It's the question from these threads:
Asking for suggestions about square numbers
Don suggested my trying to explain it more clearly because my scribbles were too messy
Please allow me to continue here because I can't add more photos in the old post T_T I know this is inappropriate manner, but I don't know what else to do... It won't happen again after this.
(Let's continue)
I can't explain this one... but it's a way to calculate. I found it out from processes mentioned above. (Please ignore the green 11^2 part).
Other two examples of the calculation.
Let's move to the ^3, start with the differences between 5^3 and 6^3
calculate version of the differences
And calculate version from the ^3 table.
and that's all for as far as I wrote them down... Got to go back to work since I have been slacking off for 2 days T-T
It's that I found such stuff fun and I want to learn more about it. Thank you JMoravitz and J.G., who kindly suggested some some information. I think I'm too new to math +_+; I need to learn the meaning of the symbols first .. They're like outerspace language to me now. But I'll try! Other suggestions (maybe in basic math first) are very welcome.