Tables of trigonometry have been used by the Babylonians for thousands of years. This is evidenced by the discovery of clay artifacts, shaped like books and aged 3700 years, in the early 1900s in southern Iraq by American archaeologists and diplomats Edgar Banks.
Babylonia is an ancient civilization located in the central-southern region of Mesopotamia. The Mesopotamian region includes the Sumerians, Akkad, and Assyria.
Reveals the history of Babylon
This area is very important because it became one of the earliest places of human life together in one civilization. The Babylonian population, often called Babylon, has a single written language that they use to study world-related matters around them.
The history that the Babylonians were the first to write from left to right and many made many documents inscribed. Babylonian mathematics refers to all mathematics developed by the Mesopotamians who are now Iraq since the beginning of Sumer until the beginning of the Hellenistic civilization. It was named "Babylonian Mathematics" because of the central role of the Babylonian region as a place to learn.
Hundreds of plates of clay were found as a source of Babylonian history dug up since the 1850s. The plates are written using a nail-shaped letter. The plates are written when the clay is still wet, and then burned in a furnace or dried under the hot sun even some of them are home-based work.
The Scientists Reveal the Phenomenon of Plimpton Trigonometry
At that time, no one could read the table known as the Plimpton 332. A few months ago, experts from the Department of Mathematics and Statistics at the University of New South Wales (UNSW), Australia, managed to read the intent of the table.
Mansfield realized that the information he needed was in missing pieces of P322 that had been reconstructed by other researchers. “Those two ratios from the reconstruction really made P322 into a clean and easy-to-use trigonometric table,” he says. He and Wildberger concluded that the Babylonians expressed trigonometry in terms of exact ratios of the lengths of the sides of right triangles, rather than by angles, using their base 60 form of mathematics, they report today in Historia Mathematica. “This is a whole different way of looking at trigonometry,” Mansfield says. “We prefer sines and cosines … but we have to really get outside our own culture to see from their perspective to be able to understand it.
[1]
UNSW Mathematical and Statistical Scientist Daniel Mansfield says Plimpton 332 is the oldest and most accurate trigonometric table in the world, possibly used by architects to build temples, palaces, and canals. The Babylonians developed trigonometry 1,500 years before the Greeks and used sophisticated mathematical methods that can change the way we count.
Current trigonometric differences and Plimpton 332, Babiloni's mathematics using the basic 60, or sexagesimal, and not the current 10 systems. Because 60 is so much easier divided into three, the experts who studied the tablet, found that the calculations are much more accurate.
Relevance
This Plimpton illustrates the right-angle triangle shape using new trigonometric types based on ratios, not angles and circles. The old table contains not only the world's oldest trigonometric tables but is also the only truly accurate trigonometric table, for a very different Babylonian approach to arithmetic and geometry.
The Babylonians discovered their own unique form of trigonometry during the Old Babylonian period (1900-1600BCE), more than 1,500 years earlier than the Greek form. Remarkably, their trigonometry contains none of the hallmarks of our modern trigonometry - it does not use angles and it does not use the approximation. The Babylonians had a completely different conceptualization of a right triangle. They saw it as half of a rectangle, and due to their sophisticated sexagesimal (base 60) number system, they were able to construct a wide variety of right triangles using only exact ratios. [2]
This means having great relevance for our modern world. Babylonian Babylon may have been out of fashion for over 3000 years but has practical applications that may be in surveying, computer graphics, and education. This is a rare example of the ancient world that teaches us something new.
Earlier, Greek astronomer, Hipparchus was considered the father of trigonometry, with a 'chorus table' inside a circle. This is considered the oldest trigonometric table. The table read by Hipparchus found in the ancient city of Sumni, Larsa was between 1822 and 1762 BC. It's now in Rare Book and Manuscript Library at Columbia University New York. So Plimpton 322 preceded Hipparchus for more than 10 centuries.
The Mathematical Facts
Recent mathematical evidence suggests that the inscribed tablet is the work of the Sumerians, who built an ancient civilization in Mesopotamia. They developed a complicated system of metrology since 3000 BC. From about 2500 BC, the Sumerians wrote the multiplication tables on clay plates relating to geometry and division. The current trace of the Babylonian number system also refers to this period.
Most of the known clay tablets date from 1800 to 1600 BC and cover topics of fractions, algebra, quadratic and cubic equations, and the calculation of regular numbers, inverse multiplication, and twin prime numbers.
The plates also include multiplication tables and methods of solving linear equations and quadratic equations. The Babylonian tablet 7289 BC provides almost an accurate for √2 to five decimal places.
