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... 20 exp 3) + (0 x 20 exp 2) + (0 x 20) + (0 x 1) = 8000 Mayan 1000 is (1 x (18 x 20 exp 2) ) + (0 x (18 x 20) ) + (0 x 20) + (0 x 1) = 7200 The Mayan culture was a viable culture, however primitive, and it might have gone on to greatness in modern times if it had survived the European onslaught. The Europeans brought Smallpox from Europe to the Mayan territory in what is now Music. This decimated the population so that there are few descendants today. We can speculate that they simply never needed any pure math, but only used it for very practical concrete records. It stands to reason that one might never need to count anything that one did not have immediately available. One does not count cows one does not have.
The use of zero as a notation of having none of a quantity simply was not practical. "While Babylonian astronomers' place-value notation was apparently lost in the collapse of their civilization, three other cultures later reinvented remarkably similar systems. Chinese scientists, in the second century before Christ, devised a place-value code devoid of the digit 0 and using the bases 5 and 10... Indian mathematicians, finally, bequeathed humanity the place-value notation in base 10 that is now in use throughout the world. " 4 (Dehaene, Stanislas 1997) The Mayan culture was already mentioned. "A series of strokes seem to provide a more transparent way of denoting numbers, one that is easier to learn. And perhaps this was the implicit logic of the Sumerian, Chinese, and Mayan scientists. However we have seen that it is incorrect. " 4 (Dehaene 1997, 100) The position of an integer determines the quantity it represents, the principle involved is called positional notation.
The decimal system of positional notation is due to the Hindus; and they are credited with the first use of zero as a quantity, though there is no definitive proof of this. The use of zero as a quantity tis then thought to have been carried by traders to China and thence to Greece, where it was finally used by astronomers. The major reason the use of zero did not evolve earlier in Greek, was likely that most Greek mathematics were based on geometry, and were not at all concerned with quantity. Around 500 AD, Ariybhata, in India, devised a positional system for numbers, and he called his place holder kha. There are some arguments that the zero was actually used by Greek astronomers first, and then its use migrated back to India, but they are not very popular. What is absolutely known is that the use of zero as a quantity cand be substantiated for around 650 A.
D. in India. There are some earlier manuscripts which show a dot used as a place holder, but there are also some documents which show the dot as represented an unknown quantity. A stone table dated for 876 is the first documented use of zero as we know it.
The character was smaller than the one we use, but it was the same shape. The Greek astronomers also used this character. However, it was still not a quantity. Indian mathematicians Brahmagupta, Mahavira and Bhaskara tried to resolve the difficulty of understanding zero as a quantity in a book. Brahmagupta, in the seventh century, explained that if you subtract any number from itself, you get zero. He also postulated that the sum of zero and a negative number would be negative, and the sum of zealand a positive number would be positive.
Of course, the sum od zero and zero would be zero. Subtraction was a little more difficult to explain, but we can see the beginning of a number line when he postulates that subtracting any negative number from zero would be positive, and subtracting any positive number from zero would be negative. Subtract zero from a positive and it is positive with the reverse tru for subtracting zero from a negative. Of course zero minus zero is zero.
He also discovered that multiplying by zero is zero, but seems to have tripped on division, postulating that n divided by zero would be n/ 0. It seems to have simply gotten away from him, brilliant as he must have been to get this far. We still have trouble explaining this to our children so they understand it. About 200 years later, Mahavira wrote Ganita Sara Samgraha as an updating of Brahmagupta's book. He correctly states that: -... a number multiplied by zero is zero, and a number remains the same when zero is subtracted from it.
