Hi Guys.
I know that is a simple formula to test the squareness of any orthogonal triangle. (what we call a square)
But I don’t remember the equation.
Any other tricks to test the square without the help of a ruler?
I have one trick here but I like to see few others.
Thanks for your help.
YCF
Replies
Are you refering to 3/4/5 - 6/8/10 - 12/16/24 or something different.
To check a square or rectangle I measure diagonals.
Am I getting led into some kind of trick?
Without a ruler, can't you use a straight line and.... oh nevermind, geometry is not flowing through my birdbrain.
On the subject of math (the science of patterns) yesterday I read an interview with a mathmatician who claims birds can do trigonomitry.
Mike
Trust in God, but row away from the rocks.
3,4,5 or any multiple of those works - 6,8,10 etcfor larger triagles - like foundations etc its, its..how the heck do i type it..
a(sguared) times b(squared) = c (squared) where a and b are the sides that are suposed to be at a square angle you'll need a calculator for this one...
a² + b² = c²
Plus, not times.
Here's a cool experiment which proves the formula a² + b² = c²
First, draw a right angle triangle on paper - grid paper helps. Write a and b next to the sides that are at right angle. Write c next to the hypothenuse side - the long diagonal.
To this triangle, draw in the sides of three squares, each of which has a, b, and c as one of its sides. Now you have a weird shape: the original right angle triangle, with a square sprouting from each of its sides. It happens that the area of square a plus square b is equal to the area of square c. That's what squaring means!
You can prove the math by cutting out each square into pieces and pasting them onto square c. The pieces will exactly cover c, if you fiddle with it long enough. If the experiment was carried out on plywood, the weight of square a plus b would equal the weight of square c.
A friend showed me this litteral interpretation of a² + b² = c²
http://costofwar.com/
Edited 9/29/2005 12:03 am ET by Pierre1
That is a consequence of the pythagorean theorem (i.e. the formula). It is probably derived from trigonometry. The formula for a circle is: x² + y² = r², which I think comes from Sin²(t) + Cos²(t) = 1 where t is the angle (i.e. when the circle has a radius of one).
Lew, I always have a hard time remembering what a sine and cosine are, and how to use them practically. I've read and re-read several articles on it in FHB/Taunton, but it doesn's stick. Thank god for my CM-IV. :-)
I'm stupid when it comes to that level of geometry/algebra. Too bad, because I realize that knowing the value of one angle and the length of one side yields all other values for a right angle triangle. http://costofwar.com/
Did you know that the square is the only arguement that works in the Pythagorean formula?A³ + B³ does NOT equal C³And no other arguement works either. I saw a show on PBS about a guy who figured out a way to prove that no other number would work. Don't remember the details, and I didn't understand the explanation anyway. Just thought it was interesting...
Do Lipton Tea employees take coffee breaks?
"A³ + B³ does NOT equal C³"
I put your premise to the test and you are right:
Using the good old 3-4-5 right angle proof. Lets see if 3³+ 4³ = 5³
3³= 27
4³= 64
5³= 125
27 + 64 = 91 (not 125)
I agree, this stuff is interesting.http://costofwar.com/
Too be a little geeky here, the fact this only works with powers of 2 is called Fermat's Last Theorem and remained unproven for centuries. It was considered the chief problem in mathematics and wasn't proven until a few years ago by a professor at princeton.As for checking if a square is square: I'd use it to draw an "L" and then flip it over to draw a "backwards L" keeping the vertical line the same. The two horizontal segements should be in line. If not then you've got a non-90 degree square.
As I recall, Fermat asserted that he had a simple elegant proof of this theorem but it was too large to fit in the margin of his book. Too large indeed! The modern proof is about a 400 page document. So: are we still missing something, or was Fermat mistaken?Joe Bartok
Fermat had really teeny handwriting. ;-)
Its generally accepted he didn't know how to do the proof or whatever he had in his head must have had a flaw. The modern proof has so much new high level math its unlikely he knew how to do it.
Pierre,
If remembering the formulas is the problem, maybe this simple saying we used in school will help. It's dumb enough to get stuck in my memory.
Saddle Our Horses sine = opposite over hypotenuse s = o/h
(or: sine = opposite divided by the hypotenuse)
Canter Away Happily cosine = adjacent over hypotenuse c = a/h
Toward Other Adventures tangent =opposite over adjacent t = o/h
I think it was Mike Smith who mentioned the name, "Sohcahtoa" to remember the same order.
