Through the living jeff
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fun fact:
multiply practically any number by nine, (haven’t tested if its always true, but…
1344x9=12,096, right?
1+2+6=9
0+9=9
they all add up to nine
its kinda cool
SpoilerSpoilerSpoileralso how I learned my nine multiples
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I made a graph
And it’s not just 1 (but you have to go into other number systems for it to be obvious)
This is, of course, talking about the fact that the sqrt of repeated ones approaches a value (sort of)
SO
1111 and such are the result of a geometric series
Which can be represented as (r^n - 1)/(r-1)
r is 10, and n is the number of digits.
When you sqrt that, depending on if n is even, you get some 33.33 - the same amount of threes as ones originally.
So I thought, hey, you divide these, they can be 3.3 repeating.
AND SO
the ((r^n-1)/(r-1))^0.5/(10^(0.5n-1)) gives that effect.
Now, let’s say n goes to infinity. Desmos can’t handle that, but we can just use 100. It would be 3.3333….
But what if we used other values for r?
AND ITS SUPER COOL
The equation simplifies to
r/((r-1)^0.5)
Which is interesting.
AND
Take the answer to that, convert it to base r, AND IT BECOMES COOL
17, which had 4 in the denominator, gives 4.44 repeating.
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