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Hey Joe and all of those who are in the know:
How can you find the side of a square that has the same value or area of a circle with a given diameter, useing only the framing square?
brisketbean
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bean.
I don't know the answer to that as I don't quite understand the question. But here's a few more good ones that I know my guys could answer.
How do you scrape the ice off the framing lumber using only a framing square?, or, how do you get the dried concrete off used form boards?
or how do you rip the carpenter off for 45$ by borrowing only his framing square?
what's the difference between a framing square and a rafter square?
" the real value in a tool is how skillful is the user"
carpin' in balmy MI.
Le Carp.
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I don't think this is where 'bean' was headed but what the heck. I once helped a brother-in-law frame his house as a return for him helping(?) me frame some of mine. When I'm framing walls on the deck, I tend to keep my Stanley prybar handy to use as a lever or whatever on recalcitrant studding, I also keep a rafter square handy to do those things that one usually uses a square for. Did I mention that the brother-in-law was a retired auto mechanic? My square of choice those days was one that had been bequeathed to me from my late father, a master carpenter, that he had used for who knows how many years on countless jobs. It was more than a bit special, so I kinda lost it when I looked over to see the brother-in-law, standing firmly on arm of my square while reefing up on the other arm using it to lever a stud into place. Ree-lax he retorted, as he bent it back into shape over his knee.
Wirin' in 40F Ontario
*What brisketbean meant was, how do you find the side dimension (length, width) of a geometric square whose area equals that of a circle with a known diameter, using only a framing square? I don't know, but I can say that a square with a side measurement .886 that of a circle's diameter will have an area approximately equal to the circle's. Can you get that with a square?
*Maybe I'm being Norwegian here, but why would I possibly want to calculate this measurement, with or without a framing square?Puzzled.
*I put it on the tablesaw and turn the beast on. With a little vibration, you'd be surprised how little time it takes for the square to contact the whirring blade. And boy, does it fly! Great sport, not for the faint of heart.
*Per,You've been given the task of painting a set number of solid circles on a home's exterior siding and have calculated the exact paint required, remembering your high school geometry. The homeowner changes her mind and wants solid squares instead. You can't get more paint, so you need to know what size squares to paint to avoid running out prematurely. Happens all the time.
*Steel squares are great for boomerangin' off the second deck. They don't come back, and thats a good thing!Aluminum squares, now that's a different story! I've scraped the ice off my windshield many times. Heres the specifics: hold the bladein your left hand...Thawing in MI,Blue"Cover me. I'm changing lanes."
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You can't, if what you mean is to use the steel square to somehow geometrically draw the correct-sized square firgure (as opposed to just measuring the diameter of the circle in inches and multiplying by .886).
This is an old geomtric problem, called "squaring the circle". You might remember from high school geometry that it took the Ancients awhile to prove that this was impossible. It has something to do with the reason that pi is referred to as a "transcendental number".
*This method is probably not exact, but it's close. Put the square inside the circle with the outside corner just touching the perimeter. Rotate the square until the length of the chord measured on one leg is twice the length measured on the other leg. The long dimension is the width of a square with the same area as the circle. I tried this with a 10" circle and fit the square inside with readings of 4.5" and 9", close to the 8.86" you would expect, assuming Barry's answer is correct. Not perfect, but close enough to estimate paint coverage!
*Gentlemen: As per the "steel" square as opposed to the aluminum square, there was no aluminum squareat the time my source was writen, 1875. The method is as follows; set a bevel to 9 3/4on the tongue and 11 inches on the blade. Then move the bevel to the diameter of the circle on the blade and the tongue gives the answer. The source is from Fred T Hodgson's book Practical Uses Of The Steel Square. The book has a lot of little known uses for the square, andis a great resource to show us just how ignorant we are compared to carpenters from a hundred years ago. still learning brisketbean
*Gentlemen; Another interesting use for the square is calculating the circumference of an oval or elipsewith the square, anyone know how its done? brisketbean
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well I'll be. All those things you can do with it. And I thought it was for opening paint tins!!:)
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"useing only the framing square"
"set a bevel" !?
Seems you've changed the rules on us, might be easier to just use the end of the square to push the buttons on one's calcualtor :)
BTW how many of you know what the hudredths scale on a rafter square is for (no, it's not for fileing your fingernails)
Jay (who doesn't even own a rafter square, I use a CAD program to caluclate that kind of stuff, I just have a cheap framing square that doesn't have rafter tables on it)
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brisketbean,
I would be careful using the word "oval." An ellipse may be an oval, but an oval may not necessarily be an ellipse. A two-dimensional egg is an oval, for instance. As in the previous puzzler, one wonders why.
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back in the old days the framimg square was the carpenters calculator. Its like any other tool you just need to learn how to all of its asets.
