The idea here is to get a smooth logarithmic division of each order of magnitude...

athenot · on July 30, 2015

That happens to be the series used for the Euro currency:

[0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, 500]

tshaddox · on July 30, 2015

Yep, that's a good way to minimize both the number of denominations offered and the number of bills/coins needed to make change for a given amount of money.

The USD is close, too. Bills are in 1, 2, 5, although the $2 bill is rare. For some reason our coins are irregular, although people in my experience find all coins a bother.

The "ideal" set of 3 denominations would be 1, 2.15, and 4.64.

haimez · on July 31, 2015

Is it at all surprising? Coins don't fit in wallets, represent small denominations, and are therefore not worth the trouble.

athenot · on July 31, 2015

That's because the highest US coin in practice is $0.25—even though $1 coins exist, they are not widespread and overlap with the $1 bill.

Contrast with the Euro where the highest coin is €2 and bills start at €5.

Also prices tend to be inclusive of sales tax / VAT in Europe, so a €9.99 widget can be purchased with a €10 bill and you get 1 single €0.01 coin in change. Whereas your $9.99 widget will be $10.79 (at 7% tax), so you'll get 3 dimes and a nickel (4x the amount of change) assuming you handed over $11. Most likely, you had a $20 so you also get lots of $1 bills with your coins. :)

ars · on July 31, 2015

I tried using $1 coins for a while. I found then too bulky and heavy with zero advantage over paper.

I would only use them routinely if forced.

In some US stores they set prices so that the total is an even total after tax.

dragontamer · on July 31, 2015

I actually found the contrary. 25 coins hold surprisingly well in a pocket, much easier than a thick set of 25-bills IMO.

25-Bills get wet with sweat and insulate your legs. I kinda prefer 25-coins over that.

IshKebab · on July 31, 2015

I think most currency uses that. Dollars are a weird exception.

kragen · on Aug 1, 2015

You don’t have to make it so complicated!

    : user@debian:~; python
    Python 2.7.3 (default, Mar 13 2014, 11:03:55) 
    [GCC 4.7.2] on linux2
    Type "help", "copyright", "credits" or "license" for more information.
    >>> import numpy as np
    >>> (10**(1+np.arange(24)/24.0)).reshape((2,3,4)).round()
    array([[[ 10.,  11.,  12.,  13.],
            [ 15.,  16.,  18.,  20.],
            [ 22.,  24.,  26.,  29.]],

           [[ 32.,  35.,  38.,  42.],
            [ 46.,  51.,  56.,  62.],
            [ 68.,  75.,  83.,  91.]]])
    >>> (10**(2+np.arange(48)/48.0)).reshape((2,3,8)).round()
    array([[[ 100.,  105.,  110.,  115.,  121.,  127.,  133.,  140.],
            [ 147.,  154.,  162.,  169.,  178.,  187.,  196.,  205.],
            [ 215.,  226.,  237.,  249.,  261.,  274.,  287.,  301.]],

           [[ 316.,  332.,  348.,  365.,  383.,  402.,  422.,  442.],
            [ 464.,  487.,  511.,  536.,  562.,  590.,  619.,  649.],
            [ 681.,  715.,  750.,  787.,  825.,  866.,  909.,  953.]]])
    >>>

Hmm, Ruby has a numpy-like thing too, no? NArray, it’s called? There are a few minor differences, but you can do the same thing:

    : user@debian:~; irb
    irb(main):001:0> require 'narray'
    => true
    irb(main):002:0> (10*10**(NArray.float(24).indgen!/24)).round.reshape(4,3,2)
    => NArray(ref).int(4,3,2): 
    [ [ [ 10, 11, 12, 13 ], 
        [ 15, 16, 18, 20 ], 
        [ 22, 24, 26, 29 ] ], 
      [ [ 32, 35, 38, 42 ], 
        [ 46, 51, 56, 62 ], 
        [ 68, 75, 83, 91 ] ] ]
    irb(main):003:0> (100*10**(NArray.float(48).indgen!/48)).round.reshape(8,3,2)
    => NArray(ref).int(8,3,2): 
    [ [ [ 100, 105, 110, 115, 121, 127, 133, 140 ], 
        [ 147, 154, 162, 169, 178, 187, 196, 205 ], 
        [ 215, 226, 237, 249, 261, 274, 287, 301 ] ], 
      [ [ 316, 332, 348, 365, 383, 402, 422, 442 ], 
        [ 464, 487, 511, 536, 562, 590, 619, 649 ], 
        [ 681, 715, 750, 787, 825, 866, 909, 953 ] ] ]
    irb(main):004:0>

Presumably 12, 24, and 48 were chosen because they are https://en.wikipedia.org/wiki/Highly_composite_numbers, and 96 and 192 for compatibility with 48 (since the HCNs in that neighborhood — 60, 120, and 180 — aren’t divisible by 48.)

(Related joke: How do we know the Babylonians were idiots? Because the day doesn’t have 83160 seconds.)