I've been trying to decide whether to point this out, but I guess it is of interest: the 1-2-5 series increases by the same sequence of factors (2, 2, 2.5) as the 1-2.5-5 sequence. The only difference is which factor you use first.
Starting with 1c, to get to the next denominations in a 1-2-5 system, we multiply by 2, then 2.5, then 2, 2, 2.5, 2, 2, 2.5, etc. Starting with 1c, to get to the next denominations in a 1-2.5-5 system, we multiply by 2.5, then 2, 2, 2.5, 2, 2, 2.5, etc. The advantage for 1-2-5 is that it's more natural for decimal arithmetic, since each denomination has only one nonzero digit in its decimal representation. The other problem with the US system is that it isn't a "pure" 1-2.5-5 or 1-2-5 system, though lack of purity is arguably just an aesthetic concern. A possible advantage of the US system is that fewer different denominations are in common use, thus reducing the number of different kinds of coins and bills that a cashier needs to stock. A cash drawer in the US needs just 8 slots: 1c, 5c, 10c, 25c, $1, $5, $10, $20. Compare to the 11 slots I assume (for example) a European cash drawer would need (I have no firsthand experience; correct me if I'm wrong): 1c, 2c, 5c, 10c, 20c, 50c, 1, 2, 5, 10, 20. However, if reducing the number of denominations were a goal, I suppose the ideal system would be more like 1c, 5c, 25c, $1, $5, $25. --- Jon Saxton <[EMAIL PROTECTED]> wrote: > I have lived in the USA for about 17 years and I have had plenty of time > to get used to the 25c coin. However I still find the 20c coin of > Australia much more convenient. (I have other issues with the design of > Australian coins but that is another story.) It seems more natural to > make 45c by giving two 20c and a 5c rather than a 25c and two 10c. > > I can't say anything about the coinage of the Netherlands but the reason > for the 25c coin in the USA (and most other countries in the Americas) > is historical. > > By the beginning of the 18th century the Spanish dollar, a silver coin > of about 1 oz with a denomination of 8 reales, had become one of the > major world trading currencies. The English phrase "pieces of eight" > referred to this coin. In the mid 1820s there were even moves to make > the dollar the official currency of the Australian colonies but that was > quashed by the British government. > > Although there were coins of 1, 2 and 4 reales, they were relatively > scarce so for want of small change it was common practice to cut the > Spanish dollar. The easiest cuts were binary, and they corresponded to > the smaller denominations. So one cut yielded a half dollar, two cuts > yielded a quarter and a third cut yielded what was known colloquially as > a bit. (Hence the term "2 bits" meaning a quarter dollar.) > > When the United States established its own coinage in the late 18th > century it used the Spanish dollar as the basic unit. The innovation > was to divide the unit into tenths and hundredths but it was not so easy > to ignore the binary divisions. Hence the 25c coin was struck. As far > as I am aware there was never a 12.5c coin but the binary divisions > afflicted the stock market for 200 years. Even today there are vestiges > of the reales legacy: interest rates are almost invariably quoted in > eighths of a percent, and so are many state sales tax rates. > > The 25c coin is the anomaly in the USA and Canada. US banknotes follow > the 1-2-5 pattern (although for some reason the $2 note is not in common > use, and Canadians have $1 and $2 coins). > > I remember seeing $25 notes somewhere - perhaps Aruba. If I am correct > then that would probably be the Dutch influence. > > > > Martin Vlietstra wrote: > > I am a frequent visitor to the Netherlands. Prior to the adoption of the > > Euro, I found that I > had to take a little more care when handling the Dutch currency compared to > the currency of > other countries - their series was 5c, 10c, 25c, 1G, 2.5G with 5G, 10G, 25G > and 50G notes. > > > > In contrast, the Euro was well researched in terms of ergonomics - it has > > 1c, 2c, 5c, 10, 20c, > 50c, â¬1 and â¬2 coins with â¬5, â¬10, â¬20, â¬50, â¬100, â¬200 and > â¬500 notes. The > 1c and 2c coins are very small and two countries (Netherlands and Finland) do > not use them, > otherwise the coins are well thought out - each has a different milling > pattern. The notes are > all different sizes, each 3mm higher and 6mm longer than it predecessor. > There is however a > question as to whether â¬200 and â¬500 notes are needed. > > > > -----Original Message----- > > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ziser, Jesse > > Sent: 26 April 2008 06:12 > > To: U.S. Metric Association > > Subject: [USMA:40800] Re: Unknown series > > > > --- Pat Naughtin <[EMAIL PROTECTED]> wrote: > > > > > >> On 2008/04/26, at 9:43 AM, Ziser, Jesse wrote: > >> > >>> The Online Encyclopedia of Integer Sequences calls it the > >>> "Hyperinflation Sequence for Banknotes". > >>> http://www.research.att.com/~njas/sequences/A051109 > >>> > >> That is surely a fancy name for a relatively simple series. I wonder > >> whether the choice of the (1, 2, 5, â¦) series has anything to do with > >> limiting how many coins or notes are given as change during a cash > >> transaction. I find the (1, 2, 5, â¦) series easy to handle for this > >> purpose than the (1, 5, 10, 25, 50, â¦) coins used in the USA, but this > >> may only be because I am more familiar with Australian coins. > >> > > > > I don't disagree with you. I can see how the U.S. system of denominations > > might not be the > best. > > I wonder whether the fact that the US was one of the first countries to use > > decimal currency > means > > we are likely to have a less refined system than others. Incidentally, the > > "50" in that > sequence > > is very rare. I've only seen a few half-dollar coins in my life. The > > dollar coins were > pretty > > rare too, until they were recently reintroduced in "golden" form. > > > > > > > > > > ____________________________________________________________________________________ > > Be a better friend, newshound, and > > know-it-all with Yahoo! Mobile. Try it now. > http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ > > > > > > > > > > ____________________________________________________________________________________ Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now. http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ
