- f(1) = 8
- f(2) = 5.25
- f(3) = 3.5
- f(4) ≈ 2.4
- f(5) ≈ 1.67
And going the other way f(n-1) = (11/7 f(n) - 1/4) we get laserdiscs?
- f(1) = 8
- f(0) ≈ 12.32
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
