| Names |
Dattaraya Ramchandra
(D.R.) KAPREKAR |
| Date of
Birth |
January 17, 1905
– Dahanu, Maharashtra, India. |
| Date of
Death |
1986 (Date not
known) |
| Identity |
Indian School
teacher, Mathematician |
|
Date-wise Events / Works |
- 1927: He won the Wrangler
R. P. Paranjpe Mathematical Prize for an original piece of
work in mathematics.
- March 1975: His
international fame arrived when Martin Gardner wrote about
Kaprekar in his column of Mathematical Games for Scientific
American.
- 1963: Kaprekar defined the
property which has come to be known as self numbers, which
are integers that cannot be generated by taking some other
number and adding its own digits to it.
|
| Special
Achievements / Events |
- He discovered several results in number theory,
including a class of numbers and a constant named after him.
- In addition to the Kaprekar constant and the
Kaprekar numbers which were named after him, he also
constructed certain types of magic squares related to the
Copernicus magic square.
- Initially his ideas were not taken seriously by Indian
mathematicians, and his results were published largely in
low-level mathematics journals or privately published.
- He showed that Kaprekar Constant 6174 is reached
in the limit as one repeatedly subtracts the highest and
lowest numbers that can be constructed from a set of four
digits that are not all identical.
- A similar constant for 3 digits is 495.
- A Kaprekar number is a positive integer with the
property that if it is squared, then its representation can
be partitioned into two positive integer parts whose sum is
equal to the original number (e.g. 55, since 55*55=3025, and
30+25=55); other similar numbers are 9, 45, 99 etc.
- For example, 15 is not a self number, since it can be
generated from 12: 12 + 1 + 2 = 15. But 20 is a self number,
since it cannot be generated from any other integer. These
are sometimes referred to as Devlali numbers (after the town
where he lived).
- Kaprekar also described the numbers which are defined by
the property that they are divisible by the sum of their own
digits. For example 12 is divisible by 1 + 2 = 3. Such
number were called Harshad numbers.
- These were later also called Niven numbers after a 1997
lecture on these by the Canadian mathematician Ivan M.
Niven.
- Kaprekar also studied the Demlo numbers, named after a
train station where he got the idea of studying them. These
are the numbers 1, 121, 12321, …, which are the squares of
the 1, 11, 111, … .
- He ia also known as GANITANAND. (गणितानंद).
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