Matemáticas Babilónicas
Los babilónicos vivieron en Mesopotamia en medio de los ríos Tigris y Éufrates, ellos desarrollaron diversos avances matemáticos los cuales se conocen hasta nuestros días, toda su simbología tanto de escritura y numeración fue escrita en tablillas de arcilla mojada y cocidas al sol que hasta hoy se conservan algunas. La mayoría de tabillas poseían operaciones y problemas matemáticos, lo más llamativo de las escrituras babilónicas es que habían desarrollado tablas para las diferentes operaciones matemáticas, multiplicar, números recíprocos, potencias, cuadrados que utilizaban para dividir.
La división fue la operación más complicada para ellos fue la división, no poseían un algoritmo para poder desarrollarla y por eso utilizaban fórmulas más complejas, también la representación de números era algo complejo, esta dificultad se presentó por que su sistema de numeración no posea un cero por tanto al representar cantidades como 2062 debían basarse en el contexto que aplicaba.
La mayoría de problemas eran cuestiones de la vida diaria, como cuentas, prestamos, intereses. En álgebra, podían resolver problemas de primero, segundo, tercero y hasta cuarto grado, así como ecuaciones simples. En cuanto a la geometría, ya conocían el famoso teorema de Pitágoras y además utilizaban y estudiaban los triángulos y sus propiedades.
Los babilónicos, fueron los pioneros en la medición del tiempo, dividieron el día en 24 horas, las horas en 60 minutos y los minutos en 60 segundos, este es el sistema que utilizamos actualmente y es un sistema sexagesimal (base 60).
Los babilónicos fueron muy ordenados en el registro de sus fórmulas matemáticas ya que en la actualidad se conservan las tablillas de arcilla y se han traducido para analizar sus procesos matemáticos, los símbolos utilizados para representar los números eran muy sencillos aunque la representación de las cantidades superiores se dificultaba.
Según historiadores matemáticos, los estudios de las primeras civilizaciones para abordar el inicio del conteo según las necesidades de los antepasados, se basaron en agrupaciones de diferentes formas de tal manera que significara una forma de expresar una cantidad aunque no todas podrían asegurarse que fueran para situaciones de conteo, si no para expresar otras formas de pensamiento filosófico como el de mantener el orden de la vida de una manera equilibrada.
Las primeras muestras de agrupaciones relacionadas con un sistema de conteo, se han encontrado grabadas en su mayoría en huesos de extremidades de animales que cazaban, en piedras o cuernos, los cuales se han estudiado muy detalladamente y se han encontrado relaciones con números pares e impares hasta con números primos y algunas operaciones de aritmética. Algunas de estas piezas encontradas, llevan grabadas agrupaciones en base quince y en base treinta más o menos, que hacen referencia a los periodos lunares de un mes ya que una de las primeras necesidades fue medir el tiempo que además conduce hacia la mujer, planteando teorías que fueron las primeras matemáticas que necesitaban medir el tiempo de embarazo y los periodos menstruales.
Para representar los números eran muy sencillos aunque la representación de las cantidades superiores se dificultaba.
Matemáticas en el Egipto Antiguo
Egipto, conocida como una de las civilizaciones antiguas con mayor desarrollo tecnológico, había desarrollado conocimientos que son ciertamente considerados muy avanzados, en cuanto a matemáticas, podían desarrollar cualquier tipo de problema matemático que se les presentara y todo lo relacionaban según su necesidad, por ejemplo, cuando se inundaba el río Nilo, tenían que volver a delimitar los linderos ya que anualmente el río se los borraba, también se consideraban maestros en geometría por la construcción de pirámides y grandes templos además de organización en el comercio y repartos de bienes.
