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Metalworking (rec.crafts.metalworking) Discuss various aspects of working with metal, such as machining, welding, metal joining, screwing, casting, hardening/tempering, blacksmithing/forging, spinning and hammer work, sheet metal work. |
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#1
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Mathematical mm/inch and triangle oddities
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 pocke****ches :-). 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. |
#2
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Mathematical mm/inch and triangle oddities
On Mon, 31 Dec 2007 09:47:53 -0800 (PST), Tim Shoppa
wrote: 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 pocke****ches :-). 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. 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 http://www.myvirtualnetwork.com/mklotz |
#3
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Mathematical mm/inch and triangle oddities
On Dec 31, 12:56*pm, Marv wrote:
On Mon, 31 Dec 2007 09:47:53 -0800 (PST), Tim Shoppa wrote: 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 pocke****ches :-). 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. pi~=355/113 with an error of only 0.002% (22/7 is in error by 0.9%) 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. |
#4
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Mathematical mm/inch and triangle oddities
On Dec 31, 12:47 pm, Tim Shoppa wrote:
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 pocke****ches :-). 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. 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 |
#5
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Mathematical mm/inch and triangle oddities
On Dec 31, 1:12 pm, wrote:
On Dec 31, 12:47 pm, Tim Shoppa wrote: 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 pocke****ches :-). 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. 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 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! Thanks for any advice. Wolfgang |
#6
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Mathematical mm/inch and triangle oddities
I'm all caught up! The only unread messages in this thread are from Gunner.
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#7
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Mathematical mm/inch and triangle oddities
"Leo Lichtman" wrote:
I'm all caught up! The only unread messages in this thread are from Gunner. Damn, must be winter in your part of the world. Wes |
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