ZERO by Eli Draizen Introduction In the Middle Ages zero was sometimes thought of a "the creation of the devil" because it was nothing, which scared people. Now it is not scary because we know more about it and it is part of our everyday life. If you had three cookies and that's all there were, and you ate them, there would be zero left. That is a pretty familiar concept to people today. Throughout history, zero has been used numerous times and in different ways. For instance, zero had many names and symbols, unlike now. Different cultures had their own variation of zero. Their number systems were used in a variety of ways such as in base 60, 20, and 10. Zero plays a role in non-Euclidean geometry, which involves curves. Finally, properties of zero have been discovered throughout history.   Names for zero Since the beginning of history there have been many names and signs for zero. Through time names and symbols have evolved from "Sunya" in the 7th century, meaning 'empty' or 'void' in Sanskrit, the language of ancient India. We can trace it through Arabic 9th century which was called "as-skrit." Later it appears in Latin, in the 15th century, forming into zefirum. A century later the French and Italians had names such as "chiffre" and "zevero." Next the German word was ziffir in the 16th century. Starting from India we can see how the ideas of zero were shared and spread from east to west. For that reason it can be called "The Traveling Zeros."   Modern Number Systems (Base 10) The modern day system of base 10 is used by every culture in the world. It took a long time to create the base 10 system. The system has ten symbols from 0 to 9. These ten symbols can be combined to create any number in the universe. It is good to understand how the basics of the system work. For example, after the ten sequence from 0 to 9, the zero comes back as a place holder and pushes the number over. The zero now reappears in the units place and a one Is added to create ten (10). The one is now in the tens place. There is much more about the base ten system but it doesn't all revolve around zero.,p>  India Some of the origins of zero were invented in India. The properties of zero were first mentioned in 628 A.D. The Indian astronomer, Brahmagupta, was the first to think zero was nothing, void. He combined many ideas into one word, sunya, meaning empty, worthlessness, absence, etc. India is where Base 10 was invented and also where zero was moved from just a pace-holder to a number, such as n - n = 0.   Babylonia The Babylonians used to use a Base 60 system. This means that instead of 1 - 9 they used 1 - 60. Their zero was a place-holder, not technically a zero. If you subtract n - n it leaves nothingness, not zero, or no remaining value. They use the symbol to represent zero such as 2 0 15. Their 2015 wouldn't be the same as ours. It would be 2 X 60^2 + 0 X 60^1 + 10 + 5; 3615. The Babylonian system was pretty confusing. Mayan The Mayan system is hard to understand because it is a base of variations of 20. The Mayan symbol for zero looks kind of like a seashell or a human eye. It is also a place-holder. Here is an example of how the different bases systems work: Base 10: 43752 Base 60: 43572 = 4 X 60 ^4 + 3 X 60^3 + 5 X 6-^2 + 2 X 1 Base 20 (Mayan): 43572 = 4 (360 X 20 X 20) + 3 (360 X 20) + 5 X 360 + 7 X 20 + 2 X1 As you can see, the Mayan Base 20 system was very complicated!  Properties of Zero It is interesting to learn about the many properties of zero. First, every number has an additive opposite, or negative, for example -8 + 8 + 0. Next, if N equals any number then, N plus or minus 0 equals N; the amount doesn't change (zero is now the additive identity.) Third, N multiplied by zero equals zero. Fourth, zero divided by N equals zero. Finally, N divided by zero is impossible because no matter how many zeros you put in it will still equal zero, not N. We use these properties of zero every day.  Zero and Geometry Zero is a part of geometry in many ways. First, it is important to understand both Euclidian and non-Euclidian geometry. Euclidian geometry is of flat space and does not involve curves. Non-Euclidian geometry is about curve space. Zero describes how the curves are shaped; positive curvature looks like a smile, negative curvature looks like a frown, and zero is a flat line with no emotion. One Euclidian theory is that all angles of a triangle added together equal 180 degrees. But since the non-Euclidian angles are curved, the sum of the angles no longer equals 180 degrees; the triangles don't match. Since everything is curved and zero is nothing, zero is a straight line.  Infinity A study of zero is not complete without infinity, ¥, because zero in the sense of nothingness is the opposite of infinity. Zero in the sense of a place holder, however, is a symbol that leads us to infinity. For example, you can add as many zeros after the first number, 2015 < 20015 < 200015 < 20150 < 201500 < 2015000 < 215000000000000000 < ¥. We know that Infinity exists because you can always add one to the highest number, 2015000 plus one equals 2015001. This process can be repeated forever, so there is no finite amount of numbers. It's good to incorporate infinity because it explains the two sides of zero; as a place holder, and nothingness.   Conclusion Zero started in India and has become a part of us today. Not a day goes by when zero is not used or thought about. The signs for zero have changed over the years and has become a 0 symbol that is used in every culture. I hope you learned about zero, but for more fascinating information about zero, go to http://www.angelfire.com/ma4/zeromathproject.

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