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I forgot to mention: Throw that speed square thingy out there in the mud too!!!
Blue, freezing and framing in MI
"Montana -- At least our cows are sane!"
*If you find me calcualting ovals, and circles with my steel square, please do me a favor: bury the blade in my head and put me out of my misery!Bring on the new days!Blue, calculating with , surprise, a calculator in MI"If we aren't supposed to eat animals, why are they made of meat?"
*I was taught that the hundreth scale is to convert fractions. I think you are supposed to hold a different ruler up to the scale. The user then compares the decimal to the fraction, thus eliminating the need to do the tough math. You know, .25 x 16, .5 x 8, etc. Wonder why they don't have a thousandths foot scale? I might actually use that sometime!I doubt it.Jay, I too used the cheaper "homeowner" square for many, many years. Stanleys original was the best. You could beat the hell out of it, and it wouldn't break. It was easily rebent to shape, never showing stress cracks. It was so resilient, Stanley figured out, that you would only need one every five years (the edges rounded off). Oh how I miss the old days ( I shoulda bought 10 of them)!Question for you and Joe. Why do you use Cad to calclulate on-site figures? How does it work?Blue, using a dual power in MI"Few women admit their age; Fewer men act it."
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Barry:
Your selected use for the first formula was
great, as fast as your mind works you could do well on the spin team at the whitehouse, no offense intended,or question of your character
implied, just that you are creative.
The first one is good for calculating storage capacity for square as opposed to round spaces.
The second is good to calculate for instance the length of rope lighting element for the ovaled
brick dome ceiling we are putting in one of our current jobs. It is kind of hard to measure the circumference of an oval that is `10' in the air.
I am not sure why this works but it probaly has something to do with the tangent of the bevel or something. possibly Ken Drake could explain the relationships. Most of the trig and algebra is way over my head, and I have to have simple ways
to accomplish these calculations.
Got to go have an early Valentines dinner with the boss since our kids are loaned out for the evening, will post the method for finding the circumference of the elipse later.
brisketbean
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'Bean
Is it ok if I quote from one of my dad's books (Steel Square and It's Uses published 1941, Geographical Publishing Co., Chi. Ill) or would that be cheating? How about how to find the distance of open water between two shores?? I learned how to find the height of something (tree, cliff) in Boy Scouts, but this book just goes on and on.
Kinda cold in Ontario
_patrick
*You lay the boy scouts end to end, figuring that the average boy scout is 5'4" feet long. 990 boy scout to the mile. -David
*A friend from high school geometry class called me up because she, as a dressmaker, needed to cut an ellipetical shape for a wedding dress train. I went into the X^2/a^2 + Y^2/b^2 = 1 stuff and how to draw one with a length of string and two push pins. I didn't think to tell her to use a framing square!
*Hey Per Swede,Watch the Norwegian cracks, I had a Norwegian Grandmother. On the other hand My Grandfather was Swedish so a part of me agrees with you. I like to use a framing square as a back scratcher. Must be the Norweian side.
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Patrick;
Quote from whatever resource that is pertinent to
the subject at hand, I saw the solution to measuring
objects that are out of reach in the book Im useing
also. If we only had more time to read and study the
resources that are at hand. I have the pleasure of working with a couple of good apprentices and carpenters that are growing in knowledge and ability
every day, as they learn how and do the tasks that I used to have to do it gives me a chance to concentrate on some of the finer points and pass them along to the others. It seems that I went through about a 10 year period of time without the benefit of good men to work with, men that wanted to improve themselves and do something besides get a check, get high, get drunk and screw up my jobs along with thier lives and families. It is a true pleasure to work with people that have goals and direction in life, I am a blessed man enjoying life at its best, now if the days just had another 6 hours added to them for diversions.
brisketbean
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Okay, forget that burying the square in my head! But if I ever have to calculate the length of rope, hang me with it!
Blue, looking for his "square" book in MI
"Consciousness: That annoying time between naps."
*Cripes, 'BeanYou get about 21 hours of sunlight a day down there near the equator, what do ya need another 6 hours for???Pass the Dr.Pepper
*David - Your post reminds me of a comment I heard once:"If you laid all the economists in the world end to end, they wouldn't reach a conclusion"Sorry for getting off the subject. How about just telling us these uses for framing suqares, instead of all the quizzing ?
*Well, at least the glass is half full....sorry to hear about your grandad though...maybe some bad herring or too much aquavit clouded his judgement...just kidding....framing squares work really well at holding blueprints & plans down on breezy days...2 work better than 1.
*Per Swede, unfortunately my grand mother, as I hear it, spent so much time surpressing her heritage that very little of it made it way down.I, being from Minnesota, am a freak for wild rice. I don't mean that crap in the stores, I mean the stuff that goes for about as much as cocaine a pound and is worht twice that. That is about all I have of either heritage.