A small book called the Pocket Reference, published by Sequoia Publishing has the tables. (and a lot of outher useful stuff)
oldfred
Our HS Geometry teacher challenged us to come up with some of those (mnemonics??). The ones that I still remember are "Sally's Oily Hair" & "Tripped On Acid".
Thanks for that mnemonic fred.http://costofwar.com/
Without a measuring tape or ruler, you could use two sticks and clamp them together to touch each corner across the diagonal, then hope that those clamped sticks will also exactly touch the other two corners. If not, adjust the sqaure and try again until the clamped sticks touch across the two diagonals. (Each time you adjust the square, you will have to move and reclamp the sticks on the first diagonal "measurement".) Hope I am making sense to you.
Dino
By square do you mean a box with 4 equal sides?
Just asking because some people will say square when they are refering to a rectangle.
Doug
FWIW, Even before Pythagorus, the Babylonians used 3,4,5 and 5, 12, 13 , plus others, for their building trades, see
http://aleph0.clarku.edu/~djoyce/mathhist/plimpnote.html
for a list of what they used. -- first hit on search for (babylonians 345 triangle)
Just asking because some people will say square when they are refering to a rectangle.
Yes.. The squareness of a rectangle. Or the squareness of the two legs of an orthogonal rectangle.
YCF Dino
4 x 4 =16 x 4 = 64 no?
Remodeling Contractor just outside the Glass City.
Quittin' Time
64, yes
dino, among the other irrelevant goodies in this document there's a formula for solving Pythagorean Triples ... right triangles whose sides whole numbers.
You'll find the same formula if you scroll down this Trig Formula Reference web page.Joe Bartok
dino-
are we having fun yet? :o)
r u a feckless dastard?
rez.
Last time that I was into this stuff,
(geometry and math) it was in high school.
I remember that I was trying for years to solve one of the unsolved geometry tasks. Something about dividing an unequal corner into three equals? (something like that)
Back then it was fun. Now that I got older, I'm just looking for the simple and easy way that can inspire me to make something up.
And thanks to all of you guys ...I think, We're up to something here.
This weekend I'm working on making the Perfect Square, by not making the square-square at all.
Thanks guys.
rez. pictures Monday.
YCF Dino
>I remember that I was trying for years to solve one of the unsolved geometry tasks. Something about dividing an unequal corner into three equals? (something like that).Dino, trisecting an angle is, in fact, impossible and provably so. Good thing you stopped trying.
We can trisect an angle; it just can't be done under the rules of Euclidean geometry with straightedge and compass only. I remember attempting this in high school as well (longer ago than I'd care to admit) and having a heated debate with my math instructor.
If we cheat we can Trisect an Angle.
And framing square users, check out this Trisection of an Angle link. Click on "Cheating (using other tools)".Joe Bartok
Going back to the right triangles:
Any triangle inscribed in a semi-circle is a right triangle. So, if we find the center of the longest side of a triangle and set the point of our compass (or trammels, or a pencil on a string) at this midpoint, draw a circle and if it passes through all three points of the triangle, the triangle is a right triangle.
Joe Bartok
Edited 10/5/2005 11:24 am ET by JoeBartok
OK guys.
For two years the perfect square was elusive. With all the suggestions from breaktime and a simple modification to the plastic edge of the guide...the perfect sliding square is history now.
1.We attach a true square to the fence.
2.We modified the white edge in order to allow for the square to touch the guide rail.
3. we oversize the holes on the fence that attaches to the studs of the guide control unit and...the perfect cut was made.
View Image
Here is a picture of the sliding square before. I get the final pictures tomorrow.
Thanks guys.
YCF Dino
joe.
I'm glad the high school is over. Im looking for a simple stick.
Thanks
YCF Dino
A handy formula that I use often is the relationship of the square root of 2 to a triangle with two equal sides. ( a square). Multiply the side by the square root of 2 and you get the diagonal. For example a square with 12" sides. 12x1.41 = 16.97" That would be 12 and 17 to round it out and the angle of a hip on a 12/12 roof or the length of the diagonal of a 12" corbel.
Mike.
This is a handy formula.
Thanks.
YCF Dino
Dino
You are welcome. I thought since the title of this thread was a "True Square Formula" then the square root of 2 formula would be what you wanted since it only applies to true squares. I am surprised that no one else mentioned it before me. Any self respecting framer should also know how to use the pythagorean formula too. It is handy for squaring up foundations, cutting roofs and stairs.
