Trades Math - Find The Center Of A Circle Using Squares
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- Опубліковано 28 вер 2024
- One of the easiest methods to find the center of a circle accurately is to use a compass and perpendicular bisectors. However, on a job site a compass is not always readily handy, but you’ll always find squares. So using those squares I’m going to show you how to accurately find the center of a circle using three different methods.
Machinist: That's WAY off!
Carpenter: On the money! Nice!
As a carpenter I can honestly say.." I resemble that remark! " 😅
@@D-proGram_Yousef The difference is purely the precision of the tools and how they fit together. Wood may well swell or shrink more with changes in moisture than what a machinist will tolerate with metal parts.
@@SmallSpoonBrigade Agreed. I am fully capable of splitting the proverbial hair and taking the time to find the finite absolute. But thank goodness I don't need to go there, too often having to be precise but it does pop up with concrete , foundations grades/elevations, stairs and landings,.. & finding square/ plum when you're 5 stories up hanging by your bootstraps while holding a nail gun and lumber pencil and sighting in a string line. All while it's raining sideways ..lol ahh good ol Washington State freezing rain. Carpenters, framers, siders etc seem to always be challenged for time so sometimes ill use what ever is handy. Until the finish work begins obviously. I've got nothing but respect for those welders machinist and fabricators that deal with exacts and the minutia for 8 hrs a day or more I don't have the bandwidth to do the precision long game. I'm pretty sure we're some of the last tradesmen the way things are looking. Since the next gens are pretty much no shows for the mens jobs up here. too toxic I guess LMAO 😅🤣
👍💪🔨🇺🇲
@@D-proGram_Yousef It's scary to think of what this current generation is doing. They are more concerned with being mis-pronouned, than actually learning something useful!
"Make America Masculine Again!" (Funny that the Acronym of that would be MAMA lol)
Cut to size, hammer to fit!
Brilliant, this to me is why UA-cam was invented. Helping people solve problems & teaching people useful skills. Not for just having a rant or meltdown. Very informative, thank you. 👍👍🙏
I thought is was for fabricating videos about UFOs and other nonsense, writing a lie in the title and attaching some paid advertisement to put some fraud money in the evil pockets
I see my 83026 hours on youtube is very beneficial
DIY stands for Dude, It’s on UA-cam
ua-cam.com/users/shortsr6_Qz4T-WMc@@d3j4v00
Good call, brother!
Many thanks for this. It is a great training video I will use for others to learn from.
As a blacksmith if you are a machinist or a welder, I will open a conversation on that basis. but within a few minutes I will be asking for solutions to this and other problems. That is because the smith needs to BUILD his tools and jigs. In my shop I have an engine lathe, a mill, 2 drill presses, a hundred year old ironworker, 2 anvils, press brake and will expect to make hammers, tongs, forges, bolster plates and rivet/rivet tools as needed.
This video goes to the core competency necessary to create real world items from someone elses imagination.😀👍
Unfortunately I was a shitty student. I didn’t think I needed what they were teaching (especially MATH ) would do me any good. I was thoroughly convinced that I knew it all.
I was sooo wrong on every aspect. That if not for spell check, this comment would probably look like a 2nd grader DONE it. I probably would know how to do this if the teacher would have told me (it will help you get GIRLS )
I wish I would’ve learned Math at least 4 or 5 times a day.
Thank you for posting this now I have to subscribe to your channel, for this is NOW how I learn what I should have learned 50 years ago.
At least you're learning something. That's what education is.
Wow!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I am speechless, what a neat demonstration.
Glad you liked it!
Thanks for this. Simple and true. Love it.
Now THAT was a very useful video. Thank you so much.
Glad it was helpful!
Para aquellos que alguna vez llevamos la materia de "Geometria Descriptiva", esto es un dulce. Si carezco de escuadras, con un lapiz y un hilo, utilizandolos como compás, en 2 minutos encuentro el centro, el radio, el diametro, la circunferencia, el area y cualquier angulo.
Thank you for showing us this trick!!
Thank you. I need that information at the moment, Liked and saved...
