Zero

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Zero

  1. 1. Importance0 (zero) is both a number andthe numerical digit used torepresent that number innumerals.It fulfils a central role in mathematicsas the additive identity of the integers ,realnumbers, and many other algebraicstructures. As a digit, 0 is used as aplaceholder in place value system.
  2. 2. HistoryIndiaThe concept of zero as a number and notmerely a symbol for separation is attributed toIndia, where, by the 9th century AD, practicalcalculations were carried out using zero, whichwas treated like any other number, even in caseof division. The Indian scholar Pingala circa5th-2nd century BC) used binary numbers inthe form of short and long syllables (the latterequal in length to two short syllables), makingit similar to Morse code.
  3. 3. He and his contemporary Indian scholars used theSanskrit word sunya to refer to zero or void. Theuse of a blank on a counting board to represent 0dated back in India to 4th century BC. In 498 AD,Indian mathematician and astronomer Aryabhattastated that "from place to place each is ten timesthe preceding "which is the origin of the moderndecimal-based place value notation.
  4. 4. The oldest known text to use adecimal place-value system ,including a zero, is the Jain text fromIndia entitled the lokavibhaga, dated458 AD, where shunya ("void" or"empty") was employed for thispurpose .
  5. 5. The first known use of special glyphsfor the decimal digits that includesthe indubitable appearance of asymbol for the digit zero, a smallcircle, appears on a stone inscriptionfound at the Chaturbhuja Temple atGwalior in India, dated 876 AD .There are many documents oncopper plates, with the same small oin them, dated back as far as the sixthcentury AD, but their authenticitymay be doubted.
  6. 6. As a year label0 (year)In the BC calendar era ,the year 1 BC is the first yearbefore AD 1; no room is reserved for a year zero. Bycontrast, in astronomical year numbering, the year1 BC is numbered 0, the year 2 BC is numbered −1,and so on.
  7. 7. InventionThe credit for this goes to Indianmathematicians and the number zero firstappears in a book about ‘arithmetic’ written byan Indian mathematician ‘Brahamagupta’. Zerosignifies ‘nothing’ and the current definitioncalls it an ‘additive identity’.
  8. 8. AryabhattaAryabhatta, the greatest Indian mathematician of ancientera, has been famous for his mathematical works andtheorems on astronomical bodies that have been found tobe very accurate in terms of modern calculations."Aryabhatiya", his only work to have survived has giventhe world innumerable theorems and research subjects.Mathematicians
  9. 9. His two other major contributions arethe, introduction of zero to the worldand calculating the approximate valueof pie. His works are also spread infields like include algebra, arithmetic,trigonometry, quadratic equations andthe sine table.
  10. 10. RamanujamSrinivasa Ramanujan Iyengar, the greatest Indianmathematician of 20th century, contributed immensely infields like number theory, mathematical analysis, stringtheory and crystallography.
  11. 11. Although he lived for a short span of 32 years, hecompiled nearly 3900 phenomenal results that leaveeven the best mathematical brains of today in sheerawe and wonder!His genius has been admiredby some greatestcontemporary mathematiciansof his time. He is hailed to beone of the most famousmathematicians in the field ofnumber theory.
  12. 12. ArchimedesThe greatest mathematicians of ancient era,Archimedes made phenomenal contribution in thefield of mathematics. His works include integralcalculus studies and finding various computationtechniques to determine volume and area of severalshapes including the conic section.
  13. 13. EuclidEuclid, the father of Geometry, wrote the book ,"EuclidsElements", that is considered to be the greatest piece ofhistorical works in mathematics. The book is divided into13 parts and in it, Euclid has discussed in details aboutgeometry (what is now called Euclidean geometry).His contributions are also famous in the fields of sphericalgeometry, conic sections and number theory.
  14. 14. Rules of Brahmagupta• The rules governing the use of zero appeared for the firsttime in Brahmaguptas book Brahmasputha Siddhanta(The Opening of the Universe),written in 628 AD.• Here Brahmagupta considers not only zero, but negativenumbers, and the algebraic rules for the elementaryoperations of arithmetic with such numbers.
  15. 15. In some instances, his rules differ from the modernstandard. Here are the rules of Brahmagupta:• The sum of zero and a negative number is negative.• The sum of zero and a positive number is positive.• The sum of zero and zero is zero.
  16. 16. • The sum of a positive and a negative is theirdifference; or, if their absolute values areequal, zero.• A positive or negative number when dividedby zero is a fraction with the zero asdenominator.
  17. 17. • Zero divided by a negative or positive number iseither zero or is expressed as a fraction with zero asnumerator and the finite quantity as denominator.•Zero divided by zero is zero.
  18. 18. The most difficult concept in mathematics isoperations involving zero. Zero is far fromnothing, what exactly it is can be is difficult toexplain and understand.One of the most difficult concepts in mathematics is doingoperations involving zero. Contrary to popular opinionzero is far from being nothing, but what exactly it is canbe difficult to explain and understand.
  19. 19. • When we add or subtract using zero we generallythink that what we are adding nothing, and in thissituation we would be correct in using thatthinking. However there are some cases when zeromeans something or what it means cant beaccurately described.
  20. 20. Multiplication by zero does nothing to change the generallyheld concept of zero being "nothing".When we multiplyany number by zero the result is simply zero.While this result is understood as universal, multiplicationin more advanced mathematics proves that this is notalways so. Using exponents or raising a number to a poweris one example where zero doesnt mean nothing.
  21. 21. One of the more interestingconcepts involves the fact thatdivision by zero is undefined.Proof of this statement canyield some amazing andinteresting results.
  22. 22. Thankyou

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