International Journal of Mathematics Trends and Technology
Volume 58 | Number 4 | Year 2018 | Article Id. IJMTT-V58P534 | DOI : https://doi.org/10.14445/22315373/IJMTT-V58P534
The present paper is a mathematical investigation into the division of unique numbers composed of digits in succession. The paper focuses on the division of a number (whose digits are written in the descending order in succession, starting with a two digit number) like 151413121110987654321, by its reverse counterpart number(whose digits are written in the ascending order in succession, ending with the same number that started the descent) which is 123456789101112131415. The author found out the values of the quotients of such divisions up till the division of the number 999897...321 by the number 123...979899, and observed a unique feature common to each division. It was realized that the quotients of two successive divisions of this nature have a constant di erence between them, equal to the irrational number 0.0818181... which has been termed as the Universal Constant of Division (UCD) of the rst Order. Similar analysis and extrapolation to even higher divisions (involving three digit numbers) reveals a startling yet similar feature about them. The quotients of such huge divisions are tedious to calculate and require computation instead of manual calculation in order to be evaluated. Using the value of UCD of the rst order, the author was able to express the complex division quotients in terms of an Arithmetic Progression and thus make the calculations manual and simpler. The author nishes the paper with an introspection into the nature of the Universal Constant of Division and it's analogy with the Ramanujan formula for Pi. The paper is a study out of sheer observation and tries to dwell deep into the realms of the fascinating operation of division and succession.
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[2] Charles H.C. Little, Kee L. Teo and Bruce Van Brunt, Real Analysis via Sequences and Series, 2015, Springer.
[3] Stack-exchange, Math.stack-exchange, url = https://math.stackexchange.com/
Debrup Poddar, "Universal Constant of Division of Order 1," International Journal of Mathematics Trends and Technology (IJMTT), vol. 58, no. 4, pp. 240-252, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V58P534
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