Egypt and Babylon What new thing is added beyond the west And his prediction was confirmed It's a perfect coincidence Let's take a look at some of the first Greek findings and the correct hypothesis Anaximander thought the earth was floating the Nothing is supporting it Aristotle was always opposed to the best hypothesis of the time So he was Refute anaxman's theory That is, the earth stays at the center forever Because there is no reason for it to be on one side Move in motion without moving in the other direction Aristotle says If that's true So if a person is standing In the center of the circle The order is filled with food at all points in the circle He would starve, too There is no reason to choose Choose what part of the food and not the other This argumentation appears in the scholastic philosophy But not with the day The literature is in one place It's about the free will It reappeared in the form of "the ass of the cloth" now The ass of the cloth was chosen because he could not choose between two equal piles of grass So he died of hunger Pythagoras was probably the first person to think that the earth was spherical But his reason (we have to set it up It is aesthetic, not scientific However, The scientific reason was soon discovered Anaxacola found it The moon shines through reflection And the theory of lunar eclipses is correct He himself still thinks the land is flat But the shape of the shadow of the lunar eclipse made the Pythagorean side the last conclusive argument for the sphere he The earth is seen as one of the planets They knew -- it was said to be from Pythagoras The morning star and the evening star are the same star And they think that all the stars, including the earth, are moving around in circles dynamic But not around the sun but around the center of fire They have discovered that the moon always faces the same The earth's And they thought that the earth was always facing the same fire in the center. The Mediterranean area is in and out The fire in the heart of the heart So you can never see the fire in the center The fire of the center is called "the house of Zeus" or "Mother of all gods" The sun shines through the fire of the reflection center There is another object besides the earth call Do the earth The fire distance from the center is the same On this point They have two reasons; One is scientific another It's a mysticism that comes from them The scientific reason is that they observed it correctly The eclipse is sometimes the case The sun rises above the horizon The reason for this is refraction They don't know the refraction so It is thought that in this case the eclipse must be caused by the shadow of another object on the other side of the earth Another reason for It is the sun, the moon, the five star, the earth and the anti-earth and the fire of the center constitutes ten And then the ten is the bida The mystery number of the spites The Pythagorean doctrine was attributed to ferrero He is the Thebes Life in the public The end of the first five centuries Although this doctrine is fanciful And some parts are very unscientific But it is Is very important Because it contains most of the imagination necessary to imagine the Copernican hypothesis The earth is not set Think of the center of the universe as one of the planets It is not supposed to be fixed for the eternal, but to be able to travel in space This shows a remarkable liberation from the human center Once a person is exposed to the natural image in the universe It's time for the shake There is no hard scientific argument for bringing it to the right theory There are many observations that contribute to this A little later, oenobid in anaxagola discovered the ecliptic The slope of It soon became clear that the sun was much bigger than the earth This fact supports those who deny that the earth is a thing People in the center of the eon Center fire and anti-earth Shortly after Plato's time, it was abandoned by the Pythagorean the The heraclide of the golls (from 388 to 315 B.C.) And Aristotle at the same time Both Venus and mercury revolve around the sun And the earth moves around its axis every 24 hours The insights of This insight is a very important step that no one has ever taken before Heraclide belongs to Plato school And it must be a great man But not as respectable as we might expect; He was tracing Described as a fat playboy The allistak of samo lived around 310 to 230 B.C. So he was twenty-five years older than he was. he It is the most interesting person of all ancient astronomy Because he came up with a complete Copernican hypothesis namely All planets, including earth, rotate around the sun in circles And the earth orbits its own axis every 24 hours Turn a week But the surviving alexadic's only work, "the size and distance of the day and the moon," is still on the ground The center of the ball This is a bit of a disappointment indeed In terms of the issues discussed in this book No matter What kind of theory he's taking is that there's no difference; So he probably thinks To the universal meaning of astronomers See an unnecessary objection That would add to the burden of his calculations It is an unwise move; Or he could It's only after writing this book It was the Copernican hypothesis Sir Thomas heath was in his book The book of the book, which includes the full text and the translation of the original, is the latter opinion But no matter The situation is which one The idea of the Copernican idea was hinted at by aleksandar The evidence for this is perfect Conclusion there is no doubt that The first and best evidence is the evidence of a few We have already said that a few meters is a subristak A younger man of his generation "In his letter to king Glenn of Syracuse It was written by alekstak "A book These include certain hypotheses, "and continue," his hypothesis is that stars and the sun don't move The earth It orbits the sun around the circle The sun