Very good information. Thanks!
Awesome video! Thank you so much for posting this.
here are some formula to determine other measurements of a circle
r=radius
Pi=3.1415927
2(Pi) radians=360 degrees
Conversion formulas
Radians to degrees
(R) X 180/Pi
Degrees to radians
(D) X Pi/180
Area(A)
A= (Pi)r^2
Circumference(C)
C=(2)(Pi)(r)
Radius(r)
r=C/(2)(Pi)
Arc length of a circle = radius X angle in radians.
Sector of a circle = 1/2 X angle in radians X radius squared
Angular velocity(w)= dR/dt
A change of angle in radians over a change in time.
Radians are really the most natural way to measure angles. Like the metric system is the most compatible with our base 10 number system.
Neither are based on a convention, but are scientific in nature.
Pi=C/(2)(r) or the ratio of the circumference to the diameter of any circle.
Snuggle it up into the corner of the framing square the use the 90 of the speed square on the other side to find the diameter of the circle. Move the speed square to the half way point of the measurement and mark. Do this with the speed square along both the side and top part of the framing square without moving anything but the speed square.
Really informative
Your way of explaining is very impressive
Thank you sir
Wow. i'm 68, and skilled, in the shop. WHY were we not taught this, in high school ? . In industrial arts, class ??....oh well....never too late, i guess....living,....is Learning...thankyou too much...
I arbitrarily prefer the last method. Good video.
Thank you
Ha - I did this just the other day. Google is now watching me... I needed to find the center of my street cul de sac. Using string, a 30 foot tape measure, and a laser grid maker, I used option 3. Basically, all 3 options are the same, with the goal of making a chord, bisecting it, and drawing a perpendicular. Two of those intersect in the middle.
Nice
I like the second one best.
Wonderful application.
Where I need this is some 6” ceiling lights come with a template with no marked center or center hole. Thank you.
simply draw two chords equidistant from an edge ,on opposite sides of the circle but parallel to each other. the two diagonals joining opposing ends of the chords will bisect the circle.
Requires that the chords are parallel.
Great info! Thanks.
I’m 79 years old and I never knew that !!!
Great video, thank you 😊
Deserve subscription
I appreciate it very much.
I knew one. Now I know three.
Thank you 👍
You bet!
Thank you. I'm going on 75, and never seen anything like this before. I can't believe how dumb I am.
Like with most things, if you have the right teacher, you can learn anything.
Thank you very much.
It can be done with dividers also
Nice!!!
Nice video
Thanks
Very good tips ! ... but .... for small diameter rods , a commercial centre finder works best , or if the rod is quite short , put it in a 3 jaw lathe chuck and bring up a very small drill bit to mark the centre of that rod ....... DAVE™🛑
Sorry , no have got lathe.
Shut up.
You’re absolutely right!
I believe that carpenter's square is a projectile used by aggressive lock pickers
😂
Very nice, thank you!
if Euclid had a UA-cam channel
Seems like you did an extra step on the last one. You could have just measured across the line which you scribed and half would be at the center.
I just run the ruler to the widest spot... run a line... then do it again in the opposing direction and viola... center
What I've always done to find a circle's center , is to draw a square around the outside of the circle , and then connect opposite corners .
How to summon a spawn of Satan using trade tools
What nonsense. Get a cardboard box or a bit of plywood place the circle over it and bingo mark it out from the corners. JOB DONE AND DUSTED IN NO TIME.👍
Pencil on, ruler on.
I believe you have a need and perhaps a market here. Other than attending a trade school or apprenticeship, where else can you learn this? UA-cam, like their political BS stances or not, has become our encyclopedia and the place where we as a society comes to find solutions to everyday problems and information about just about anything. Our physicians don have the time to explain to us what or why this pill may help so where do we go to find out, You Tube. I am forever grateful to individuals such as yourself who first have the knowledge and secondly care enough about others to effectively teach absolute strangers something which they can use to improve their experiences. This places you on a level which personally I respect. You have to know what your are doing and take the crap from other sources called experts and you have to know a bit about computers and photography to compose the pieces we are privileged to consume. That is extra effort that many with hate and frustration in their hearts just do not have. So there is a big breeze up your skirt sir. Keep it up. America needs people like you.
