Primeiros sinais da matemática na história | Os Mistérios da Matemática #3

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of evidence and I used to tell this to people and they would say oh you're telling me different cultures have different kinds of mathematics two and two is four everywhere well it's true two and two is four everywhere but how you write the numbers what you do with them what role mathematics society that is very different culture a new culture a society and this is a look so my first principle is ever virtually every culture has some kind of mathematics second principle is that a society develops kind of mathematics it solves problems of that particular

society wants to solve Mazzone G um econ can commence a mathematical when you think about ancient mathematics whether you're talking about the Mayans or in India or in Mesopotamia or in Egypt the the really sophisticated mathematics was to try to understand the heavens and this belief that you if you understood where the planets would be at a given time if you understand the conjunction of different planets with the position of the Sun in the heavens but that you might be able to predict when the king would you might be able to predict when a famine

would come so this was seen as very powerful information and so it was was closely guarded knowing how the Stars moved and how the heavens mood was was critical astronomy is the basis of a lot of ancient mathematics that was the motivation for studying trigonometry and for being able to figure out you know even the world isn't flat people usually knew that the world was a sphere but still you had to be able to figure out you had to be able to figure out where things were gonna be and went through what happened and if

you could predict eclipses which were a very significant thing to happen I mean if the Sun suddenly went dark I mean that was that was a major problem for people you know and if you could predict that then yes you had power and that was very important I remember reading an eminent China when the Emperor hired people to do this if they've got it wrong they they lost their jobs for sewer they had to be able to do it work correctly so so knowing the mathematics especially behind astronomy was very critical in a lot of

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View the sequences notorious Moscow no sentai goseiger gavin poder de xin trivial places on mathemagical there's some indications even even as far back as the house as in ancient Babylonia that that one of the motivations for mathematics what was for the rulers to get things right I mean you wanted to be able to do things fairly I mean I would thou is that was your job is to came to to make sure that everything worked correctly and so you needed mathematics to do that I mean even more explicitly there's a very nice book that was

written in Hebrew and Spain in the 12th century eleven yeah sometimes the early 12th century by abraham bahia and it was a book on geometry and he was he was very emphatic that you had this that people had to study geometry because you needed to do things correctly if you if you know when when somebody died and he had you had to divide up the his land among the children and the son the oldest son is probably supposed to get twice as much as the other with the other children or whatever you had to be

able to do it right and he said people don't know how to do this all the time you know if land you know and land it's not necessarily a square where it might be easy to divide it up but if different shapes then that's what he was interested in he said you know God requires that you do this correctly and we both to learn you have to learn mathematics we ought to do it correctly Adachi don't serve our inanna Teresa post evil mentions ParaNorman a necesidades de precision para govern our sauce projects a Jamila strains

construed templos computer been Sesshomaru tempo River phenomenons notorious a plan ajar Oakland CEO accolade llevar mazdan a Mentos elemento es da da da de Ciencias paramagnetic son David Victor dos a non-fatal schemata magic and the other thing you find in every advanced civilization is the study of the heavens and that the heavens are fascinating because we've got three basic periods we've got the day we've got the lunar month and we've got the solar year and they're not compatible early civilizations hoped that it would be a whole number of days that fit into a lunar month

in a whole number of lunar months that fit into a solar year but it doesn't work as nicely as that and so they began to have to work on these cycles and cycles within cycles and then once they start tracking the planets things get incredibly complicated and if you want to understand when there's going to be a lunar eclipse when there's going to be a solar eclipse now you get into really complicated use of numbers and and again you find this in every advanced civilization in the Americas or in Africa or in Europe or in

Asia they were all struggling with how to use numbers to to understand those patterns and the simple fact that the position of the Sun as it travels through the the heavens on its yearly cycle the position of the Sun is extremely important in predicting when rain will fall when the seasons occur there was this belief that the positions of the other heavenly bodies also had to be important had to have some kind of predictive power and so looking at the numerical patterns that people worked out for these astronomical bodies and trying to figure out how

to how to use them to predict first of all where the bodies would be and then what that influence might be we find this in all of these civilizations and it drove a lot of very advanced thinking in the properties of numbers and how you work with numbers properties of mathematics these patterns that people were seeing in the heavens pues pavo's de Navidad a creative oxidation where atrocity a los Dioses y el comportamiento disastrous influencial vajira dementia Vedado zombies per Derek rotation disasters arystar condenado majeeda june 14 or tanto Saburo quasi para monterossa protest samara