However, he also misses the mark with: a number remains unchanged when divided by zero. Bhaskara wrote over 500 years after Brahmagupta, but he also struggled with these ideas. He wrote: A quantity divided by zero becomes a fraction the denominator of which is zero. This fraction is termed an infinite quantity. In this quantity consisting of that which has zero for its divisor, there is no alteration, though many may be inserted or extracted; as no change takes place in the infinite and immutable God when worlds are created or destroyed, though numerous orders of beings are absorbed or put forth. If what he finally said were true then 0 times?
must be equal to every number n, so all numbers are equal. They just never got it that one simply cannot divide by zero. However, their absolutely brilliant work was carried to the Islamic and Arabic mathematicians in the west and it went forth from there to China. The hindu al-Khwarizmi wrote Al " Khwarizmi on the Hindu Art of Reckoning which describes the Indian place-value system of numerals based on 0. This was the first work denoting zero used as a quantity in a positional system of notation. However, it was not until the work of Ibn Ezra in the twelfth century that the use of zero finally travelled to Europe.
He wrote three treatises describing the use of decimal fractions and positional notation involving nine characters (numbers) and zero. The Book of Numbers describes a left to right positional system with global (wheel or circle in Arabic) as a zero quantity. Some time later in the 12 th century al-Samawal wrote, If we subtract a positive number from zero the same negative number remains... if we subtract a negative number from zero the same positive number remains. Finally, in 1247 the Chinese mathematician Ch " in Chiu-Shao wrote Mathematical treatise in nine sections which uses the symbol O for zero.
A little later, in 1303, Zhu Shijie wrote Jade Mirror Of The Four Elements which again uses the symbol O for zero. Leonardo of Pisais, also called Fibonacci, i. e. son of Bonaccio. Leonardo was the first great mathematician to advocate the adoption of the "Arabic notation", which he documented in his book: Liber Abc. Calculations using a zero was what the early Christians adopted first.
It was an easy step to make from using the abacus and the alice. The use of columns was gradually abandoned For the zero, the Latins adopted the name zephyrus, from the Arabic site (sir = empty); from which we get the word cipher. It is interesting to note that the masses, or commoners, were first to accept the new notation, while the nobility and learned intelligentsia were slow to change. Nearly 100 years later, a law had to be made in Florence forbidding bookkeepers to use Arabic notation, because there was so much fraud connected with the absence of a standard.
The symbol for zero was not completely accepted until the 1800 s. As it was throughout history, the idea that we need a representation for zero, this "nothing" in our system of numerals, continues to be a very difficult concept for students to understand. Zero has caused, and continues to cause, considerable difficulty for learners of mathematics (Wheeler and Feghali 1983; Wheeler 1987; Carpenter, Franke, and Levi 2002). 5 It is a little surprising that the history of zero covers nearly eighteen centuries from the first hint of its advent, about 200 BC, to we who grew up with it. However, if you think about it, this concept is so intangible that mathematicians are still discussing this number that isn't a number. There must be a few geniuses who really understand the nature of zero, mathematically, but few others.
We use it, but we find it very difficult to explain its actual nature. It is not nothing, but rather it is none of something. Works Cited 1. Clawson, Calvin C. 1996.
Mathematical Mysteries: The Beauty and Magic of Numbers. Cambridge, MA: Perseus Books. 2. Mc Quillin, Kristen. July 1997 (revised January 2004) A Brief History of Zero. Page 2 3. Mc Quillin, Kristen.
July 1997 (revised January 2004) A Brief History of Zero. Pps 3 - 5 4. Dehaene, Stanislas. 1997, The Number Sense: How the Mind Creates Mathematics (New York: Oxford University Press), 100 5. Anthony, Glenda J.
and Walshaw, Margaret A. , Aug. 2004. "Zero: A "None" Number? , " Teaching Children Mathematics 6. Maya, Indigenous People of Mexico and Central America. 2004. In The Columbia Encyclopedia 6 th ed. , edited by Lagass, Paul. New York: Columbia University Press. 7.
Cajori, Florian, 1919, A History of Mathematical, Macmillan 8. Struck, Dirk J. , 1948. A Concise History of Mathematics, ; Dover Publications
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