I love and hate UA-cams algorithm. This is great info to have ….. 24 hours ago .
I hear ya
Amen👍🙏🙏🙏
Perpendicular bisector of a chord passes through the center of a circle. Nice practical application of geometry. Thanks for posting.
Thank you for watching
Yep
Except I remember bisecting the chords with a compass
The perpendicular bisected of two tangents of the circle intersect at the center 4:26
This video looks like workshop talk, but is actually pure Euclidian maths.
These are great! Just a quick note on method #1: the only thing that really matters about the square placement for the first two marks is that the apex of that square angle sits on the edge of the circle. You're marking two chord lines which meet on the circle edge and are perpendicular to each other. If you do this, the hypotenuse of the triangle created will by definition pass through the centre of the circle. The point is that you don't need to fret about making these lines the same length - it will work for any placement if the apex is on the circle.
Additional triangles to double and triple check only take a few seconds
Thales' theorem!
And your explanation is why the average person struggles with math! The video presented clear simple explanations that work, without all the useless information.
@@c.j.g.6913 at least 72 people had no problem parsing this additional information. Do you find the idea of additional clarification upsetting?
A bit hard for very small stock, but in the adsence of a centre square these methods are excellent first geometric principals for locating centres on circular material.
NICE VIDEO AND EXCELLENT REMINDER TO PAY ATTENTION AT SCHOOL.
👌👍🖖
Artist and HVAC guy here, thank you so much for this. So simple, so useful.
Glad it was helpful!
I have worked in a machine shop over 40 years and never knew about this simple method. Thanks so much for sharing!
so you sold machines, or used them?
American? MAGA?
worked as a cleaner?
How do you get to even study to be a machinist without having to show basic high school geometry first? I am an American, but went to school (partial) and apprenticed in Germany, and without that knowledge which you will be tested on in entrance exams, you couldn't even become a framing carpenter!
@@Leonardo-ql1qu Oh dear!
Very good video. Clear and to the point, and very practical.
Glad it was helpful!
If they taught it like this in high school math, more of us would've paid attention! 😃
Exactly.
Amen
It might depend on the student, but I agree overall. Interestingly, as an adult, I was bummed that he didn't give a mathematically rigorous proof for the geometry, even though he offered a practical demonstration that the methods did work.
You mean, more dummies like me would pay attention
They did. You didn't pay attention.
I'm gonna immediately forget about this again until I need it some day and have to rewatch this video
lol i was thinking of a way to remember how to find this video ha ha
Here's a reminder just in case you need it very soon.
here's another reminder just in case
My teacher taught me this in 1990. Thanks to him for this useful knowledge.
The angle formed by two secants is half the included arc angle. If you draw two secants at 90 degrees they will include 180 degrees or half the circle; making the triangle's base a diameter whether or not you drew an isosceles triangle. I forgot about this trig formula after high school but it comes up again and again in machining and drafting.
I've always used method 3, which I learned in geometry class. Method 1 is cool too. Method 2 I know works well because they sell a jig, that basically "holds the squares" for you.
Not only trades math, but basic geometry that is taught in any decent high school geometry course.
It's right there, in the middle. 😂
The last method is what I learned in board drafting. We used a compass find the middle of each chord.
A much simpler method, use the framing square and triangle to measure the diameter, devide by 2, you have the radius, scribe a line at the radius distance, rotate the circle and scribe a second radius line and where it bisects is the center.
i tried to google this the other day and google assumed i was doing all of this on paper. this is a great video for practical situations where you need to find the center. i ended up fumbling my way into the second method just trying different things, but i needed to draw a perfectly plumb line through the center of my circle and i ended up holding a framing square, a combo square and a level attatched to the combo square. it was a lot of moving parts to line up, but it did the trick.