Los egipcios buscaban la manera más práctica para resolver sus problemas por lo cual no se preocuparon por darle un significado teórico a sus construcciones matemáticas, por eso se consideraban los precursores de los griegos. Poseían un dominio sobre los números y sus operaciones, además la suma era bien estructurada y no tenían problemas para resolverla, la multiplicación la hacían duplicando la suma y la división a la inversa, a pesar de esto el sistema numérico que tenían en base diez por medio de la yuxtaposición, no les permitió avanzar en más descubrimientos matemáticos pero alcanzaron a utilizar las fracciones y no presentaban problemas en resolver situaciones de ese tipo.
Para resolver sus problemas matemáticos, encargaban a un especialista para que realizara los cálculos de las construcciones que además eran muy precisos en cuanto a volumen, alcanzaron a identificar los números naturales y racionales positivos de numerador uno, resolvían ecuaciones en segundo grado y raíces cuadradas para problemas de superficie, además algo muy importante fue la aproximación del número pi=3,16 que había sido lo más exacto hasta entonces.
Algunos documentos encontrados, datan de 1600 a.c, como el papiro de Rhind y el papiro de Moscú, donde se encuentran problemas matemáticos resueltos con su proceso. Se dice también que conocían muy bien los triángulos y que ya los utilizaban como herramientas geométricas para hallar ángulos y medidas de lados por lo que sería el inicio del teorema de Pitágoras que ahora conocemos aunque no sabían cómo expresarlo.
Aporte de la civilización árabe a las
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The Babylonians lived in Mesopotamia in the middle of the Tigris and Euphrates rivers, they developed various mathematical advances which are known to this day, all their symbolism both writing and numeration was written on wet clay tablets and cooked in the sun that until now they keep some. The majority of tabillas had operations and mathematical problems, the most striking of the Babylonian writings is that they had developed tables for the different mathematical operations, multiply, reciprocal numbers, powers, squares that they used to divide.
The division was the most complicated operation for them was the division, they did not have an algorithm to develop it and therefore they used more complex formulas, also the representation of numbers was somewhat complex, this difficulty arose because their numbering system does not have a Therefore zero when representing quantities as 2062 should be based on the context that applied.
Most problems were issues of daily life, such as accounts, loans, interests. In algebra, they could solve problems of first, second, third and even fourth degree, as well as simple equations. As for geometry, they already knew the famous Pythagorean theorem and also used and studied the triangles and their properties.
The Babylonians, were the pioneers in the measurement of time, divided the day into 24 hours, the hours into 60 minutes and the minutes into 60 seconds, this is the system that we currently use and is a sexagesimal system (base 60).
The Babylonians were very ordered in the register of their mathematical formulas since at present the clay tablets are conserved and they have been translated to analyze their mathematical processes, the symbols used to represent the numbers were very simple although the representation of the higher quantities it was difficult.
According to mathematical historians, the studies of the first civilizations to approach the beginning of the count according to the needs of the ancestors, were based on groups of different forms in such a way that it meant a way of expressing a quantity although not all could be sure that they were for situations of counting, if not to express other forms of philosophical thought such as maintaining the order of life in a balanced way.
The first samples of groups related to a counting system, have been recorded mostly in bones of extremities of animals that hunted, in stones or horns, which have been studied in great detail and have found relationships with even and odd numbers even with prime numbers and some arithmetic operations. Some of these pieces found, recorded groupings based on fifteen and base thirty more or less, which refer to the lunar periods of a month since one of the first needs was to measure the time that also leads to women, raising theories which were the first mathematics that needed to measure the time of pregnancy and menstrual periods.
To represent the numbers were very simple although the representation of the higher quantities was difficult.
Egypt, known as one of the oldest civilizations with greater technological development, had developed knowledge that is certainly considered very advanced, in terms of mathematics, could develop any kind of mathematical problem that was presented to them and everything related according to their needs, for example , when the Nile River was flooded, they had to redefine the boundaries since the river was erased annually, they were also considered masters in geometry by the construction of pyramids and great temples as well as organization in commerce and distribution of goods.
