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1mon
9

Formula that produces floppy disk sizes

  • 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
vrek @programming.dev - 1mon

Interesting, is this a coincidence or is there a logic/reason it works out that way?

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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.

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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.

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kittenz - 1mon

Why those two equations?

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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~.

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yetAnotherUser @discuss.tchncs.de - 1mon

This should converge to 7/16 as n approaches infinity if I can still analyse recursive functions.

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juliebean @lemmy.zip - 1mon

that'd be just a bit larger than the short edge of a microSD card, for reference.

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subiprime - 1mon

i got 121/176... too lazy to double check lol

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subiprime - 1mon

ahh, i got two numbers mixed up, i got 7/16 this time

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