Zero

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Once upon a time there was no zero. Of course people knew if they had nothing, but there was no mathematical notation for it. Zero was independently invented only three times. The first recorded zero is attributed to the Babylonians in the 3rd century BC. A long period followed when no one else used a zero place holder. But then the Mayans, halfway around the world in Central America, independently invented zero in the fourth century CE. The final independent invention of zero in India was long debated by scholars, but seems to be set around the middle of the fifth century. It spread to Cambodia around the end of the 7th century. From India it moved into China and then to the Islamic countries. Zero finally reached western Europe in the 12th century. In today's modern mathematics, we have become accustomed to zero as a number. It's hard to believe that most ancient number systems didn't include zero. The Mayan civilization may have been among the first to have a symbol for zero. The Mayas flourished in the Yucatan peninsula of Mexico about 1300 years ago. They used the as a placeholder, in a vertical place-value system. It is considered one of their cultures greatest achievements. 

The ancient Egyptians, Romans, and Greeks alike had no symbol for zero. In Greek geometry, zero and irrational numbers were impossible. The Greeks made great strides in mathematics, but it was all done with a number system without zero. The Greek astronomer Ptolemy (ca. A.D. 150) was the first to write a zero at the end of a number. For this he used a circular symbol. 

In ancient Babylonian history there was no use of the zero. In the later Babylonian or during the Seleucid period a special symbol, which was also used as a separation mark between sentences, came into use for a zero. There's a definite possibility that the Babylonians used this mark for a zero within a number, as early as the end of the eighth century B.C. Up until the time of Aristotle, there seems to be no...
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