The Egyptians looked for the most practical way to solve their problems so they did not worry about giving a theoretical meaning to their mathematical constructions, that's why they were considered the precursors of the Greeks. They had a domain over numbers and their operations, in addition the sum was well structured and had no problem solving it, the multiplication was made by duplicating the sum and division in reverse, despite this the number system they had in base ten by In the middle of the juxtaposition, it did not allow them to advance in more mathematical discoveries but they managed to use the fractions and did not present problems in solving situations of that type.
To solve their mathematical problems, they asked a specialist to perform the calculations of the constructions that were also very precise in terms of volume, they managed to identify the natural and rational positive numbers of numerator one, they solved equations in the second degree and square roots for surface problems, also something very important was the approximation of the number pi = 3.16 that had been the most accurate until then.
Some documents found, date from 1600 a.c, as the papyrus of Rhind and the papyrus of Moscow, where mathematical problems are solved with their process. It is also said that they knew very well the triangles and that they already used them as geometric tools to find angles and side measures for what would be the beginning of the Pythagorean theorem that we now know although they did not know how to express it.
The Islamists were great contributors to this knowledge. Being the unit the most important element in mathematics, they were in charge of studying and discovering in it immutable and true things. Mathematics was an important art for those thinkers, who had discovered that numbers had to do with everything, what their environment made connection with. Pythagoras was a very important thinker for this time; I delve into the subject, not with the interest of responding to calculation problems, but the superior qualities that it represented.
This land would give a great potential of mathematical thinkers such as Pythagoras, Plato, Euclides, Archimedes, lefanto ... among others who would be of great renown and with great recognition to the present, because their ideas developed would be contributions that would spend centuries having a valid validity . And although they had large contributions, they did not have an easy-to-use numerical system.
Image result for image of the Arabic civilization numbers
https://sites.google.com/site/educmate02ipm/my-reading-list/civilizacion-arabe
The Arabs undertook to discover the zero as part of the nine known digits, the zero. But beyond that they would create an Indo-Arabic system based on its angles.
Generating with it great discoveries such as chess, invention that would have a humble collection to the king, he asked to give a grain in the first box and the next double the amount, apparently very simple principle to pay, would determine that there would be enough grain in the kingdom to pay him. However the Persian Al-Biruni would give the solution. An important Persian was Al-Karaŷí who would discover the decimal figures, discover a figure very close to the pi number, build the first machine to calculate and was the first to solve the newton binomial several centuries before it appeared newton. Innumerable are the contributions that this civilization would leave as arithmetic, trigonometry, geometry, trigonometry, algebra.
Considered as the founders of arithmetic, they made algebra an exact science, laid the foundations of analytical geometry, and gave body of science to plane and spherical trigonometry. They clarified and simplified mathematical science from being exclusive of the wise to a practical use. They found in mathematics an ideal way to express the world
Aporte de la civilización árabe a las
Los islámicos fueron grandes aportante a este saber. Siendo
la unidad el elemento más importante en las matemáticas, se encargaron ellos de
estudiar y descubrir en ella cosas inmutables y verdaderas. Las matemáticas
eran un arte importante para aquellos pensadores, que habían descubierto que los
números tenían que ver con todo, lo que su entorno hacia conexión. Pitágoras
fue un pensador muy importante para esta época; profundizo en el tema, no con
el interés de dar respuesta a problemas de cálculo, sino las cualidades
superior que esta representaba.
Esta tierra daría un gran potencial de pensadores matemáticos
como Pitágoras, platón, Euclides, Arquímedes, lefanto... entre otros quienes
serían de gran renombre y con gran reconocimiento hasta el presente, pues sus
ideas desarrolladas serian aportes que pasarían siglos teniendo una vigencia
valida. Y aunque tenían grandes aportes no tenían un sistema numérico fácil de
usar.
 |
| https://sites.google.com/site/educmate02ipm/my-reading-list/civilizacion-arabe |
Los árabes se encargaron de descubrir el cero como parte de
los nueve dígitos conocidos, el cero. Pero más allá crearían un sistema indo
arábigo basado en los ángulos del mismo.
