If you don't like math, quit reading now.
Have you ever wondered what English fractions would come the closest to an even number of millimeters when converted. I wonder about strange things and this was one. So I did a quick Excel spreadsheet to see.
Of course, five inches is exactly equal to 127 mm. But this does not "count" as it is exact and it is not a fractional value. My question was what common fractional values come the closest to a whole number of millimeters.
Under one inch and checking all 64th fractions, the one that comes closest to an exact mm conversion is 63/64". It is exactly 25.003125 mm and the difference between that and 25 mm is only 0.003125 mm or 0.000123". Just a little over one tenth. As far as I am concerned, for all practical purposes, 63/64" = 25 mm.
Checking all 64th fractions up to but not including the exact 5 inch point, this 63/64" fraction is still the closest to an exact mm conversion. But there is a tie as 257/64" or 4 1/64" is the same amount off, but in the other direction. 4 1/64" = 101.996875 mm which is exactly 0.003125 mm short of 102 mm.
So, being curious, I wondered what 64th fraction would then take third place. It turns out that there is another tie as 126/64" and 194/64" are both off by exactly 0.00625 mm or 0.000246". And again, one is over and the other is under. I suspect a pattern.
In case you didn't notice, there is a symetry in the above pairs. There are 320 64th fractions between 0" and 5" and 63/64" is the 63 such fraction while 257/64" is the 63rd one from the five inch point (320 - 257 = 63). Likewise, for the 126/64" and 194/64" pair (320 - 194 = 126). I haven't had time to check, but I suspect that ALL the others will also be in pairs. Fifth and sixth place are 131/64" and 189/64" and again they are one more and one less than an exact mm value and 320 - 131 = 189. Their difference is 0.009375 mm. Seems like the differences are also forming a sequence of multiples of the first figure (0.003125 mm). Lots of symetry here. But then, when you think about it, there should be. Hmmm, 0.003125 X 320 = 1 exactly, so the differences are just stepping by this much for each successive pair.
As far as I know, this has no practical use. I just wondered and now I know. I do find it amazing that there are common inch fractions that are this close to a whole number of millimeters. And being somewhat wierd, I felt that I should share.
Have you ever wondered what English fractions would come the closest to an even number of millimeters when converted. I wonder about strange things and this was one. So I did a quick Excel spreadsheet to see.
Of course, five inches is exactly equal to 127 mm. But this does not "count" as it is exact and it is not a fractional value. My question was what common fractional values come the closest to a whole number of millimeters.
Under one inch and checking all 64th fractions, the one that comes closest to an exact mm conversion is 63/64". It is exactly 25.003125 mm and the difference between that and 25 mm is only 0.003125 mm or 0.000123". Just a little over one tenth. As far as I am concerned, for all practical purposes, 63/64" = 25 mm.
Checking all 64th fractions up to but not including the exact 5 inch point, this 63/64" fraction is still the closest to an exact mm conversion. But there is a tie as 257/64" or 4 1/64" is the same amount off, but in the other direction. 4 1/64" = 101.996875 mm which is exactly 0.003125 mm short of 102 mm.
So, being curious, I wondered what 64th fraction would then take third place. It turns out that there is another tie as 126/64" and 194/64" are both off by exactly 0.00625 mm or 0.000246". And again, one is over and the other is under. I suspect a pattern.
In case you didn't notice, there is a symetry in the above pairs. There are 320 64th fractions between 0" and 5" and 63/64" is the 63 such fraction while 257/64" is the 63rd one from the five inch point (320 - 257 = 63). Likewise, for the 126/64" and 194/64" pair (320 - 194 = 126). I haven't had time to check, but I suspect that ALL the others will also be in pairs. Fifth and sixth place are 131/64" and 189/64" and again they are one more and one less than an exact mm value and 320 - 131 = 189. Their difference is 0.009375 mm. Seems like the differences are also forming a sequence of multiples of the first figure (0.003125 mm). Lots of symetry here. But then, when you think about it, there should be. Hmmm, 0.003125 X 320 = 1 exactly, so the differences are just stepping by this much for each successive pair.
As far as I know, this has no practical use. I just wondered and now I know. I do find it amazing that there are common inch fractions that are this close to a whole number of millimeters. And being somewhat wierd, I felt that I should share.
Comment