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Carpenters;
To find the circumference of an ellipse or oval,we proceed as follows; Set 5 5/8 inches on the tongue and 8 3/4 inches on the blade. then set the bevel to the sum of the longest and shortest diameters of the ellipse on the tongue,
and the blade gives the answer.
brisketbean
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Brisketbean,
I've been unable to get access to a computer for several days, mine is still in Houston undergoing surgery on the CPU.
A few quick comments on the circle/square question.
As has been pointed out by others, if a square and a circle have the same area, then the length of a side of the square is equal to .866 times the diameter of the circle.
The number .866, is one-half the square root of "pi". This relationship is true regardless of the size of the circle.
The solution using a framing square is to use 9 3/4" on the tongue and 11" on the blade ( body), to get the proper ratio. Since 9.75 divided by 11 = .866, you can use the framing square as you suggested to arrive at the correct answer for the length of the square.
The second problem which you present is much more difficult.
Unlike the circle, there is no known formula to calculate the exact "circumference" of an ellipse. So the best we can do, is to approximate it.
With today's high speed computers, along with some sophisticated math software program, we could get the answer to any degree of accuracy that we wished. If however, we only needed an answer that was "pretty close", we could use a method such as the one you suggested with a framing square.
If I can get my mitts on a copy of the book you mention at our local Library, I'll look into how he arrived at the numbers 5 5/8 and 8 3/4,
and try to determine the degree of accuracy of this method of approximation. My gut feeling is that this method will always slightly underestimate the actual length. Also, I suspect,
the degree of accuracy will vary somewhat from one ellipse to another depending on the "shape" of the
the ellipse.
Have blue eyed devil and Joe ever settled their bet? I was looking forward to seeing what problems they were going to come up with to see who gets all the milkbones. Keep me posted. Ken
*'BeanGee, my book agrees with your book, how 'bout dat?Perhaps a more practical way to find the circumference of a circle would be the following abridged by yours truly from 'Steel Square And It's Uses',(pub. 1941 by Geographical Publishing Co. Chi. Ill.):The circumferance of a circle may be obtained from the DIAMETER as follows: Draw a circle in some proportion to the actual work, say one inch to the foot; mark the centre of the circle 'A'; then apply the heel (outside corner) of the square to this centre; then project lines down the 'body' and the 'tongue' to intersect the circumferance of the circle and call the points 'B' and 'C'(you now have lines 'A-B' and 'A-C' like a clock saying approx. 4:40); join these two points 'B' and 'C' so you now have an Isosceles triangle (two sides equal) drawn within the circle and call this line 'B-C'(the base line of the triangle); find the centre of line 'B-C' and call this point 'D'; you now pick up the cat that you were holding between your legs . . . sorry. . . ; scribe a line (or just measure the distance)at right angles between point 'D' and the circumference and call the point on the circumference 'E'( six on the clock face); ADD this distance 'D-E' to THREE times the diameter and the circumference will be "practically correct". To find the side of the greatest square that can be inscribed in a given circle, when the diameter is given, set a bevel to 8 1/2 on the tongue and 12 on the blade; then set the bevel of the diameter on the blade and the answer will be found on the tongue.b A picture saves a thousand words.-Patrick
*To my knowledge, Joe has never accepted the bet! I got my stash of milk bones waitin' though!I was gonna ask him to figure the height of a roof with an 8/12. TEE HEE, it seemed like taking candy from a baby!Blue
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Shucks! All this is givin' me a headache, I think I'll prop up the lid of my toolbox with my framin' square and get out my thermos......
I'm enjoying this chit chat!
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While we're on this subject does any body remember when stanley made a stainless steel square? Better yet does anyone know who still makes one? I still use a framing square
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stanley still makes a SS square product id no. 45-021. I bough mine about 10 years ago and still use it.
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Brisketbean,
I wasn't able to find a copy of the book by Fred Hodgson that you mentioned, but have looked into the ellipse problem and will post some additional information regarding it tomorrow, so stand by.
Joe,
Thanks for posting the pictures of Tommy's World Famous Dodecagon. I enjoyed them. Well done Tommy!