Excellent improvisation!
you can also do these with powdered string if you want, it's kinda fun
some of us can't see exactly what you're doing on a screen on a small phone. Could you describe where you're putting the pencil mark better than just saying here and here. It doesn't tell us anything. Thank you for the video though. 2:35
OR, if you have access to a lathe, you can chuck this material up and use a center drill in the tail stock to find the center.
Here is another method. Inscribe ANY parallelogram you like inside the circle. Then criss-cross the corners of the parallelogram. The center of the circle is the center of the parallelogram.
Anytime a right angle is inscribed in a circle, the endpoints of the angle are the endpoints of a diameter.
The radius of a circle is perpendicular to the tangent line through its endpoint on the circle's circumference.
The perpendicular bisector of a chord is a line passing through the center of the circle such that it divides the chord into two equal parts and meets the chord at a right angle.
They make a center finder like the 2nd one you can buy
and as always basic math that we used to do in the old days impresses people today :P
Indeed. The old-school trigonometry that we used to learn and took for granted as the rational and straightforward way to do it, appears now as some sorcery from another dimension to the next generations, which is accustomed to "smart" phones and even AI to bail them out. Whenever I do some mental calculation in the presence of young colleagues, they respond astonished that something like that is humanly possible at all...
Useful things my math teacher failed to mention #468
😂
I love the 1st method, because it uses some basic math that is pretty counter intuitive, but easy to prove.
I remember my cousin asked me why a triangle with hypotenuse along the diameter of the circle and all 3 corners on the circle makes 90°, and I came up with a pretty clever proof.
At first I thought we just had a straight edge, but when i realized it was a square, I was reminded of that theorem.
Thank you! Great trick of the trade!
You bet!
OUTSTANDING!
Now if there was only a way to find the center of a 6 mm circle on a Toyota aluminium intake plenum....🤔
I don't know if I'll ever need this. But interestingly enough you could do the last method with just a tape measure.
Using it as a straight edge you could do 3 sides, then using the tape as a straight edge you could connect the 3 lines and find the center.
And you could find the center on much larger circles (for however large your tape is), with whatever tolerance you allow.
The angle in a semicircle is a right angle. Any lines from the ends of the diameter will intersect on the arc at a right angle. First year secondary school (🇬🇧) 54 years ago, circle theorems I guess, and never used- not in house, garden, farming, hunting, shooting/sniping, angling, ware house, dealer/croupier, degree in history, motorcycle, 4x2, 4x4, street, dirt.
All 3 a total waste of time. Just measure width divide in half. Then measure in from any 2 or more points. And it will always cross the center. Or if your square is bigger then the circle. Put the square touching the top and side. The mark 45 degrees twice. Or mark 45 degrees and half of the width on the top or side. And the 45 with cross the center of your other line. I deal with cutting perfect circles out of corrugated metal multiple times a day. And I don't have time for these 3 methods. I measure it. Divide in half. And make that half measurement from any two points of the outer circle. Will always be the center. Then I make a quick pattern out of cardboard. To make multiple cut out that same size. And if you circle is not perfectly round. But can be traced on paper. Make a paper copy. Fold it in half twice. And you'll have the center. Event if it's a oval.
You and ICWeld are my favorite tradesmen/fabricators/welders/mechanics on youtube! Lots of skills in those pockets
Thank you. I hope to be able to devote more time to this channel in the near future.
with all that , why didn't you just measure from one side to the other From the farthest horizontal points
and then measure from one side to the other from the farthest vertical points
and where the intersect is your centre
Only requires 1 simple ruler
Just FYI, you need something with a 90 degree reference for this.
If you don't have something with 90 degrees, use a compass and straightedge and construct a 90 degree angle.
Back in the Pre-MAGA era, they tought this in Primary School .
You know ~
Book Learnin !!!
Excellent video and straight to the point ~ no B/S and stretching out video for 5 minutes describing the type of scribe, where you got the measuring tools from and how to unbox them etc, before describing tip!
