I gotta be that guy: Why is this the first post on the front page of Hacker News? Is basic arithmetic really so fascinating to the computer people?
After endless stuff on startups, basic arithmetic is a breath of fresh air.
1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..
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Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..
#72And this is usefull or simply neat?
Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..
#73Way back, I found out that there are an infinity of such patterns. I was really awed by that!
http://blog.zyrthofar.com/2012/07/multiplying-recurring-deci...
Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..
#74The pattern will break down once you get past 8192, which is 2^13. That means that the pattern continues for an impressive 52 significant figures (well, it actually breaks down on the 52nd digit, which will be a 3 instead of a 2). The reason it works is that 9998 = 10^4 - 2. You can expand as 1 / (10^n - 2) = 1/10^n * 1/(1 - 2/10^n) = 1/10^n * (1 + 2/10^n + 2^2 /10^2n + 2^3 /10^3n + ...) which gives the observed patt…
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Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..
#75In high school, I was pretty fond of plugging 11^n to get rows of Pascal's triangle. It breaks down at row 5, but inserting 0's in the middle extends it (e.g. 101^n, 1001^n, 10001^n). 11^0 1 11^1 1 1 11^2 1 2 1 11^3 1 3 3 1 11^4 1 4 6 4 1
We had a calc problem in high school on a test that would get you extra credit if you simplified the answer down to... something simple, and in order to do so you'd have to know Pascal's triangle.
Needless to say, I didn't get it, but one guy in our class, like an 8th grader, did. He was pretty smart.
Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..
#76You are all genius. The first person found it is definitely outstanding. There are so much mathematic magic out there that always made me feel fascinating. I'm amazed by the nature of this world which can be described by math. It's unbelievable. So I made my logo utilizing one of it. http://bit.ly/1gre9Bh
Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..
#77You don't need wolfram if you have unix's bc:
echo "scale=10000;1/999999999999999999999999998" | bc
Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..
#78[deleted]
Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..
#79Is anyone able to do this in hexadecimal?
Wolfram Alpha interprets 1/0x9999998 or 1/0xffffffe correctly as hex input, but still shows the output as decimal approximation, while a hexadecimal approximation would be more useful here. I would be really curious what this thing looks like in other numeric bases.
Unfortunately, the "Other base conversions" section only shows up to 7 or so digits after the point and doesn't allow expanding.
EDIT: found it! I didn't know bc in linux was this awesome! echo "obase=16;ibase=16;scale=1000;1/FFFE" | bc .0001000200040008001000200040008001000200040008001000200040008001000 (....)
Re: 1/9998 = 0.0001 0002 0004 0008 0016 0032 0064 0128 0256..
#80I gotta be that guy: Why is this the first post on the front page of Hacker News? Is basic arithmetic really so fascinating to the computer people?
I'd say that hackers are fascinated by neat tricks. Arithmetic tricks are just a subset of those.