Beginning Time to Anciment Egypt and Babylonia
By: Anita Mayasari/08301244026/PM NR'08
In the period before about 4000 B.C. we don't have the records of historical data. But it can be changed by "conjectural supplementation" which more known as guessing. Our earliest historical records indicate that by about 4000 B.C. peoples had already developed an elementary number system, a calender, and a system of weight and measure. Experiment have indicate that even some of animals have an elementary skill to count. And be based on this experiment we can conclusion that primitive man could distinguish between certain quantities.
Mathematics had to became more sophisticated like their culture which sophisticated too. When they stop the roaming hunter and became to settled farmer, a counting grew to be importance. They needed to know it to count their sheep were missing. Caused villages and trade grew, so they had to be able to deal with others on a consistent and fair basis. Trade and commerce required a higher level of mathematical ability. Peoples very needed a new tool that could be used to surpass these increased complexities. this developing society required a number system. The first number system maybe consisted of something like "1, 2, many". Some primitive tribes in now still use "1, 2, many" like their number system. Eventually "1, 2, many " became to "1, 2, 3, 4,..." (the system of counting we use today). These number system did not employ the some figures which we use today. In fact, they worked on different principles. An early method we use a scratches in the dirt, one scratches for one, two for two, and so on. If they began to deal with greater quantities, this system became too cumbersome so shortcuts were introduced. One symbol might take the places of ten others. In the Egyptian Hieroglyphic system.
These early number system had not two features which extremely useful in our modern number system:
1. There was no zero
2. Positional notations was not used
"Positional notations" is number system simply means that the positions of a digits determines its relative magnitude. For example the number 575 use the digit 5 twice, the first 5 has a value of five hundreds, the second 5 has a value of only five ones. The some symbol is used in two different positions. The positions of the digit a affects the numerical value. one the other hand, the system of scratches in the dirt does not employ positional notation. A system of positional notation was used by the Babylonian number system was almost complicated and since it was based on sixty instead of ten. And their also no symbol for zero. But they confess of zero as a number and the invention of a symbol for zero came sometimes between 300 B.C. and 750 A.D.
While prehistoric people had not apparent real usage for fractions, and the more advanced ancient civilizations did need and use fraction. In Egyptian Hieroglyphic numeral system, find examples fractions.
The Babylonians who were very good at generals computations skills, also had a knowledge of reciprocals, squares,cubes and multiplications tables the Babylonians even began to develop algebra. They could solve quadratic equations and some equations of a degree greater than two. Both ancient Egyptian and Babylonian mathematics advanced to a level which allowed for some manipulation of fractions, some elementary algebraic operations, and some basis geometry treatment.
As the roaming primitive hunters settled down and established communities, certain geometric problems naturally arose. Measurement of distances, areas, and volumes became important. Farmers wanted to be able to relocate their land boundaries after a river flood. In Egypt, for example, the Nile would periodically flood and after its course. Farmers also wanted to determine the amount of grain they had so that they could trade wisely. They wanted to know how much grain a particular building would hold. The Babylonians were mathematically superior to the Egyptians, especially at computations and algebra. The Egyptians lived quiet, peaceful lives in the fertile Nile valley, which was geographically immune to foreign invasions. In contrast, the Babylonians were susceptible to invasions, and they led stimulating, challenging live as various government assumed power. This may account for their mathematical superiority. Both the Egyptians and the Babylonians could find the areas of square,rectangle, and certain simple triangles. They could find the volume of cubes and boxes. The Egyptians could even find the volume of a truncated pyramid. Eric Temple Bell, a renowned historian of mathematics, has called the solutions.
The beginnings of algebra and geometry were mostly elementary and practical. Very little "theory" was being developed. The Egyptians and Babylonians were interested in mathematics because it could be used to solve many of their daily problems. Their concern was with how to obtain results rather than with why those results occur. Efforts were applied to specific problems and no movement toward abstraction and generalizations was initiated. While there were some theoretical pursuits, the mathematical developments from the beginning of man to the ancient Egyptian and Babylonian civilizations can be characterized as "utilitarian". The value of mathematical results were judged mostly by their usefulness in practical situations.
This concept of "utilitarianism" gradually changed with economic and political changed. In the period of roughly 1300 -600 B.C., wars and migrations weakened both Egypt and Babylonia as the Greek. Phoenician, Hebrew, and Assyrian civilizations became stronger. Technological progress included a changed from the Bronze Age to the Iron Age. Tools became easier and cheaper to produce. Agriculture, trade, and warfare were directly affected by the Iron Age and by its accompanying technological progress. The Egyptians and Babylonians lost their leadership in scholarly pursuits, and the Greeks eventually assumed this role. However, the Greek did much more than continue where the Egyptians and Babylonians left off. The Greeks injected a new life and spirit into intellectual pursuits, and this is particularly evident in their development of mathematics.
