# Mathematical mm/inch and triangle oddities

• posted
A couple of things I've noticed over the years:
19mm is really really close to 3/4". It's actually 0.748 inches but
I'm not sure any equipment I work with has the bolt heads cut to
better than two thousandths, at least not until I get down to the
pocketwatches :-).
The ratio of height to base for a equilateral (60 degree for all
angles) triangle is really really close to 13:15. (Of course the real
number is sqrt(3)/2 =~ 0.8660, but that's surprisingly close to 13:15
=~ 0.8666).
Is there any deep numerological signifigance to these, or just random
luck?
It is nice to use a 3/4" socket and 19mm socket nearly
interchangeably. I think the spark plug hex on my lawnmower is
officially 3/4" but don't really know. Many (most?) auto lug nuts are
19mm or 3/4" but I don't know which ones are officially which or what.
The 13:15 ratio for an equilateral triangle comes out really nice for
laying out hexagonal grids in "nice" numbers.
Tim.
• posted
pi~=355/113 with an error of only 0.002% (22/7 is in error by 0.9%)
You can find a rational fraction approximation to any decimal number by the process of continued fractions. This procedure is implemented in the RFRAC program on my page.
Regards, Marv
Home Shop Freeware - Tools for People Who Build Things
• posted
Yes, that's true! Next time I go to grab the pi-inches socket and don't find it, I'll just use the 355/113" socket!
Tim.
• posted
11mm is a skosh smaller than 7/16, good for a slightly worn bolt/nut head.
Another great match is, 15/16 (or 7/8).
Dave
• posted
Other good "fits" are 5/32" @ 4mm, 5/16" @ 8mm, and 5/8" @ 16mm.
At times I have fitted a 16mm bore pulley onto a 5/8" dia. shaft..... .002" thick shim wrapped around the shaft and you're good to go!
Right now I have the task of fitting, interchangeably, 14mm bore change gears with 4mm key way, onto a 12mm shaft with 3mm key way. The gears cannot be modified because they still have to fit the 14mm shaft.
Any bright ideas without too much work??? I thought of a top-hat type adapter with a slot, and a step key. Problem is that a 12mm bore gear has to go onto the shaft first, followed by the 14mm bore gear.
This is on the gear hobber I acquired some months ago, where the feed gears have 14mm bores and the index gears have 12mm bores. The gears are otherwise interchangeable and I don't want to buy any more gears than absolutely necessary: these come with a standard bore of 10mm!
BTW if any of you have Module 1, 20 deg. pressure angle metric gears kicking around with tooth count between say 40 and 100 (don't need the whole set) please email me. I'd be pleased to help unclutter your shop! :-)).
I've just hobbed the first set of gears, 32 DP, 14 1/2 PA, 28 teeth, in brass. What a sweet process. The gears look and run great. Much faster than milling! Even with the machine set-up from scratch, ie. set stroke, change index gears and feed gears, set depth of cut, etc.
THE way to go!
Without cutting oil brass hobs well. For steel gears I better get sulphurized cutting oil. Any suggestions?? I'd like an oil that doesn't smell throughout the house since my shop is in the basement. My wife, fortunately, is most understanding but, better not push my luck with some foul-smelling goo!