Kit YatesNov 13
Did you know
111111111 × 111111111 = 12345678987654321?
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Show threadKit Yates
It's the culmination of a series of cool calculations:
1 × 1 = 1
11 × 11 = 121
111 × 111 = 12321
1111 × 1111 = 1234321
11111 × 11111 = 123454321
111111 × 111111 = 12345654321
1111111 × 1111111 = 1234567654321
11111111 × 11111111 = 123456787654321
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Nov 13 at 8:00amWeb
Show threadKatjaNov 13
@kityates ok never thought maths would make me smile 😃
Show threadBob DownieNov 13
@kityates What happens when you go to base 11?
Show threadPete KirkhamNov 13
@geomannie @kityates it's all the same up to 111111111 * 111111111 = 12345678987654321 base N for N >= 10, then you get one more case without overflow for each increment of N thereafter
Show threadfoldworksNov 28

@PeteKirkham @geomannie @kityates TIL this number pattern from John Grant’s A Book of Numbers (1982).

I wonder if there is more (or less) to this than meets the eye, when compare with 11111 × 11111 = 123454321, etc?

#til #mathematics #number #pattern #arithmetic

Show threadrowan {forest witch}Nov 29

@foldworks @PeteKirkham @geomannie @kityates It works in different bases:

(digits increasing from 1) * (base - 2) + (increasing digit from 1) = (digits decreasing from highest in base)

It's ... not well defined for base 2.

Show threadfoldworksNov 29
@storybead @PeteKirkham @geomannie @kityates
I thought rewriting the pattern like this might give some insight, but now I'm not so sure 🤔
Show threadfoldworksDec 1

@storybead @PeteKirkham @geomannie @kityates

Using BASE and DECIMAL functions in LibreOffice for hexadecimal (before overflow). Took longer to do than I thought it would…

#mathematics #number #pattern #arithmetic #LibreOffice #LibreOfficeCalc

Show threadrowan {forest witch}Dec 1

@foldworks @PeteKirkham @geomannie @kityates yep. I did the first few in octal, hex, and base 3. My partner, who really maths the math, came up with a better theorem and proof by induction of the general case.

base 2:
1 x 0 + 1 = 1

base 3:
1 x 1 + 1 = 2
12 x 1 + 2 = 21

I think it would be neat to try to visualize this in some 2 or 3 dimensional graphing space, but I don't know quite how to approach that.

Show threadfoldworksDec 2

@storybead @PeteKirkham @geomannie @kityates
I like the duodecimal version but didn't use X and E for 10 and 11 😀

Yeah, I wonder if there's some visualisation that could make clear what's going on