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Hello fellow builders. A funny thing happened on the job the other day. I needed to use Pythagorem’s theorem to figure the length of a diagonal when I realized the ‘ol calculator batteries were dead. It’s funny how dependant we have become on those littles things.
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For a right triangle (must have one and only one 90* angle, LOL). A**2 + B**2 = C**2. The two short sides squared and added equal the long side squared. You then have to take the square root of C. Essentially, C raised to the 1/2.
Chris
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Well Brian, Chris has it right. A squared plus B squared (where A&B intersect at a right angle) equals C. You then get the square root of C and that is your distance. The only question I have is how do you get a square root without a calculator?
The Squarest,
Pete Draganic
*My thought exactly Pete. I've never invested in a construction type calculator but even my $5.00 solar powered version has a square root function. The batteries never go dead but I have been seen converting inches into decimals in front of the headlights.JonC
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I remember learning how to do sq. roots longhand, although I sure don't remember now! Maybe its the 25 or so years since I did it last. It is really amazing how used to using a calculator one becomes! If it isn't a 3,4,5 or multiple, a calculator is a must, unless you happen to have a good (old?) algebra text to show you the long way. Good luck!
*Brian;Ever use a slide rule? Square root is found by going from top bar to bottom bar on the slide line. No batteries to go flat & it will work without the sun.Cheers; JE
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If sides A and B of a right triangle are of equal length, then side C will be at a 45 degree angle and you can multiply either A or B by 1.414 (actually 1.4142136) to get the length of C. Of if you don't need real accuracy, multiply by 1.5 and cut it a little short. :-)
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Hey Guys,
The next time you buy a framing square don't through the booklet away.
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Of course a 3-4-5 triangle is easy to remember and, by using simple multiples can be extended for more accuracy. But there are many other combinations of integers that work: 3,4,5 (9+16=25); 5,12,13 (25+144=169); 7,24,25 (49+576=625); 8,15,17 (64+225=289); 9,12,15 (81+144=225); 20,21,29 (400+441=841) and so on. Plus multiples of any of those.
In 1979 I was the last student in my high school who could use a slide rule. Finally found a Keuffel & Esser Log Log Duplex Trig slide rule (the one that built Hoover Dam, all the planes in WWII, and got us to the moon) in an antique store (it has 20 scales). Really nice and very prescisely marked. Anyone who likes fine tools would appreciate it. Can do any calculation to 3 places, some to 4 significant figures. -David
*Pete...A**2 + B**2 = C**2, not C....square root of C**2, obviously, is C. Chris...let's don't confuse people talking about C to the 1/2 power.Brian
*Hey! It's still there. I went digging in the bottom of the drawer under this computer and the slide rule is still there. If I did learn to use it 40 years ago I sure don't remember now. And I was in an old tool shop just yesterday and they had a patented circular slide rule that doubled as a pencil holder cup. At least that one would be doing me some good.I don't remember how to do manual sq.rt. either though I guess in a few hours I could reverse engineer it with 25, 64, 49 or some known easy ones. But maybe the cheapest quickest thing is to just keep a bunch of those free in the mail just for reading our brochure calclators in the tool box, lunch box, glove compartment etc. etc.Or now we have the ever more ubiquitous cell phone. Call someboy with a caculator. Maybe the dime a minute lady can start selling the dial a sq.rt. #. Just $.50! Boy we are dependent on our toys.
*Brian,I know how to find the square root using the longhand method but it's just to difficult to explain here. If you are curious, stop down at the local library and look it up in a high school algebra book.I always have two calculators with me on the job, a Construction Master IV ( about $80) and a Texas Instruments TI 30X ( about $13 ) I carry the Constuction Master in my toolbag at all times wrapped in one of those flexible cloth beer coolers with velcro. Once you understand how to use it, it becomes an indispensible tool. I carry an extra battery for it also so that I don't get shut down right in the middle of cutting a roof, or a set of stairs. I keep the Texas Instrument calc. in the van to do an occassional trig problem.The beauty of the Construction Master is that it "thinks" in feet and inches. No changing from decimals to fractions necessary. To solve simple right triangle problems just enter one leg of the triangle as the rise, the other leg as the run, and push diagonal to get your answer to the nearest 16th of an inch. ( the "legs" are the two sides of the triangle that form the 90 degree angle)
*Whoa Guys! We need to think a little more creatively here. When faced with this problem here is what worked for me (day or night):1. Attach jumper cable to positive of truck battery.2. Duct tape busted Sears tape to negative.3. Run both inside field office (truck cab).4. Wire in serial (use baling wire) appropriate sticks of nails to drop 12v to 6v or 3.5v needed by artificial brain (calculator). NOTE: nail sticks must be wire collated and it's best NOT to rest nails on seat cover (scrap drywall is MUCH better)5. The answer will come to you in a flash.6. Drive to 7-11 to get a cup of coffee to pat self on back for ingenuity--observe that the calculator battery you need is ON SALE at checkout display. Coffee tastes bitter--make note to pat self on back with coffee from Amoco station next time. Thor
*Hey B,if you have a gable end measuring 20' across by 10' high and you need to know the distance from gutter to ridge, you do this. A squared plus B squared equals "X" you then get the square root of "X" and that is your distance you need.So... 10' (half the width of the gable end) squared is 100' plus 10' height squared is 100'. add them together and you get 200'. the square root of 200 is 14.142. convert that to feet and inches and you have roughly 14' 9/64" or in the field that would closely translate to 14' 1/8".this is how i came to say a squared plus b squared equals c then get the square root of c. I suppose to be more accurate i could have said a and b to the second power and then square the answer.Pete [email protected]
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You can find the square root by approximation pretty quickly. You can see what two integers the square root is between (say 3 and 4). Then multiply 3.5 x 3.5. The answer will be bigger or samller than your desired answer. Adjust your guess up or down and multiply again. You can get two decimal place (0.1 inch, or about 3/32) accuracy in a couple of minutes. Of course, if you need to figure out a bunch of square roots--go buy a new battery.
