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my turn to ask math questions.
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.
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.