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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

#151

Post by __s »

wallace_f wrote: post #102
lota-putty wrote: post #67

Earlier quoted context omitted.

What if we had just 4 digits on each limb or even 6 perhaps. How does those numbers look in base 8 or 12.

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…

So you know how you can tell if something is a multiple of 2 or 5 based on the last digit? & all those shortcuts you get with multiplying by 5? For base 12 you'll lose that, but then get to do it for multiples of 2,3,4,6

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

#152

Post by jsjohnst »

Division and multiplication by 5 and 8 should be fairly easy for most folks, imho. Lot easier than trying to remember the closest Fibonacci number to me.

Quick, what’s the closest Fibonacci number to 150? Can you do that faster than 150/5*8 in your head? What about 500?

The reverse is almost as easy. Even with numbers not as evenly divisible, say 490km, most will know 490/8 is about 61 quickly. Multiple that by 5 and you 305mi.

Maybe I’m just better at basic speed math than average, but I still feel it’s easier for most people.

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

#153

Post by specialist »

prawn wrote: post #54
learnstats2 wrote: post #15

It'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.

Nice. Wish I'd thought of that. FWIW, I played points based games like cribbage with my youngsters to better encourage mental maths.

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

#154

Post by wallace_f »

__s wrote: post #151
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…

So you know how you can tell if something is a multiple of 2 or 5 based on the last digit? & all those shortcuts you get with multiplying by 5? For base 12 you'll lose that, but then get to do it for multiples of 2,3,4,6

Yea I guess in base 4, 5 would be 11.

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

#155

Post by Accacin »

ghaff wrote: post #30
toolslive wrote: post #28

Earlier quoted context omitted.

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.

PSI is very commonplace though I'm not in a field where I use it in an engineering way. (I actually had to think for a second to come up with the SI equivalent.) Pounds are one of the real bugbears of imperial in mechanical engineering with lb-f and slugs (i.e. "pounds" conflates mass and weight). Always hated that. I'd convert things to metric and then convert back when I had to work in Imperial. And I still hear st…

Yeah, a lot of people in the UK use stones for weight. Even young people in my experience.

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

#156

Post by mabbo »

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

Yes! I'm a Canadian whose brain works in km but I spent a year and a bit working a job that had me flying to (and subsequently driving around) places across the USA. All the time I'd be finding myself going "Okay, 30 mph... what the heck is that?".

Double four times, and divide by ten as soon as possible (ie: the first time you see a zero on the end, drop it).

So 30 mph => 3 (drop the zero) => 6 => 12 => 24 => 48 km/h

The nice thing about this method is that you know that the kph is going to be more than mph, but less than double it, so you don't have to count the doublings very well- when you're in the right range, you're at the right number.

Example: 135 miles to destination is how many km? Okay, double to 270; drop the zero to 27; double to 54; double to 108;... we're still less than the mph, so we must need to double again to get 216 km. Now we're between 135 and 2*135, so we must be at the answer. 216 km. (actual answer is 217.3).

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

#159

Post by srl »

jsjohnst wrote: post #152

Division and multiplication by 5 and 8 should be fairly easy for most folks, imho. Lot easier than trying to remember the closest Fibonacci number to me. Quick, what’s the closest Fibonacci number to 150? Can you do that faster than 150/5*8 in your head? What about 500? The reverse is almost as easy. Even with numbers not as evenly divisible, say 490km, most will know 490/8 is about 61 quickly. Multiple that by 5 and…

I'm admittedly pretty bad at basic speed math (even dividing by 5 takes me a bit -- and I know it shouldn't). I use the same fibonacci trick, and at least for me it really is much easier.

It's important to remember that all arithemtic tricks are made more useful when combined with others. I don't know what fibonacci number is close to 500, but I don't need to: 5 -> 8 means 500 -> 800. Really, the only fibonaccis I have memorized are 2,3,5,8,13,21.

150 is harder, but I would use the same trick. 13->21, so 150->230 plus a bit. Maybe 240.

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

#160

Post by crdrost »

mabbo wrote: post #156
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

Yes! I'm a Canadian whose brain works in km but I spent a year and a bit working a job that had me flying to (and subsequently driving around) places across the USA. All the time I'd be finding myself going "Okay, 30 mph... what the heck is that?". Double four times, and divide by ten as soon as possible (ie: the first time you see a zero on the end, drop it). So 30 mph => 3 (drop the zero) => 6 => 12 => 24 => 48 km/…

You can also add a half and a tenth.

135, half is 67, a tenth is 13, add those two together to get 80, 135+80=215.

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