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okay so you go and look at well we've got a lot of stuff from Egypt but there's a lot we don't know about Egyptian mathematics but we know they built the pyramids and we knew know that they could find the volume of pyramids and the volume of pyramids with the top cut off and we certainly know that they could solve problems when the Nile flooded in Egypt it got rid of all the boundary markers and then when the Nile floods receded they had to go lay out the the fields again okay so you learn geometry

to do that you later geometry to build pyramids you learn computation methods to build pyramids too because an incredible job of all the workers that you have to organize and all the stones that you have to figure out where they are and where they should go it's a tremendous accounting problem so Egyptians could could do all kinds of cool stuff if you really the introduction to the papyrus which is this one of the major documents we have of ancient Egyptian mathematics it says to figure out all secrets or something they were dealing with how to

divide up beer and bread which was for instance one of the ways they paid their workers something and figure out various things about that there are some geometrical ideas measuring you can see some interesting things about pyramids and they did calculations the Egyptians what one of the things that's interesting about Egyptian mathematics they had this way of expressing fractions all as sums of what we would call unit fractions so they would never write something like two-fifths or something they would always think of it as a sum of unit fractions so two fifths is like one

third plus one 15th so they certainly had power and they were the ones who understood how to do the calculation of sides that's what I say mathematics was a sort was certainly a source of power [Music] no way Jose disappear poder non-jew Adagio casamento s vessel asado era pauses acidosis conocimiento Matamata potentials Masaryk impartial odd o us o describers USS Ponce re-spread Monte registros proceses dr. Conte see their cupola auras own meadows Elena's Grande's coaster signs samosas yesterday's describers can use permit interim Amazon Luce puja Mathematica Kara's a dementia we dodged all ages rumata maximize

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had to figure out who owned what and how to divide it up and all that and they they developed various techniques techniques that we you often call solving quadratic equations their calculations were much more sophisticated than the Egyptians they they developed this place value system of base 60 and they could they could calculate all sorts of things from square roots the various of kinds of measurements and they all sometimes they they did them to all sorts of to a very very many places we would call decimal places [Music] who's Babylon useless ability or image Pythagoras

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profunda inclusive in sobre la posibilidad a JVM cleared or Mathematica portrait to do [Music] we don't know enough about the Mayans you know the Spanish when they came in and conquered central conquered Mexico and Central America they destroyed a lot of the Mayan documents so we know they had a fairly sophisticated mathematical system made they use base 20 in general and they could calculate dates and from how long a rain was and when wind when a certain King was born or when he died and things like that and they had this very extended collectible system

we don't know too much about other parts of their mathematics other than what you can infer from the fact that they they also did a lot of building and clearly to do building you needed to know mathematics you know there's some of the buildings are set up you know with astronomical orientations so they certainly understood motions in the sky they in particular they we know that they followed Venus and they and its appearance in the sky it's determined a lot of their pieces of their calendar [Music] mais aguacate una Gracie the Malaga Pentimento mati modulation

for Carlos episode serve our mo chief [Music] Oh inverse AC pergunta rien para que como Mathematica podría ser Russia lazada persevere say be apropos ito era has ponderable que las Cuevas [Music] these kinds of observations can be found in all of the advanced civilizations but something very special happened in Greece starting about the 4th century into the 3rd century before the Common Era and that was the marriage of mathematics with philosophy and the thing about the Greek philosophers is that they firmly believe that you can't make any assertion without backing it up without having a

justification for it and so that came into mathematics before that when you look at the at the Babylonians you look at the Indians you look at the Egyptians they had devised all of these rules than the work and there were also rules that tend to be kept by a small clique of people usually a priestly class of some sort this was esoteric knowledge because this was knowledge that would help you when you're standing up in the heavens but but the Greeks were much more open about their mathematical knowledge and they also wanted to be able

to justify it absolutely when I make a particular mathematical claim it's not just because my teacher has told me this is so I want to be able to justify it what was unique about the Greeks is that they had proof by contradiction in geometry nobody else seems to have done that and the way you prove something by contradiction is you assume the opposite of what you're trying to prove and then you show that that leads to a contradiction and therefore the thing you're trying to prove must be true but the idea that you would try

to prove something in geometry which is after all supposed to be about truths by assuming that it's false that seems like a really really weird thing to do and but the Greeks because geometry and philosophy grew up hand-in-hand and because philosophical arguments used the principle of contradiction it was a natural thing for them to do and the real person who led this effort was was human so we're now looking around the year of 300 before the Common Era Euclid almost certainly was not our team alone certainly was the head of the school and and he

said would be the standard for mathematics in the thousands of years since that which was that you need to carefully justify any mathematical claim that you made and you do it by having very precise definitions say exactly what your terminology means that this goes right back to in philosophy precise definitions of what do you mean by different terms and then what are your assumptions clearly state the assumptions that you made and then given those clear definitions and those clear assumptions you can begin to build um Euclid also happened to work in Alexandria the museum the

temple of the muses that have just been established there and that would continue for six seven hundred years to be the most exciting center of mathematics in the entire world that's really an incredible legacy six to seven hundred years this one location is the center for all that was going on in between mathematics and I think one of the other things that contributed to the power of Greek mathematics was to have a center and one of the things that he did was to greatly refined trigonometry this the study of angles and how they relate to

two arc lengths and cord lengths that's something that had come up in earlier astronomical work of weeks and again when I say Greeks I really mean that Hellenistic civilization and the whole eastern Mediterranean but around the second century before the Common Era these tools of what today we refer to was trigonometry developed in the earliest forms Ptolemy went a great deal toward extending this and then sometime around that same time second third maybe as late as the fourth century of the Common Era these ideas from the Hellenistic eastern Mediterranean spread to South Asia and were

picked up by Indian astronomers and about the same time that mathematics was fading in the eastern Mediterranean it was beginning to roll [Music] [Music] [Music]