It has been conjectured that Babylonian advances in mathematics were probably facilitated by the fact that 60 has many divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 - in fact, 60 is the smallest integer divisible by all integers from 1 to 6), and the continued modern-day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 x 6) degrees in a circle, are all testaments to the ancient Babylonian system. It is for similar reasons that 12 (which has factors of 1, 2, 3, 4 and 6) has been such a popular multiple historically (e.g. 12 months, 12 inches, 12 pence, 2 x 12 hours, etc). [3]
The Babylonian mathematical text is very numerous and very well edited. The Babylonian mathematical system is sexagesimal or base number 60. Major advances in mathematics occur for two reasons.
The first, the number 60 has many divisors that are 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30, which makes calculations much easier. The second the Babylonians had a real number system where the left-handed digits had a larger value such as a 10-based number.
Attainment in other mathematical sciences is the discovery of the value of the square root, even the Babylonian scientists have demonstrated Pythagorean theory, long before Pythagoras itself arose with his theory and this is proved by Dennis Ramsey who translated an ancient record dating from 1900 BC.
The Babylonians were also familiar with the general rule of measuring an area. They measure the circumference of the circle 3 times the diameter and its breadth as one of twelve squares of the circle, and if the count is true, then the value of π will be worth 3.
Sumerian and Babylonian mathematics was based on a sexagesimal, or base 60, numeric system, which could be counted physically using the twelve knuckles, on one hand, the five fingers on the other hand. Unlike those of the Egyptians, Greeks, and Romans, Babylonian numbers used a true place-value system, where digits written in the left column represented larger values, much as in the modern decimal system, although of course using base 60, not base 10. Thus, 1 1 1 in the Babylonian system represented 3,600 plus 60 plus 1, or 3,661. [4]
Babylonian mathematics was written using the sexagesimal number system (base-60). The use of sexagesimal numbers can be seen in the use of time units of 60 seconds for a minute, 60 minutes for one hour, and on the use of angular units of 360 (60 x 6) degrees for one round of circles.
The use of seconds and minutes on a circular arc representing fractional degrees. The progress of the Babylonians in mathematics is supported by the fact that 60 has many divisors.
The Babylonians had a true place-value system, where the numbers written on the left-hand lane represented a larger value, as in the decimal system.
However, there is a lack of equality of decimal point, so the value of the place of a symbol is often to be approximated by context. At this time also has not found the number zero.
For a certain positional system, a convention is required of numbers that denote the uniqueness of a number. For example decimal 12345 means:
1 x 104 + 2 x 103 + 3 x 102 + 4x 10 + 5
The positional sexagesimal positional system Babylonia embraces the method of writing as above, ie that the rightmost position is for units up to 59, one side to the left is for 60 x n, where 1 is less than = n less than = 59 and so on. Now we use a notation where numbers are separated by commas, for example, 1.57,46,40 denotes sexagesimal numbers 1 × 60 ranks 3 added 57 times 60 power two plus 46kali 60 added 40. That is, in decimal notation is worth 424000.
But there are still problems with this system. Since two are expressed with two characters each representing a unit, and 61 are denoted by one character for one unit as the first number and as the second number is an identical character for one unit then the sexagesimal numbers Babylonia 1,1 and 2 are essentially expressed similarly. However, this is not the real issue because the spaces between the characters show the differences.
In symbols for 2, both characters stating the units are grazed together and become single symbols. In number 1.1 there is a space between them.
One more serious problem is the fact that there is no zero to declare an empty position. Sexagesimal numbers denoting the numbers 1 and 1.0 for 1 and 60 decimal places have exactly the same statements and spaces do not make a difference. Perhaps the subsequent Babylonian civilization has established a symbol to declare emptiness.
Conclusion
Babylonia is an ancient civilization located in the central-southern region of Mesopotamia. History says that the Babylonians were the first to write from left to right, and many made many documents inscribed. More than 400 clay plates were found as a source of Babylonian history unearthed since the 1850s. The plates are written using nail-shaped writing.
Attainment in other mathematical sciences is the discovery of the value of the square root, even Babylonian scientists have demonstrated Pythagorean theory, long before Pythagoras itself arose with his theory. The Babylonians were also familiar with the general rule of measuring an area. This distance measurement is converted to one mile-the time used to measure the Sun's journey, which represents the length of time.
Babylonian mathematics was written using the sexagesimal number system (base-60). The use of sexagesimal numbers can be seen in the use of time units of 60 seconds for a minute, 60 minutes for one hour, and at the use of angle units of 360 (60 x 6) degrees for one circle round, also the use of seconds and minutes in circular arcs representing fractions level.
Major advances in mathematics occur for two reasons. First, the number 60 has many divisors that are 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30, which makes calculations much easier. In addition, the Babylonians had a real number system where the left-handed digits had a larger value such as a 10-based number.
Reference
EndNote:
1. Ancient-babylonian-tablet-source
2. First-trigonometrysource
3. Sumerian source
4. Story of mathematics source
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This is very informative. Thanks
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