In the period before about 4000 B.C. we don't have the records of historical data. But it can be changed by "conjectural supplementation" which more known as guessing. Our earliest historical records indicate that by about 4000 B.C. peoples had already developed an elementary number system, a calender, and a system of weight and measure. Experiment have indicate that even some of animals have an elementary skill to count. And be based on this experiment we can conclusion that primitive man could distinguish between certain quantities.
Mathematics had to became more sophisticated like their culture which sophisticated too. When they stop the roaming hunter and became to settled farmer, a counting grew to be importance. They needed to know it to count their sheep were missing. Caused villages and trade grew, so they had to be able to deal with others on a consistent and fair basis. Trade and commerce required a higher level of mathematical ability. Peoples very needed a new tool that could be used to surpass these increased complexities. this developing society required a number system. The first number system maybe consisted of something like "1, 2, many". Some primitive tribes in now still use "1, 2, many" like their number system. Eventually "1, 2, many " became to "1, 2, 3, 4,..." (the system of counting we use today). These number system did not employ the some figures which we use today. In fact, they worked on different principles. An early method we use a scratches in the dirt, one scratches for one, two for two, and so on. If they began to deal with greater quantities, this system became too cumbersome so shortcuts were introduced. One symbol might take the places of ten others. In the Egyptian Hieroglyphic system.
These early number system had not two features which extremely useful in our modern number system:
1. There was no zero
2. Positional notations was not used
"Positional notations" is number system simply means that the positions of a digits determines its relative magnitude. For example the number 575 use the digit 5 twice, the first 5 has a value of five hundreds, the second 5 has a value of only five ones. The some symbol is used in two different positions. The positions of the digit a affects the numerical value. one the other hand, the system of scratches in the dirt does not employ positional notation. A system of positional notation was used by the Babylonian number system was almost complicated and since it was based on sixty instead of ten. And their also no symbol for zero. But they confess of zero as a number and the invention of a symbol for zero came sometimes between 300 B.C. and 750 A.D.
While prehistoric people had not apparent real usage for fractions, and the more advanced ancient civilizations did need and use fraction. In Egyptian Hieroglyphic numeral system, find examples fractions.
The Babylonians who were very good at generals computations skills, also had a knowledge of reciprocals, squares,cubes and multiplications tables the Babylonians even began to develop algebra. They could solve quadratic equations and some equations of a degree greater than two. Both ancient Egyptian and Babylonian mathematics advanced to a level which allowed for some manipulation of fractions, some elementary algebraic operations, and some basis geometry treatment.
As the roaming primitive hunters settled down and established communities, certain geometric problems naturally arose. Measurement of distances, areas, and volumes became important. Farmers wanted to be able to relocate their land boundaries after a river flood. In Egypt, for example, the Nile would periodically flood and after its course. Farmers also wanted to determine the amount of grain they had so that they could trade wisely. They wanted to know how much grain a particular building would hold. The Babylonians were mathematically superior to the Egyptians, especially at computations and algebra. The Egyptians lived quiet, peaceful lives in the fertile Nile valley, which was geographically immune to foreign invasions. In contrast, the Babylonians were susceptible to invasions, and they led stimulating, challenging live as various government assumed power. This may account for their mathematical superiority. Both the Egyptians and the Babylonians could find the areas of square,rectangle, and certain simple triangles. They could find the volume of cubes and boxes. The Egyptians could even find the volume of a truncated pyramid. Eric Temple Bell, a renowned historian of mathematics, has called the solutions.
The beginnings of algebra and geometry were mostly elementary and practical. Very little "theory" was being developed. The Egyptians and Babylonians were interested in mathematics because it could be used to solve many of their daily problems. Their concern was with how to obtain results rather than with why those results occur. Efforts were applied to specific problems and no movement toward abstraction and generalizations was initiated. While there were some theoretical pursuits, the mathematical developments from the beginning of man to the ancient Egyptian and Babylonian civilizations can be characterized as "utilitarian". The value of mathematical results were judged mostly by their usefulness in practical situations.
This concept of "utilitarianism" gradually changed with economic and political changed. In the period of roughly 1300 -600 B.C., wars and migrations weakened both Egypt and Babylonia as the Greek. Phoenician, Hebrew, and Assyrian civilizations became stronger. Technological progress included a changed from the Bronze Age to the Iron Age. Tools became easier and cheaper to produce. Agriculture, trade, and warfare were directly affected by the Iron Age and by its accompanying technological progress. The Egyptians and Babylonians lost their leadership in scholarly pursuits, and the Greeks eventually assumed this role. However, the Greek did much more than continue where the Egyptians and Babylonians left off. The Greeks injected a new life and spirit into intellectual pursuits, and this is particularly evident in their development of mathematics.
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