The even more useful conversion for me is inch to centimetre: F(n)in ~ F(n+2)cm
The Golden Ratio squared is 2.618 which is pretty close to 2.54.
A mathematician's way of converting miles to kilometers
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Re: A mathematician's way of converting miles to kilometers
#52What's interesting is that the absolute error converges to ~0.5399705049968784% (or a floating-point type or constant imprecision were introduced).
Re: A mathematician's way of converting miles to kilometers
#53Earlier quoted context omitted.
> that SI is generally used for engineering Except when it isn't? Are you telling me SI is used in engineering everywhere in the US? I've heard too many stories (especially accidents) to believe that in any way.
don't they still use pounds per square inch ? Now, in Europe (excluding the UK) they also still use some weird units from the past. Calories for example, and horse (!!) power.
A calorie was originally defined as as the amount of heat required at a pressure of 1 standard atmosphere to raise the temperature of 1 gram of water 1° Celsius.
But you're right that is sort of a weird unit from the past insofar as it's related to the SI system but isn't formally part of it. (It's basically now defined by its ratio to joules.)
Re: A mathematician's way of converting miles to kilometers
#54It's both easier and more accurate to multiply by 1.6
I thought the same. As Australians in the US for a few months recently, I'd regularly ask my 6-7yo son to convert miles to kilometres as a test - say, 53 miles into km. Multiply by eight and divide by five (or divide by five first in cases where that was quicker). He found it straightforward enough.
Re: A mathematician's way of converting miles to kilometers
#55I've been doing it like that as well for years. Most people you explain it (replace the number with a sum of fibonacci numbers, and for each one, take the next) to come back with "but it becomes less accurate for larger numbers, right?". After you say "hm, no!" there's a pause, and then the penny drops: Golden ratio! Anyway, I can't remember where I learned it.
It's better for large numbers since the asymptotic property dominates. It's questionable for small numbers since then the effect of the initial condition dominates. For example, the tweet's argument works the same way for the Fibonacci sequence that goes 1,3,4,7,11,... but obviously that gives different numbers.
Re: A mathematician's way of converting miles to kilometers
#56My way: x1.5 for speed limits, x2 for hikes.
Why x2?
Re: A mathematician's way of converting miles to kilometers
#57Earlier quoted context omitted.
There are a fair number of people who seem to take personal offense that the US (and to some degree the UK) don't use SI for everyday types of things and add it to their laundry list of grievances about the US generally. Never mind the fact that SI is generally used for engineering and other areas where it has legitimate advantages (which miles vs. kilometers doesn't really in day-to-day life).
> which miles vs. kilometers doesn't really in day-to-day life Standard units are much more useful in carpentry. It's a lot easier when you can divide by 2,3,4, and 6.
Unless you are working with wold and the measurements are all nonlinear lies.
https://en.m.wikipedia.org/wiki/Lumber#Dimensional_lumber
Re: A mathematician's way of converting miles to kilometers
#58What's interesting is that the absolute error converges to ~0.5399705049968784% (or a floating-point type or constant imprecision were introduced).
What's interesting about that number?
Re: A mathematician's way of converting miles to kilometers
#59Re: A mathematician's way of converting miles to kilometers
#60Earlier quoted context omitted.
Anybody who's taken CS 101 can estimate 1.6 * n too since they spend half the year in base2 or base16. It's 1 (n) + 6 (n)/10 since we're using base 10. For example, 5mi to ~8km: 1 (5) + 6 (5)/10 = 5 + 30/10 or 5 + 3.
That's how I was taught to do it in primary school, yes it's simple, but I don't see what bases 2 or 16 have to do with it?
10*X km is Y-base-16 miles, for single digit numbers.