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A mathematician's way of converting miles to kilometers

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Re: A mathematician's way of converting miles to kilometers

#121

Post by mlyle »

joppy wrote: post #110
wallace_f wrote: post #102

Earlier quoted context omitted.

I never bought this argument, but I'm not confident about it. Isn't base 10 inherently intuitive because of the obvious reasons? IE an order of magnitude is just another 0? Since I learned about base 2, etc, long ago, I always thought there was something magically elegant about base10 and never understood this? The explanation I've always heard, being 10 fingere, doesn't seem to explain all the elegance with base 10…

Base 10 is intuitive because we are taught to work in base 10. If we worked in base 7, then multiplication by seven would be just another 0. (And if we worked in base 7, we would probably have defined “an order of magnitude” to be a multiplication by 7, rather than 10).

Though probably a base with a couple convenient small factors is useful. Especially 2, since parity (even/odd) is so useful.

Past cultures thought even more factors were good, e.g. sexagesimal with 2, 2, 3, and 5. It means that e.g. the expansion of 1/3rd and 1/6th don't form a repeating fraction in sexagesimal notation.

Re: A mathematician's way of converting miles to kilometers

#122

Post by mlyle »

fhars wrote: post #79
sergioj97 wrote: post #66

Earlier quoted context omitted.

I agree it's not worth the hate, but in my opinion SI units are much more convenient. Using your own example, miles vs kilometers may not feel like a big difference, but the fact that you have proportional units (mm, cm, m, km) for any possible distance has the potential to save you a lot of trouble. Having completely different units for the same thing (land miles / nautical miles for distance), usually not proportio…

My favourite use of units is still the „2mm Scale Association“, a British model railroad club that builds their trains at a scale or two millimeteres to the foot (which is slightly larger than the standard N-track). It always blows my mind when I try to think how people come up with a scale like that.

Kinda a crazy ratio, but not -really-.

If you have modelmaking tools measured in mm, and a bunch of legacy dimensions of trains and buildings that are often round numbers of feet, it becomes tempting to use a scale like this. After all, you tend to get round numbers of mm to make things...

It might be convenient to make a starmap where e.g. 10 light years is 1 cm. Yes, the actual dilation factor is strange, but it's pretty easy to plot a set of cartesian coordinates measured in light years on a 1 cm grid.

Re: A mathematician's way of converting miles to kilometers

#124

Post by alaaalawi »

mkl wrote: post #88
rocqua wrote: post #78

Earlier quoted context omitted.

Pi is sqrt of 10 for all practical purposes.

Some practical purposes, maybe. Even 3.14 is a lot more accurate.

or 355 / 113. I memorized 113355. good enough for a lot. initially got it from https://colorforth.github.io/pi.htm

Re: A mathematician's way of converting miles to kilometers

#125

Post by Sharlin »

_Microft wrote: post #100

Isn't that rather the physicists way? Works well enough, used in a way not quite as intended by mathematicians, ... Disclaimer: I am physicist myself.

Mathematicians' way:

    Let a = distance in km;
        b = distance in mi; and
        φ = the conversion factor from mi to km.

    Then, a = φb.

Re: A mathematician's way of converting miles to kilometers

#127

Post by kurthr »

xkgt wrote: post #101
eps wrote: post #4

In related news - pounds to kilos is "divide by 2, less 10%". Very precise too. 160lbs = 80 - 8 = 72kg

Any similar shortcut for feet inches to cm? I find this conversion to be slower to compute than miles to km or lbs to kg.

A yard is 0.9m.

1.1 yard per m or 1yd and 4in.

A foot is 30cm.

An inch is 2.5cm.

4in per 10cm.

2m is 6ft 8in =180+20=2m

5f 4in is 150+10=1.6m

1.6m is 3ft 4in + 24in=5ft 4in

Even converting to and back isn't bad... work in a machine shop for a while and it will be second nature. Also metric/standard tools do not cross the line on the floor, only you and the work piece on different pieces of equipment. 25um looks like a mil, but it's not!

Re: A mathematician's way of converting miles to kilometers

#128

Post by achow »

cjbenedikt wrote: post #108
xkgt wrote: post #101

Earlier quoted context omitted.

Any similar shortcut for feet inches to cm? I find this conversion to be slower to compute than miles to km or lbs to kg.

Fahrenheit to Celsius: (100F -30)/2= 35C

Not quite. It is 37.78.

In temperature couple of degrees means a lot.

Re: A mathematician's way of converting miles to kilometers

#129

Post by mynegation »

gingabriska wrote: post #6

Triple the initial number, add a zero at the end, now halve the resulting number is good enough for my purpose. Brain is surprisingly good at doubling, tripling and halving operations. And visually added zero is quite easy too.

If you are going that route, why not multiply by 8 and divide by 5 for a much better approximation. But to be honest for me it has always been easier to directly multiply by 1.6 (or 1.5 for your case)

Re: A mathematician's way of converting miles to kilometers

#130

Post by arcticbull »

cjbenedikt wrote: post #108
xkgt wrote: post #101

Earlier quoted context omitted.

Any similar shortcut for feet inches to cm? I find this conversion to be slower to compute than miles to km or lbs to kg.

Fahrenheit to Celsius: (100F -30)/2= 35C

Just remember 100F was Fahrenheit's wife's body temperature when she had a low grade fever. Normal body temperature is 36.8C, and with a low fever it's between 37 and 38C. It's so easy! haha.
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