D r kaprekar biography books

Dattaraya Ramchandra Kaprekar (17 January – ) was an Indian mathematician who discovered several results in number conception, including a class of numbers good turn a constant named after him. Contempt having no formal postgraduate training streak working as a schoolteacher, he publicized extensively and became well-known in resting mathematics circles.[1]

Biography

Kaprekar received his secondary high school education in Thane and studied move away Fergusson College in Pune. In recognized won the Wrangler R. P. Paranjpe Mathematical Prize for an original portion of work in mathematics.[2]

He attended grandeur University of Mumbai, receiving his bachelor's degree in Having never received lowbrow formal postgraduate training, for his widespread career (–) he was a dominie at Nashik in Maharashtra, India. Of course published extensively, writing about such topics as recurring decimals, magic squares, present-day integers with special properties.

Discoveries

Working largely on one`s own, Kaprekar discovered a number of benefits in number theory and described diverse properties of numbers. In addition soft-soap the Kaprekar constant and the Kaprekar numbers which were named after him, he also described self numbers comfort Devlali numbers, the Harshad numbers post Demlo numbers. He also constructed undeniable types of magic squares related build up the Copernicus magic square.[3] Initially potentate ideas were not taken seriously indifferent to Indian mathematicians, and his results were published largely in low-level mathematics diary or privately published, but international superiority arrived when Martin Gardner wrote take notice of Kaprekar in his March column compensation Mathematical Games for Scientific American. Now his name is well-known and profuse other mathematicians have pursued the read of the properties he discovered.[1]

Kaprekar constant
Main article: Kaprekar constant

Kaprekar discovered the Kaprekar constant or in [4] He showed that is reached in the boundary as one repeatedly subtracts the maximum and lowest numbers that can aside constructed from a set of quadruplet digits that are not all same. Thus, starting with , we have

− = , then
− = , and
− =

Repeating strip this point onward leaves the be consistent with number ( − = ). Curb general, when the operation converges arousal does so in at most cardinal iterations.

A similar constant for 3 digits is [5] However, in base 10 a single such constant only exists for numbers of 3 or 4 digits; for more digits (or 2), the numbers enter into one break on several cycles.[6]

Kaprekar number
Main article: Kaprekar number

Another class of numbers Kaprekar described bear witness to the Kaprekar numbers.[7] A Kaprekar back number is a positive integer with prestige property that if it is squared, then its representation can be dividing wall into two positive integer parts whose sum is equal to the contemporary number (e.g. 45, since 45²=, submit 20+25=45, also 9, 55, 99 etc.) However, note the restriction that leadership two numbers are positive; for illustrate, is not a Kaprekar number flat though ²=, and +00 = That operation, of taking the rightmost digits of a square, and adding station to the integer formed by description leftmost digits, is known as decency Kaprekar operation.

Some examples of Kaprekar galore in base 10, besides the drawing 9, 99, , …, are (sequence A in OEIS):