And going the other way f(n-1) = (^11^/~7~ f(n) - ^1^/~4~) we get laserdiscs?
f(1) = 8
f(0) ≈ 12.32
vrek @programming.dev - 1mon
Interesting, is this a coincidence or is there a logic/reason it works out that way?
11
Cevilia (she/they/…) - 1mon
The logic/reason it works out that way is I solved the simultaneous equations a(8+b)=5.25 and a(5.25+b)=3.5.
4
vrek @programming.dev - 1mon
Ah ok. I was more wondering if it related to the bit density on magnetic tape or speed of the stepper motor available for a reasonable price at the time or something like that.
2
kittenz - 1mon
Why those two equations?
1
Cevilia (she/they/…) - 1mon
Because that's the sequence I wanted the result to be - 8 ➡️ 5.25 ➡️ 3.5
I knew they wouldn't multiply or divide exactly so there'd need to be a second term in there.
a turned out to be ^7^/~11~, and b turned out to be ^1^/~4~.
5
yetAnotherUser @discuss.tchncs.de - 1mon
This should converge to 7/16 as n approaches infinity if I can still analyse recursive functions.
7
juliebean @lemmy.zip - 1mon
that'd be just a bit larger than the short edge of a microSD card, for reference.
4
subiprime - 1mon
i got 121/176... too lazy to double check lol
3
subiprime - 1mon
ahh, i got two numbers mixed up, i got 7/16 this time
Cevilia in onehundredninetysix
Formula that produces floppy disk sizes
And going the other way f(n-1) = (^11^/~7~ f(n) - ^1^/~4~) we get laserdiscs?
Interesting, is this a coincidence or is there a logic/reason it works out that way?
The logic/reason it works out that way is I solved the simultaneous equations a(8+b)=5.25 and a(5.25+b)=3.5.
Ah ok. I was more wondering if it related to the bit density on magnetic tape or speed of the stepper motor available for a reasonable price at the time or something like that.
Why those two equations?
Because that's the sequence I wanted the result to be - 8 ➡️ 5.25 ➡️ 3.5
I knew they wouldn't multiply or divide exactly so there'd need to be a second term in there.
a turned out to be ^7^/~11~, and b turned out to be ^1^/~4~.
This should converge to 7/16 as n approaches infinity if I can still analyse recursive functions.
that'd be just a bit larger than the short edge of a microSD card, for reference.
i got 121/176... too lazy to double check lol
ahh, i got two numbers mixed up, i got 7/16 this time