[USMA:36361] Multiple Units for Energy

[Bill Hooper]

On 2006 Mar 23 , at 3:54 PM, Pat Naughtin wrote: As a mathematician you might like to figure how many conversion factors you need to convert from any one of the 68 words used to describe energy (to) any of the others. The answer is 2278. This does NOT count the conversions both ways; e.g. conversion from joules to calories and conversion from calories to joules are not counted as two separate conversion factors. Also, the conversion from a unit to itself is not counted because it is obvious (and always equal to 1). If you want it spelled out in detail, see below. Regards, Bill Hooper Fernandina Beach, Florida, USA ========================= You start with a table of 68 rows and columns listing all 68 energy units going across and the same 68 energy units going down. Each space would contain the conversion factor from the one unit to the other. The total number of spaces in such a table would be 68-squared.  Next, subtract the number of spaces in the table would show a unit "converted" to itself (one space for each unit); that is subtract 68. Now you have: 68^2 - 68 Finally, so as not to count each pair twice (once converting one way and again converting the other way), cut this result in half. The result is: (68^2 - 68) / 2  = 2278 By the way, if you DID want to count the conversion one way and the same conversion the other way as two separate conversions, then the total number of conversion factors is twice as much, or 4556 Just don't divide by 2 above.