is in the middle of the orbit." There is a passage in Plutarch's book It is the greeks' responsibility to punish him for the ungodly crime Because he makes the universe The stove (that is, the earth) moves This is the idea that he imagines that the sky is stationary and the ground is moving along the oblique circle At the same time and ring It rotates on its own axis The result of the simplification of the phenomenon." Creander was a contemporary of alessandro about He died in 232 BC "Said Plutarch in another paragraph The idea came to him only as an idea A hypothesis But seleucius, the successor to the alitsydak, sees it as a definite idea (seleucus The heyday was about 150 BC And then there's the idea of a very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very Yang center said But they did not say that he proposed this doctrine merely as a hypothesis Even though he was talk That's probably the same as Galileo two thousand years later It's because of fear of the effects of religious prejudice Caused by We're talking about kleinander's attitude There is a good reason for this fear The Copernican hypothesis was brought up by the yalistak (either formally or experimentally) It was explicitly accepted by seleucius But it was not accepted by any other ancient astronomer This kind of The general objection was mainly due to the reason of hibaku The hibaku peak was 161 to 126 B.C. Hess took hebgu It is described as "the greatest astronomer of the ancient times" So, the first system is hibachus who talks about trigonometry; he The discovery of precession; He calculated the length of the lunar month And the error is less than one second; He improved the day of the arrystak Calculation of the size and distance of the moon; He wrote about 850 stars And the latitude and longitude of them To oppose alex The sun center hypothesis of dack He adopted and improved the creation of the alvronny (about 220 BC) The theory of revolving circles; This doctrine was developed and became known in Ptolemy's system It is based on the peak of the second AD The name of Ptolemy, the astronomer of the century Copernicus stumbled upon some of the almost forgotten subristak's hypothesis Not knowing much, though; He was encouraged by his creation of an ancient authority otherwise The hypothesis is astronomical for future generations The effect of learning is actually going to be zero The ancient astronomers calculated the size of the earth, the size of the moon, the size of the moon and the distance from the sun to the moon It's all valid But they are hampered by a lack of precision instruments Thought of this Many of their results It's amazing The diameter of the earth is 7 850 miles This is fifty miles less than it is Ptolemy calculates that the average distance of the moon is 29 and a half times the diameter of the earth. The correct number is about 30.2 times they None of them are close to the size and distance of the sun They all estimated it too low their Estimate the diameter of the earth the Alekdad is 180 times Ciba gu is one 245 times Bosidoni is 6 546 times; The correct number is 11 726 times We can see that these calculations are improving only Ptolemy's calculations show a regression. The extrapolations from bocioni are about half the correct Numbers In general Their images of the solar system It's not too far from the truth Greek astronomy is geometrical rather than dynamic The ancient people thought of the motion of the heavenly bodies as an equal round transport dynamic Or the composition of the circle They don't have a strong concept The celestial sphere is all in motion It's different The heavenly bodies are fixed on the celestial sphere In the time of Newton and the theory of gravity A new conception of geometry was introduced point It is strange that In Einstein's general theory of relativity, we saw an idea returning to geometry The cow The concept of force in the sense of meaning has been abandoned The problem with astronomers is that they are known to be moving on the celestial sphere How can I use the hypothesis to introduce the third coordinate The depth of In order to make the phenomenon as simple as possible The advantage of the Copernican hypothesis lies not in the truth but in Jane Jie; From the relativity of motion That doesn't really happen. What's the problem with sex The greeks are in pursuit of "Jane The hypothesis of the phenomenon This is, in fact, scientifically correct Although not completely intentional Just compare their predecessors and their descendants (until Copernicus) That's enough to make every one People believe in their truly amazing genius Two other very great people The third A few metres of the age of the arbora It ended the list of the top Greek mathematicians A few meade is Syracuse The king's friend Maybe his cousin When the Romans took the city in 212 BC, they were killed Alvronny is from green In the year of the year, we lived in Alexandria He was not only a mathematician It's also a physicist and a stream Body static, And he is known primarily for his research on conic curves I don't know about the two Talk about more Because they came in too late What impact does philosophy have After these two people Although respectable work continued in Alexandria But the great age is the knot The beam Under Roman rule The greeks lost the confidence they had gained with political freedom And in the loss of When you lose that confidence They have produced a kind of callous respect for their predecessors The killing of the Roman army A few meters, Rome was the symbol of the creative thought that killed the whole of the hellenistic world = = = = = = = = See the mathematics of Greece. Volume one On page 145 Greek mathematics Vol. 2 On page 153 He was the teacher of Cicero It was the second half of the second century BC "The alessadar of samo The ancient Copernicus. By Sir Thomas heath Oxford The 1913 edition The following is based on this book