Generando con ello grandes descubrimientos como el ajedrez,
invento que tendría un humilde cobro al rey, el pidió que le dieran un grano en
el primer casilla y en la siguiente doblaran la cantidad, de principio
aparentemente muy sencillo de pagar, determinaría que no habría suficiente
grano en el reino para pagarle. Sin embargo el persa Al-Biruni daría la
solución. Un persa importante fue Al-Karaŷí
quien descubriría las cifras decimales, descubriría una cifra muy
cercana a el numero pi, construyo la primera máquina para calcular y fue el
primero en resolver el binomio de newton varios siglos antes de que apareciera
newton. Innumerables son los aportes que esta civilización dejaría como la
aritmética, trigonometría, geometría, trigonometría, álgebra.
Considerados como los fundadores de la
aritmética, hicieron del álgebra una ciencia exacta, sentaron las bases de la
geometría analítica, y dieron cuerpo de ciencia a la trigonometría plana y
esférica. Aclaran y simplificaron la ciencia matemática pasando de ser exclusivo
de los sabios a un uso práctico. Ellos encontraron en las matemáticas una manera ideal de expresar el mundo.
Mayas
Tras la obra evangelizadora de los españoles liderados por
fray diego, incendiarían toneladas de manuscritos que guardaban celosamente los
caiques mayas, pues ellos a ahora eran una potencia. Su forma de contar, su
calendario, y todos los hallazgos astronómicos, tenían gran misterio.
Los mayas fueron una cultura muy tuvieron gran
reconocimiento, por su interés en medir
el tiempo y comprender los cielos, para ello era necesario tener un gran manejo
de las matemáticas y desarrollo de las mismas. Mediante sus descubrimientos
encontraron el cero y aunque básicamente se considere la ausencia de cantidad,
sería un número importante para la representación de números complejo,
confirmando la existencia de los números negativos. Y aunque se atribuye
también a los hindúes realmente fueron los mayas ya que lo hallaron seiscientos
años antes.
Usaron solo tres símbolos para expresar su sistema numérico,
un punto, una barra y un símbolo para el cero. Sus sistema numérico es conocido
como vigesimal, ya que hacían grupos de a veinte y con ello lograban potenciar
grandes cantidades. Realmente muy astuto pues solo usaban estos tres símbolos.
http://significadodelosnumeros.com/wp-content/uploads/2018/02/numeros-mayas.jpg
la creación del Ábaco fue otro gran recurso, pues mediante materiales muy
sencillos, con semillas y madera, lograrían un conteo de unidades.
Babylonian Mathematics
The Babylonians lived in Mesopotamia in the middle of the Tigris and Euphrates rivers, they developed various mathematical advances which are known to this day, all their symbolism both writing and numeration was written on wet clay tablets and cooked in the sun that until now they keep some. The majority of tabillas had operations and mathematical problems, the most striking of the Babylonian writings is that they had developed tables for the different mathematical operations, multiply, reciprocal numbers, powers, squares that they used to divide.
The division was the most complicated operation for them was the division, they did not have an algorithm to develop it and therefore they used more complex formulas, also the representation of numbers was somewhat complex, this difficulty arose because their numbering system does not have a Therefore zero when representing quantities as 2062 should be based on the context that applied.
Most problems were issues of daily life, such as accounts, loans, interests. In algebra, they could solve problems of first, second, third and even fourth degree, as well as simple equations. As for geometry, they already knew the famous Pythagorean theorem and also used and studied the triangles and their properties.
The Babylonians, were the pioneers in the measurement of time, divided the day into 24 hours, the hours into 60 minutes and the minutes into 60 seconds, this is the system that we currently use and is a sexagesimal system (base 60).
The Babylonians were very ordered in the register of their mathematical formulas since at present the clay tablets are conserved and they have been translated to analyze their mathematical processes, the symbols used to represent the numbers were very simple although the representation of the higher quantities it was difficult.
According to mathematical historians, the studies of the first civilizations to approach the beginning of the count according to the needs of the ancestors, were based on groups of different forms in such a way that it meant a way of expressing a quantity although not all could be sure that they were for situations of counting, if not to express other forms of philosophical thought such as maintaining the order of life in a balanced way.