User stuartburton1167 is correct: "On the first method you should’ve said that each leg of the square should read the same length to the edge." This can be proved by contradiction as follows. Draw it out such that each leg of the square is the same length to the edge. Then draw it out (wih a diffent color pen) such that the length to the edge of one leg of the square is the NOT even close to the length to the edge of the other leg of the square. Contemplate the result on the tree of woo, TX Tradesman.
I didn’t say that the two legs of the square had to be equal distance to the edge of the circle, because they don’t have to be. It’s called Thales’ Theorem.
"When are we ever going to have to use this stuff?"
''You?... never, but those going into the trades will benefit ''.
You can also just find the diameter, scribe it, then mark the radius perpendicular ... because.. it's half the diameter. If you have correctly marked the diameter then the radius will always start from the middle. ... he actually made this harder... you can't find the center of a circle using an object that's not actually a circle. You will get close. Adding all this extra math doesn't make it easier or more correct
Learned this as part of my welding course
My Father said I did not know enough curse words to be a plumber
And that a bricklayer makes as much as a machinist😮
"why do kids even need to learn math in high school you never use it in real life! just teach them a trade, like welding or plumbing"
The welding or plumbing trade:
Why don’t you just measure the width of the circle and draw a line at the widest point and then turn and do that again? Two lines and it’s done in seconds.
Perfect example of the usefulness of the kind of stuff the "When will I ever use this in real life" brigade moan about re school curriculums being too "academic"
Using a perpendicular bisectors of chords. Each time you take a random chord and bisect it with a perpendicular line you'll pass through the center. Imagine the diameter of a circle... The bisector there is actually the center and any chord you can draw will have its perpendicular bisector pass through the center.
In the real world there's error introduced by us using the rule, using the protractor, drawing the lines, or measuring, and any other not mentioned right now. Doing the chord trick requires a minimum of two iterations to actually find the center, but due to error doing it a few more times may help with precision, or confidence at least.
The true center of Pi is equal to the seemingly infinite number of Pi. The only way to compensate, is to make the center larger than Pi. Which encompasses the true center, but also a seemingly infinite number of NOT centers.
Put on a piece of paper and draw the circle. Fold I half and using the transparency of the paper to align the two half circles. Fold again again using transparency to align the quarter of circle. Cut a tiny piece of the corner, unfold and boom, hole would be right in the circle and the round piece you want to mark.
Unfortunately in method 1 and two you are using a theoretical point. How sharp is the corner on the squaire? Does it have a bure or a small radius on it? Having said that I can't find a way to determine the radius of an arc without a cord length On papae a cord can be drawn. In the real world, where does the arc become straight to the tangent. Example, the radii of a folding table corner. Where does the arc end and the straight edge start? In my machine shop I have radius gauges, a rotary table and a test indicator. The rotary table can pick it up or make a gauge that fits. But that point where the radii stops is a theoretical point due to deburring or a burr.
If you don't have anything other than a writing stick, freehand draw three chords approximately equally around the outside of the circle and you will end up with a small triangle in the centre then freehand a line from each apex of the triangle to approximately the centre of the opposite side of the triangle and you should be very close to the centre, and if not, remember to bring more tools with you next time.
It's a bit convoluted, but if you push the circle up against a wall so the wall becomes tangential to the circle, then put one side of your square on the wall so the very corner meets the circle where the circle touches the wall - scribe a line down the side of the square which goes through the centre. rotate the circle and do it again.
If you have a lathe, it doesn't matter where you mark the centre - after a couple hundred revs, the circle will be concentric with YOUR centre.😂
You actually showed me four ways. Thank you!!
Can also set the circle against a wall and measure out x. Then you rotate it untill you create a pattern that reveals centre
Seems like so much work , when it is so easy to just measure from the edge of the circle from two points approximately 90° off the edge
hang a string twice
Based on squares being used #2 is fastest . Now ask a sheetmetal guy how to use a dividing compass to find the middle .
Could you have made a line from the tip f the 1st two lines to the 3rd using the 90deg f the square?
Why didn't you title this video "Find the general center of a circle using squares"?
Why is Ave so nice and politely spoken here. Maybe I'm lost here. 😂