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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

#141

Post by simonh »

mlyle wrote: post #121
joppy wrote: post #110

Earlier quoted context omitted.

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.

I’m convinced base 12 would be far superior to base 10. It has four common factors: 6, 4, 3 and 2, rather than just one. This would make handling common whole number fractions in place value form much easier. It’s also easy to count to 12 on one hand - just point to your finger bones with your thumb. That way with two hands you can count all the way up to 24 (in base 10 equivalent).

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

#142

Post by joshgachnang »

js2 wrote: post #133

A runner's way of converting miles to kilometers: 1 mile = 1609 meters. 3.1 miles = 5 kilometers. 6.2 miles = 10 kilometers. ... 26 miles, 385 yards = 42.195 kilometers. 100 miles = 160.9 kilometers. Sorry, that's as far as I've run.

Nice humblebrag. But agreed, the 5km = 3.1mi touchstone is helpful.

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

#143

Post by jameshart »

bena wrote: post #116
phkahler wrote: post #34

Earlier quoted context omitted.

How many km is 4 miles? That's not on the list of numbers.

Just under 7. Or 6.666... Because knowing a km is 3/5 of a mile is more useful. It follows that a mile is 5/3 of a km. From there it's basic math. 4 * 5 is 20. 20 / 3 is 6.666...

Or 5/8 of a mile if you want a more accurate approximation. Or 8/13. Or 13/21.

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

#144

Post by JoeAltmaier »

simonh wrote: post #141
mlyle wrote: post #121

Earlier quoted context omitted.

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.

I’m convinced base 12 would be far superior to base 10. It has four common factors: 6, 4, 3 and 2, rather than just one. This would make handling common whole number fractions in place value form much easier. It’s also easy to count to 12 on one hand - just point to your finger bones with your thumb. That way with two hands you can count all the way up to 24 (in base 10 equivalent).

Me too! And telling if a large number was a multiple of 2, 3, 4, 6 would be trivial - just check the last digit!

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

#145

Post by furyofantares »

mkagenius wrote: post #33
learnstats2 wrote: post #15

It's both easier and more accurate to multiply by 1.6

Not if you just remember 3,5,8,13 . You do not need to remember all fibonacci numbers, just the above and rest you can multiple by 2,5,10 and get them

For me, I think it’s pretty close for the numbers that are right on, and multiplying is way easier for intermediate numbers.

50->80 is one beat in my brain, it’s basically immediate because I know the first many Fibonacci numbers.

But multiplying by 1.6 is only two beats, it’s “add a half” and then “add a tenth”, each of which come just as automatically as recalling a two Fibonacci numbers. 50->75->80.

For the in-between numbers, 1.6 seems way easier. 40->60->64 is much quicker for me than averaging 50 and 80.

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

#146

Post by wallace_f »

smcameron wrote: post #109
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…

In base 8 (if we'd had 8 fingers), an "order of magnitude" would have been defined as "times 8" instead of "times 10", so it would also be adding another 0. Same with base 12. Base 16 would have the further advantage that we could easily halve, quarter, eighth, or 16th any number ending in 0 to a whole integer (in base 10, we can only halve, fifth, or tenth).

Yea you are obviously right now that I think about it, and I still have such a strong willingness to think there is something special about the number 10.

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

#147

Post by rrss »

castratikron wrote: post #139
_Microft wrote: post #119

Earlier quoted context omitted.

Ha, I saw a downvote there! I'm fine with that - on the condition that you never, ever treat a differential operator like a fraction again ;)

Physicists have their own battles, like electrical engineers using Ohm's Law as a definition of impedance.

What's the battle there? How do physicists define impedance?

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

#148

Post by RcouF1uZ4gsC »

As a programmer, I am much more facile with powers of 2, than Fibonacci. My way is to double the number 4 times (multiplying by 16) and divide by 10.

So for example 55 mph,

double 4 times: 110, 220, 440, 880

divide by 10: 88

So 55 mph is approximately 88 km/h

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

#149

Post by biggio »

RcouF1uZ4gsC wrote: post #148

As a programmer, I am much more facile with powers of 2, than Fibonacci. My way is to double the number 4 times (multiplying by 16) and divide by 10. So for example 55 mph, double 4 times: 110, 220, 440, 880 divide by 10: 88 So 55 mph is approximately 88 km/h

This is the method I'm using :D
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