The first samples of groups related to a counting system, have been recorded mostly in bones of extremities of animals that hunted, in stones or horns, which have been studied in great detail and have found relationships with even and odd numbers even with prime numbers and some arithmetic operations. Some of these pieces found, recorded groupings based on fifteen and base thirty more or less, which refer to the lunar periods of a month since one of the first needs was to measure the time that also leads to women, raising theories which were the first mathematics that needed to measure the time of pregnancy and menstrual periods.
To represent the numbers were very simple although the representation of the higher quantities was difficult.
Mathematics in Ancient Egypt
Egypt, known as one of the oldest civilizations with greater technological development, had developed knowledge that is certainly considered very advanced, in terms of mathematics, could develop any kind of mathematical problem that was presented to them and everything related according to their needs, for example , when the Nile River was flooded, they had to redefine the boundaries since the river was erased annually, they were also considered masters in geometry by the construction of pyramids and great temples as well as organization in commerce and distribution of goods.
The Egyptians looked for the most practical way to solve their problems so they did not worry about giving a theoretical meaning to their mathematical constructions, that's why they were considered the precursors of the Greeks. They had a domain over numbers and their operations, in addition the sum was well structured and had no problem solving it, the multiplication was made by duplicating the sum and division in reverse, despite this the number system they had in base ten by In the middle of the juxtaposition, it did not allow them to advance in more mathematical discoveries but they managed to use the fractions and did not present problems in solving situations of that type.
To solve their mathematical problems, they asked a specialist to perform the calculations of the constructions that were also very precise in terms of volume, they managed to identify the natural and rational positive numbers of numerator one, they solved equations in the second degree and square roots for surface problems, also something very important was the approximation of the number pi = 3.16 that had been the most accurate until then.
Some documents found, date from 1600 a.c, as the papyrus of Rhind and the papyrus of Moscow, where mathematical problems are solved with their process. It is also said that they knew very well the triangles and that they already used them as geometric tools to find angles and side measures for what would be the beginning of the Pythagorean theorem that we now know although they did not know how to express it.
Contribution of the Arab civilization to mathematics
The Islamists were great contributors to this knowledge. Being the unit the most important element in mathematics, they were in charge of studying and discovering in it immutable and true things. Mathematics was an important art for those thinkers, who had discovered that numbers had to do with everything, what their environment made connection with. Pythagoras was a very important thinker for this time; I delve into the subject, not with the interest of responding to calculation problems, but the superior qualities that it represented.
This land would give a great potential of mathematical thinkers such as Pythagoras, Plato, Euclides, Archimedes, lefanto ... among others who would be of great renown and with great recognition to the present, because their ideas developed would be contributions that would spend centuries having a valid validity . And although they had large contributions, they did not have an easy-to-use numerical system.
Image result for image of the Arabic civilization numbers
https://sites.google.com/site/educmate02ipm/my-reading-list/civilizacion-arabe
The Arabs undertook to discover the zero as part of the nine known digits, the zero. But beyond that they would create an Indo-Arabic system based on its angles.
Generating with it great discoveries such as chess, invention that would have a humble collection to the king, he asked to give a grain in the first box and the next double the amount, apparently very simple principle to pay, would determine that there would be enough grain in the kingdom to pay him. However the Persian Al-Biruni would give the solution. An important Persian was Al-Karaŷí who would discover the decimal figures, discover a figure very close to the pi number, build the first machine to calculate and was the first to solve the newton binomial several centuries before it appeared newton. Innumerable are the contributions that this civilization would leave as arithmetic, trigonometry, geometry, trigonometry, algebra.
Considered as the founders of arithmetic, they made algebra an exact science, laid the foundations of analytical geometry, and gave body of science to plane and spherical trigonometry. They clarified and simplified mathematical science from being exclusive of the wise to a practical use. They found in mathematics an ideal way to express the world
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