6174

Karve, Vaibhav

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https://hdl.handle.net/2142/103709 Copy

Description

Title

6174

Author(s)

Karve, Vaibhav

Issue Date

2019

Keyword(s)

Mathematics

Abstract

Visualizing Kaprekar's Process: 1. Pick a 4-digit number, using at least two different digits. 2. Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary. 3. Subtract the smaller number from the bigger number. 4. Go back to step 2. and repeat. The above process will always reach its fixed point, 6174. Thus spake D.R.Kaprekar (1905-1986) -- school teacher, recreational number theorist and Indian mathematician. This is a graph of the process. Every four-digit number is a point on one of the circles. Every iteration outlined by Kaprekar is a path. His algorithm might be mechanical but the patterns emerging from it are anything but. At the center is the number 6174 (indicated by the red dot) to which all others are inexorably drawn. This plot itself was generated algorithmically using a combination of Python, TikZ, and LaTeX.

Type of Resource

• text
• image

Permalink

http://hdl.handle.net/2142/103709

Copyright and License Information

Copyright 2019 Vaibhav Karve

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