By random luck I found this intriguing geometric pattern of summing in the numerical keypad. I'm curious if it is related to the base 10 system or how the numerical keypad was arranged, but couldn't find any info on the internet outside some fringe websites.
Let me explain. You start by summing the first row with the reverse of it like,
123+321=444
Then noticed that 444*2 is 888 which is equal of the first column summed with with its reverse,
147+741=888
Then you have 444*2.5 which is the sum of the diagonals, like
753+357=159+951=1110
It just goes on
444*3=1332=369+963
444*4=1776=789+987
Also some other patterns that matches the multiples of 444
111+333=444
111+777=888
444+666=111+999=333+777=1110
333+999=1332
777+999=1776
111+333+777+999=444*5=2220
Is there any mathematical explanation for this?
The main thing is that the keys in a straight line are in arithmetic progression. The three numbers are of the form $a,a+d,a+2d$. When you reverse this sequence and add, youu get $2a+2d,2a+2d,2a+2d$. That explains why you get three digits the same. For the top row you have $a=1,d=1$ so $2a+2d=4$, which is why you get $444$. For the left column you have $a=1,d=3$ so $2a+2d=8$ and you get $888$. One diagonal has $a=3,d=2$ and the other has $a=1,d=4$, both of which give $2a+2d=10$