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DScott: Find the number on the A scale (e.g. 25) and look for the square root on the D Scale (e.g. 5). Like all slide rule operations, you have to have a sense of scale. If you look at the wrong "25", the one that's really 2.5, 250, etc. then you'll get an answer of 1.58, 15.8 etc.
Alternatively, start at 2.5 on the D scale and find the log of 2.5 on the L scale (.3981). For the log of 25, add 1 (cause 25 is 10 x 2.5) giving 1.3981. Divide by 2 (square root) in your head giving .699 on the L scale which correspondes to 5 on the D scale, your answer. More involved but more versatile. Divide by 3 for cubic roots. Multiple by thirty for compound interest calculations on your home loan, etc.
Here's another possiblity: Call the quick answer desk at the public library and ask them. Librarians are always happy to help. -David
*I have to go with John E. -- just use your framing square! It doesn't have the elegance of old Pythagwhatever (OED, Pythagorean, from Pythagoras, a Greek philosopher and mathematician also known for his belief in the transmigration of souls; of course, maybe he took the theorem from someone else) thing, but will give you a fairly precise answer, plus a little sketch of your triangle on whatever piece of wood happens to be nearby.We had to learn how to do the sq rt manually too. I deliberately forgot how -- something to do with successive guesses. Get a solar calculator.
*Here is the manual method: Using estimation, multiplication and long divisionSeries of 'perfect squares': 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400Delta perfect squares: 3, 5, 7, 9, 11, 13, 15, 17…(this is the difference between two perfect squares in series, ie: 36 -25 = 11. Eleven then is the Delta between 25 and 36.Determine the perfect squares less than and greater than your number:Subtract the difference between these perfect squares = Delta perfect squareSubtract the less than perfect square from your unknown =Square differenceDivide the Square difference by the Delta perfect square to 3 decimal places.Add this answer (a decimal fraction) to the lesser perfect square = square root.Check by multiplying your square root by itself to see if it = your unknownQED.Example: Find square root of 273.You know that 16 squared = 256Multiply 17 x 17 to find the next perfect square in series = 289.Now you know that your answer will be between 16 and 17.Subtract to find Delta perfect square: 289 - 256 = 33Subtract lesser perfect square (256) from your unknown: 273 - 256 = 17Divide this number into the Delta perfect square with long division: 17/33 = 0.515151…(this series always is a 2-number repeater - interesting!)Add this fraction to the lesser of the perfect squares: 0.515 + 16 = 16.515 this is your answerCheck by multiplying 16.515 x 16.515 = 272.7 which rounds to 273! Depending on how well you guess, this could be faster than Martin G's answer. Obviously if you don't have a calculator or a framing square handy, you probably should just go to lunch...
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Something really weird happened with my name and I can't edit it. I am known as blue: a.k.a. blue_eyed_devil on dalnet, irc. My real name is Jim.
Brian, the easiest way to calculate a diagonal on site with out the calculator is with the framing square. I'm assuming that you know both legs of the triangle.
Solution: Divide each number by any number (I usually use 12). This will usually provide you with small enough increments to use the framing square. Lay the framing square on an edge using the derived numbers. Mark these two points. Measure the distance between those two points and multiply by 12 (your chosen number).
Example: the two legs are: 120" and 288"
Solution: 120/12=10, 288/12=24.
Hold and mark the square at 10" and 24". When you measure between the two marks, you will find the distance to measure 26". 26X12=312"
Shortcut: use you tape to measure between the two numbers on the square, and multiply by twelve.
altenative: using the two numbers, step the framing square off twelwe times.
tip: to minimize error, use the smallest divisor so that the numbers will still fit on the square.
You will still have to do the basic math to convert the inevitable parts of a foot and inches.
blue, freezing and framing in MI
"I took an IQ test and the results were negative."
*"A"(squared) plus "B" (squared) equal "C" (squared). A and B are the sides and C is the hypotenuse or diagonal of a right triangle.
*Isaac Asimov wrote a short story about a young boy in the future who could do simple math in his head. Everyone was amazed and wondered how he did it.
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My dad used to tell a joke about the pythagorean theorum, the lengthy details of which I forgot long ago, but the punch line has remained with me to this day. . . "The sqaw on the hippopotamus was equal to the son's of the sqaws on the other two hides"
*Fred,Laughing for ten minutes! Have a good day,Jack : )
*FHB Editors,This Thread is worthy!Have a good day,Jack : )
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Hello fellow builders. A funny thing happened on the job the other day. I needed to use Pythagorem's theorem to figure the length of a diagonal when I realized the 'ol calculator batteries were dead. It's funny how dependant we have become on those littles things.
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To QED, thank you kindly for giving me the magic trick and thanks to everyone who responded. Not only did I buy new batteries, but I treated myself to a new Construction Master (dropped the old one off a fire-escape long ago)