*brisketbean,Here's a little more information about calculating the length or "circumference" of an ellipse.Let's start with something we do know, namely, the formula for the circumference of a circle. If we use 3.14as an approximation for "pi", then the formula is:2 x pi x radius = 2 x 3.14 x radiusSince the radius is always equal to one-half of the diameter of a circle, another way to write the formula would be 3.14 x diameterFor example if the diameter of a given circle was knownto be 10 feet, then its circumference would be3.14 x 10 feet = 31.4 feet, or 31' 4 13/16"Now suppose we are working with an ellipse that is almost circular. It is just slighty longer than it is wide. Suppose it is 10 feet long and 8 feet wide. Wouldn't it be logical if we took the average of these two numbers and thought of it as the "average diameter" of theellipse, if you will, and then multiploed it by 3.14 to get the circumference????? 3.14 x !/2 x ( 10 + 8 ) = 1.57 x ( 10 + 8 ) = 28.26 feet or, 28' 3 1/8"As it turns out, this answer is within about 2 inches of being exact, so this method gives us a very, very, good approximation. We are so happy with this method that we decide to generalize it into a formula.TO FIND THE "CIRCUMFERENCE OF AN ELLIPSE", ADD THE LONGEST DIAMETER OF THE ELLIPSE ( ITS LENGTH ) TO THE SHORTEST DIAMETER OF THE ELLIPSE ( ITS WIDTH ) AND THEN MULTIPLYBY 1.57Now, look at the numbers that Fred Hodgson suggests thatwe use on the framing square to find the length of an ellipse, 8 3/4 and 5 5/8. If you divide 8 3/4 by 5 5/8, you get 1.5556 as an answer correct to four decimal places. He then suggests that we multiply this by the sum of the longest diameter of the ellipse and the shortest diameter of the ellipse to find the circumference.1.5556 x 18 feet = 28' 0"This result also is very good as an approximation, being within about 5 inches of the exact answer, but it is not quite as good as our first result.For the type of ellipses that we frame in ceilings ofhouses, either one of these numbers will give you a good approximation. Where they fail, is when working with very long and narrow ellipses. In these type of ellipses, the answer may be off by as much as 24%. To generalize, the "rounder" the ellipse is, the more accurate the answer will be.Hey Joe, ARE YOU OUT THERE? What's the deal with the milkbones and the double or nothing bet with blue eyed devil? If you can't think of a good problem for him to solve, let me know. I'll make one up and send it to you for half of the milkbones. You pay postage. Ken
*Been waiting about that bet????????????
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along with the normal uses I have for my framing square i use it at work to set up rocket motor static firings. plumb, level and square is all the same in bulding trades to rocket science.
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They're great for cleaning crap out of the space between rough stair stringers and walls, before putting the skirt boards in. How does all that junk get in there?
*How light is it?Can your read the numbers?Blue
*Joe, I posted the question on the homepage as a new topic. I'm assuming that you'll accept the bet! Good luck!Blue
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THE WEIGHT IS ABOUT THE SAME AS A STEEL SQUARE, ITS A COMPROMISE BETWEEN THE RUST RESISTANCE OF ALUMINUM AND THE WEAR RESISTANCE OF STEEL. NUMBERS,SCALES, AND TABLES ARE FILLED WITH YELLOW COLOR. I CAN READ IT OK, I LIKE TO TRY A BLACK OR BLUED ONE WITH YELLOW NUMBERS I THINK THAT WOULD BE THE BEST. ONLY ONE DRAW BACK IS THE POISHED SURFACE REFLECTS A LOT OF LIGHT WHEN I WORK IN THE DIRECT SUN. I STILL WISH THEY MADE THEM LIKE THEY USE TO THICK AT THE HEEL TAPERING DOWN THE TONGUE AND BODY, TEMPERED STEEL SO IT LASTED A LONG TIME. FORGIVE ME I'M JUST A LITTLE OLD FASHIONED.
LOOKING FOR SPRING IN THE HILLS
BILL
*DOES ANY WORK ON BARNS OUT THERE? I'M CURRENTLY RECONSTRUCTING A 130 YEAR OLD BARN AND AM INSTALLING AUTOMATIC DOORS ON IT. THE INSTALLATION IS DONE BUT I FORSEE SOME FUTURE PROBLEMS AND I WUNDER IF ANYONE HAS DONE THIS BEFORE. I AWAIT YOUR REPLIES. HERMAN
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Herman,
Now that's an uncommon use for a framing square....How many squares to build the doors and openers?..And what's the future problem...carpenters stopping by and removing squares like picking strawberries?
Tell us more,
Jack : )
*I find that old dark/rusty steel framing squares make good angle brackets for shelves, short walls, corner reinforcement etc. Just drill some holes so that the nails fit tight and nail or screw them to the framing. Who says old fashioned framing squares don't have any good use? ;-)
*Thats funny Gary! Maybe I'll weld them old heavy things to my hood as an ornament!Blue
*No fair! I'll have to get my own worldwide network working to solve the problem if you help old "7.167 pitch Joe" out!Blue
*BlueCheck the date of Ken's post. . . it's a done deal. . .. you snookered booger!!!
*What's a date?Blue
*sticky, chewy thing they grow in the middle east. . . a little south of Mi.
*
Hey Joe and all of those who are in the know:
How can you find the side of a square that has the same value or area of a circle with a given diameter, useing only the framing square?
brisketbean