- #1

bahamagreen

- 1,014

- 52

- TL;DR Summary
- The number of decimal repeats feeds segments of the square with same digits

I was doing some probability calculations that include squaring a number between 0 and 1.

When I approximate 2/3 using 0.6 or 0.66 or 0.666 etc. I get an interesting series of growing same digit segments...

0.6^2=0.36

0.66^2=0.4356

0.666^2=0.443556

0.6666^2=0.44435556

0.66666^2=0.4444355556

0.666666^2=0.444443555556

And (2/3)^2=0.4444444444444...

Similar thing squaring 1/3 approximated as 0.3 or 0.33 or 0.333 etc.

What is this called?

Is it an artifact of base 10?

Sometimes a long division yields a repeating remainder so a similar string of repeats forms, but this is multiplication that produces two growing strings that preserve the digits that separate the strings.

When I approximate 2/3 using 0.6 or 0.66 or 0.666 etc. I get an interesting series of growing same digit segments...

0.6^2=0.36

0.66^2=0.4356

0.666^2=0.443556

0.6666^2=0.44435556

0.66666^2=0.4444355556

0.666666^2=0.444443555556

And (2/3)^2=0.4444444444444...

Similar thing squaring 1/3 approximated as 0.3 or 0.33 or 0.333 etc.

What is this called?

Is it an artifact of base 10?

Sometimes a long division yields a repeating remainder so a similar string of repeats forms, but this is multiplication that produces two growing strings that preserve the digits that separate the strings.