my turn to ask math questions.

[fox]

I'm turning myself around a bit with a thing I'm trying to set up that has to do with squares.

Suppose for every x minutes you spend doing activity A, you have to spend x² minutes doing activity B. No problem, right? If you do A for two minutes, you do B for four. If you do A for three minutes, you do B for nine. If you do A for fifteen minutes, you do B for three hours and 45 minutes. That's where I'm running into trouble, is switching between orders of magnitude. If you do A for an hour, that's 60 minutes, so you do B for 60*60 = 3600 minutes, or 60 hours, or two and a half days. So far so good, right?

If you do A for a solid week, that's 168 hours, by my calculations. So now you do B for 168*168 = 28,224 hours, or (divided by 24 hours per day) 1176 days, or (divided by 365 days per year) three years and almost a quarter.

If you do A for a solid month, that's 30 days, so you do B for 30*30 = 900 days ...

... but how can a square month be shorter than a square week? Even if I make the month 31 days, I only get 961.


The obvious answer is that I've skipped some necessary step somewhere, but for the life of me, I can't work out what I'm doing wrong. Someone who didn't need special tutoring in geometry and trig, help me out, wouldya?


I may have worked it out myself: is the answer that if I want to talk about how many minutes I have to do B, I have to work out how many minutes I've done A, and shortcutting to days and weeks and months and so on isn't going to work until I've got a total? Because (7*24)²/24 is just not the same thing as 7²? Because if I do the month example with hours, I get 720*720 = 518,400 hours, or (divided etc.) 21,600 days, which is rather more than three years, I admit.

Comments

[darthfox.livejournal.com]

I was actually trying to think about fractions in the first place, but I had to split and I could see that that way lay madness. And that was the end of my intention of making the hour the base unit of this problem. (Because if I do set it up where for x hours doing A you do x^2 hours of B, and you do 15 minutes of A, how the hell long do you spend on B? Not three minutes and three quarters, as you say -- but not three hours and three quarters, either, because I'm trying to square the hours, not the minutes. ARGH.)

(See, it's better that I left math when I did. Minutes is fine. I'd much rather multiply everything in my life by 60 for the next day and a half than try to work out how to square fractions of hours without squaring fractions. For the degree to which this is all going to matter, I've already spent too long worrying about it. [g])

[thalia]

I'm mostly dying to know why you're thinking about this in the first place.

And remember, with positive fractions less than one, when you square them they get smaller. Freaks my GMAT students out every time. So, yeah, in the case here you would do 3.75 minutes of B.

[darthfox.livejournal.com]

I do remember that; but that works mathematically, not practically. Which is why the unit of analysis is now the minute. :-) Works out fine. I have done my calculations and worked out that if you do A for a solid day, you'll be doing B for close to four years; if you do A for five days, you'll be doing B for almost 99 years, which is great.

:-D