Another handy formula that is very simple for getting the angle of any slope is to divide the rise by the run and then get the inverse tangent of that. For example to find the angle of a 4/12 roof you would divide 4 by 12 which is .33. Now hit the inverse tangent button on your calculator and the answer is 18.43 degrees. If your miter saw has a vernier scale like the DeWalt then you can get a very accurate setting if you know the fraction of the degree. To get the complementary angle you just subtract that from 90 and there you are. So the complementary angle of 18.43 is 71.47.Mike Callahan, Lake Tahoe, Ca.
5-12-13?
blue
blue.
You just give me an idea.
If we have a stick 5" long and we draw a semi circle.
Extend the same stick (extendable-stick) to 12" and draw another circle
(using the same starting point.)
Then we can extend the same stick (two way extendable ) to 13"....
We can touch any point of the 5" circle with any point of the 12" circle the same time. This two points with the center of the circle should make an orthogonal triangle.
Your blue thoughts.
Thanks blue.
YCF Dino
easier to just buy an "A Square" .. the folding 3' 4' 5' aluminum triangle.
Jeff Buck Construction
Artistry In Carpentry
Pittsburgh Pa
That's exactly what I was going to say. Those A squares are great on a layout.
This is great stuff.
My problem is that I am a visual. I see things in thin air and create as I go. If there are too many numbers and figures on a print or page, they start to grow legs and leap around. I guess this is why I mostly do restoration. But after several years of being a carpenter, the brain has to pick up and retain some of this, no matter how left hemisphered one may be.
A friend of mine who's brilliant at math once started to show me what all you could do with just the simple framing square and it was mind boggling.
Making your own square is as simple as folding a piece of paper twice.
Wouldn't that depend on whether the paper had edges square to themselves to begin with?
Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!
No. Good question though.
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You could fold any raggedy edged flat surface, (Paper or Hide, t-shirt. Etc) to form perpendicular edges. The more folds you make the more angles you get. But it takes 2 folds to make a 90 and 3 to make a 45. Every subsequent fold divides by 2. One fold yields a 180 or a straight edge.
Yes. The A square is great.
My problem is that I'm working on a sliding square
That needs to be calibrated every time.
One ez way is to draw a line and flip the square and draw again. When the lines meet you have a perfect square. The goal is to be able to tsek the square without draw 2 lines.
A complete system goes to the breaktimer with the ez answer.
View Image
View Image
Edited 10/1/2005 6:46 pm ET by dinothecarpenter
I'm bewildered here a little. I’m not sure what your looking for………that you already know.<!----><!----><!---->
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The easiest way to draw a line perpendicular to another is to draw a couple of intersecting arcs. A line drawn from the two intersections of the radiuses will be perpendicular to the line drawn from the centers of the two arcs. They do not have to be equal in radius either. Once you have that drawn adjust your sliding square to that.<!----><!---->
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……….?
That's what I use to find my miter cut, bisecting the angle the way you just described. Have been doing it for so long now and have gotten so fast that when I got the Starret angle finder, I didn't trust it. Now, I sorta do.
I'm bewildered here a little. I’m not sure what your looking for………that you already know.
If we omly looking with what we already know, then weren't looking for something new.
Draw a scetch with your suggestion ...( couple of intersecting arcs.)
Then we can see if we can use this method on the sliding square.
YCF Dino
Holy smokes Dino--No lines, no measuring and the goal is square every time---that'll get the brain juice flowing---so here goes---the best I can conjure( at 11:30 on ####Sat. night) is to calabrate against a known square,Just for thoughts. couple years back a friend opened a machining business and had a CNC machine installed--One night while working the controls and getting comforable with it I had him machine me a Lexan 3-4-5 triangle. this particulare one is 1/8 material--open in the middle and if it isn't dead on I don't know what is--I check my framing , speed and saws off it--Don't see why you couldn't do the same with an adjustable square. Alum. Lexan, all depends on how much abuse you want it to take.Like I said just for thought---Hope things work out , sound exciting, like to see how it develops. Mike" I reject your reality and substitute my own"
Adam Savage---Mythbusters
Holy smokes Dino--No lines, no measuring and the goal is square every time---
Hi Mike. and this is only the squaring part of the sliding square. Then we have to make it self clamping to the panel. And who knows what else.
that'll get the brain juice flowing---so here goes---the best I can conjure( at 11:30 on ####Sat. night) is to calabrate against a known square,
That would be the ez way. The only problem is that we have plastic edges on both sides of the guide.
But I think we have enough to start playing with something similar to A Square, but only with 2 legs. One of the legs (lines) can be the sliding square itself.
