But WHY Does This Pattern Occur? Beauty of Numbers

If you multiply a number with only 1s by itself, you end up with a palindrome of the numbers in ascending and then descending order. People have called this an example of the "beauty of mathematics." If your number has N digits of 1, then its square will be the numbers 1 to N in ascending and then descending order. The pattern continues indefinitely, although it "breaks" after 9 because of carry over. I explain why the pattern happens using the method of multiplying by lines.

Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.

My Books

[philipmalan]

Another way of looking at 111x111:
111x100=11100
111x10= 01110
111x1= 00111
when it is added together it is 12321 (doesn't it look similar to the line thing?)

[druhu]

This puts a whole new definition to cross-multiplying

[goseigentwitch]

I feel like it's worth pointing out that this same pattern holds true outside of base 10. For example: in base 5, 1111x1111=1234321 and because 5 is represented as 10 in base 5, so that's when the carryover happens, but it'll always end with "4321" or in base N, it would always end in "(n-1), (n-2)...321"

[AlexanderQ]

I hoped you would continue and talk about the patterns forming in the carryover section to be able to predict answers of higher order squares.

[anurag]

"Hey this is Pressure locker here"
- Subtitles

[alessiofoglia]

No one:
Literally no one:
The subtitles: Hi, this is pressure locker

[AngryArmadillo]

I always assumed this trick worked because 11 is one more than 10 (the base for our system) but I now see that that is just a coincidence. The reputation of the unit (1) is really what makes this work. Great video!

[tboodman]

these videos are awesome you definently deserve more subscribers

[tim..indeed]

There's another pattern I have found. When you share
9 / 1
98 / 12
987 / 123
9876 / 1234
...
When you keep sharing this you get closer to 8. Can you explain this?

[tariquehassan]

Really Surprising beauty of Mathematics.. Great!

[MsHojat]

Do you guys (or MindYourDecisions ) think that it's a good idea to teach kids the line method for multiplication as the main way to do multiplication before they either happen to memorize, or are ordered to memorize a multiplication table?

Common Core seems to like to teach about drawing a ton of dots and grouping the dots, and while maybe useful at the most primitive level of teaching what multiplication represents, it seems far too much of a hassle to do with any regularity.

That said, line multiplication seems like it might be a bit abstract, and that perhaps they'd only be learning it by rote rather than the concept behind it.

[Holobrine]

How about the pattern of the blue numbers in the middle with 10 ones or higher? They go 00, 0120, and is 012340 next?

[GordonHugenay]

+MindYourDecisions can you please make a fancy video for the proof of the fundamental theorem of algebra?

[mrkaw]

Being an old school math person, I don't know how this "common core" works now, but I think kids learning math now would not understand the carryover thing.

[Vainkooooo]

u deserve a subscribe, excellent work

[banusenthil]

If i want to multiply 207- 1's with 207-1's, how to find out the answer ...is there any formula to calculate it?

[sandeepthorat]

Hey, let me add something this lines trick can be done for multiply any number by any number and it works perfectly

[humanityexe]

what, no half life 3 confirmed joke here?

[Sapphire]

Look at this:
1/9 =
1/81 = 0.01234567901...
So, the numbers being dealt in this video is the same thing but orders of magnitude larger. That means, for any n digits of 1s squared, as n tends to infinity, the value of n 1s squared is getting closer to 12345679... .

[ntinomanolo]

In the last two multiplications with 10 and 11 digits the blue numbers are 00 and 0120 which is 0 and the number in the first and second multiplication -1