Ok. Here is a thought with pictures to follow later.
a. We need a handle to hold the sliding square.
b.The handle can be the third leg of the square.??? (the long one)
c. And we need to clamp the square to the workpiece. Using the handle would be nice.
See you guys later.
YCF Dino
I have a plan..the idea you are suggesting is basically a T sq like a tablesaw fence, you want it to be self squareing and quick ( EZ) to move?
Lemme get in the shop today and take a pic of my idea..I can email you? Spheramid Enterprises Architectural Woodworks
Sphere.
This is where I'm going.
See you later with pictures.
YCF Dino
Ok..is this something we need to focus on with intent?
If it is, I am open to using my shop to do it. Spheramid Enterprises Architectural Woodworks
There are lots of ways to create right angles or perpendicular lines. I can't think of anything new about any of them. This “Sliding Square” sounds like a rip fence or a sliding table and they’ve been around forever tooo. Are you trying to reinvent the square?<!----><!----><!---->
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Anyway, here is a pic of the simple (not new) geometric principle I mentioned before. I’m sure you will recognize it.<!----><!---->
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<!---->I'm "Lost" with this one.<!---->
Here's Pic
All well and good in 2d, the orthographic in 3d is much more harder to achieve.
Conceptually, we can plot 2d, every day. In 3d or ( dare I say) 4d, we are still limited to our perceptions.
Let's not even venture into the other dimensions. Lest we have a mjor traumatic, brain fart. Spheramid Enterprises Architectural Woodworks
Exactly the same that I use. Great for an odd shaped room or in intersecting hallway or drawwing a perpendicular line into the batroom for tile layout etc. Best part is, no math!
Draw a line, I use a 4' alum yard stick and trammel point that clamp on to the edges and mark where the circle or arcs intersect and intersect and lay a straightedge through the two points, never failed yet.I cut the board twice and its still too short ! ! !
Hey Mike!
I wanna say ...good to meet ya, first all.
Now as a side note, I have a few 1/4" lexan sqs I made for trimming...a basic 45 and a few of the 30 and 22.5 and 60 shapes.
I have common holes drilled in them, 1 inch, 3/4, and a 1/2..these become radius templates and "guides" for reveals and such.
I have found that a combo sq. is time consuming to reset, with this set of 345 triangles in a tool belt, I can trim a helluva lot more better...
btw, Lexan is close to 6.2mm when they call it 1/4''..
I have adopted the Metric sys only because, it is ez ier for me.
If you can memorize .03937X ____mm= .000 yer right on the money.
I roof. Spheramid Enterprises Architectural Woodworks
thanks Sphere--Never had enough time to talk in depth with everyone so I am sure I missed some conver. time with you. I guess we'll have to pick up were we left off down south soon.Did you make those angle pieces your self or have them made?I have seen 45/45/90 availeble on the market but never any other angles...The one I have is 1/8 (3.175) so I cant beat it up to bad but has served me well and the price was right--Mike" I reject your reality and substitute my own"
Adam Savage---Mythbusters
I just made them on a mitersaw. And then lapped the edges to rid them of any saw marks and sharps. Spheramid Enterprises Architectural Woodworks
Well that's no fun---if you are going to make a angle jig ya gotta use at least a 350,000 dollar machine--I guess that is why he hasn't deversified into the angled piece of plastic market.Did you bore the holes with a fostner bit? Does the lexan bore well or get melty from the bit?In case your interested the other cool jig I have made from lexan are hardware templates for cabinet doors.The instant glue for the polycarbinate works great to make 90 degree welds.Not that I am trying to highjack Dino's threadMike" I reject your reality and substitute my own"
Adam Savage---Mythbusters
I was curious what U were after.
I was hoping it wasn't as simple as the "already invented" A Square!
Jeff Buck Construction
Artistry In Carpentry
Pittsburgh Pa
Length of common rafter per foot of run on 5/12 is 13".
3,4,5 ratios are easy to remember and good for layouts.
Other integral ratios also work (5,12,13; 8,15,17; 7,24,25; 20,21,29; 12,35,37; etc) except perhaps annoying co-workers. They have few advantages and are harder to find nice multiples of. Some (11,60,61; 21,220,221) are so acute that they are too sensitive to taping accuracy.
You can test the squareness of a square or rectangle with a piece of reasonably non-stretchy string or rope. First use the rope to measure opposing sides and make sure they're equal in length, then measure the diagnonals and make sure they're the same.
Otherwise use a measuring tape and the 3/4/5 rule or the squaw on the hippopotamus.