There are way more videos on the internet that cause humans to become even more idiotic, depressed, and mentally ill. They are what youtube or online platforms should remove. But they won't do that, because idiots watch other idiots do idiotic things. And almost all people are idiots, hence idiot uploaders get millions of subscribers / followers
Yes. Great video. The angle inscribed at the center of a circle is equal to its arc length, while an angle inscribed on the rim of the circle is half of that. The total length of a circle is 2pi radians, so the half of it will be 180 degrees at the center, which means 90 degrees at the rim of the circle. But I must mention that it is not Thales’s theorem. That theorem is about parallelism and proportions.
Well done and thank you! As a retired high school math teacher I loved your geometry! Technically you proved that "if an angle is inscribed in a semicircle, then it is a right angle." What is really needed is the converse statement, "if a right angle is inscribed in a circle, then the endpoints of the chords form a diameter." The proof of that converse statement is actually much easier than the one that you did. (A true statement does not automatically guarantee a true converse. They both require independent proofs.) But enough of that! Please forgive me for the math lesson. But I really enjoyed it!!! ;-)
Thank you sir. I'm actually a bit out of practice. I kind of kick myself sometimes for as often as I have to look up old formulas again. One that I have to look up all the time, because I don't do it enough, is cone volumes. I have always loved math, especially geometry. It is the universal language.
@@txtoolcrib Math is the closest thing to a universal language that can be achieved. But, significantly, it is not a universal language. There is no universal language. I take "universal language" to be a means to communicate anything to anyone. But Kurt Godel's incompleteness theorems demonstrate that any nontrivial language can express propositions whose correctness cannot be determined by means of that language. In other words, the proposition can be communicated but the proof of its correctness cannot. Therefore the language fails the criterion of being able to communicate "anything." It's not in fact universal. This is true not only of mathematics but of any nontrivial language, so it's not as if we've failed somehow to formulate mathematics correctly.
I like how you included that in reality, you want to do this 3 times to be sure that your point is actually the center. As once said by Adam Savage, (and probably many others) : anyone can draw a pair of lines that cross, it's only when the third line also crosses that you can be sure it's the center of your circle.
I love these videos Ben. But after you teach them they're generally so simple that I'm ashamed of the ignorance beforehand. As always, thank you for sharing. You're an incredible teacher and I am grateful you continue to do so.
I've seen the same theorem used in reverse for laying out or verifying right angles for, say, erecting walls, plotting gardens or marking boundaries for sports. It uses a long stick with pointed ends of length L (length relative to the scale of the project) and a shorter pointed stick of length L/2 (plus a bit) that pivots dead on the midpoint of L such that when folded, the 2 tips meet exactly at either end. So when you splay it out, you get your 'diameter' of an imaginary circle, a radius, and a perfect 90º angle. It can be used in the horizontal or vertical plane.
Many many years ago I took geometry in high school. I had passed algebra by the skin of my teeth (read a D) and hated the course. Then I took geometry and fell in love with proving theorems. I had not heard of this one and find it so interesting. I have been a woodworker my entire life (now 76 and still practicing my craft) and finding the center of a circle was easy. Well easy as long as my centering square was long enough. But finding the center of something beyond the 12" tool was a bit of trial and error. You have solved that proble in as little as 3 minutes and in 6 minutes told me how it worked. FANTASTIC!!
I did really well in algebra and struggled with geometry. but, watching this video renewed my interst in geometry…thanks to the algorithm that brought me here.
Now, if you only have a ruled straight-edge, you can draw any 2 chords* and mark the midpoint of each. From each end of one chord draw an arc with the same radius ( greater than 1/2 of the chord, but the longer the better) so that the arcs intersect inside the circle. Connect the midpoint of the chord to the arc intersection with a straight line and extend that line if necessary to be clearly closer to the opposite side of the circle. Repeat with the other chord. Those two lines intersect at the center of the circle and each of them is perpendicular to their chord as well as coinciding with a diameter of the circle. *A chord is a straight line segment whose ends are also on the circumference of a circle.
It is probably the most accurate method. But it is not the most practical on a circle that has already been cut out. Consider that most of the time on a construction site, you will find a slew of squares, but not a lot of compasses.
You brought back a lot memories....and offered a lot of useful tips today.. Geometry was the only math class I ever actually liked and at least for me, beyond the basic add/subtract/multiply/divide, the most useful.
I made a tool (from a youtube video) called the Thales Square, for checking corners for square. Worth looking up. Makes sense when watching second part of your video. The tool is basically a stick (line AC) with a stick (line BO) pivoting at the center of AC. If all 3 points touch (one at the corner, the other two on the "walls", then the corner is 90 degrees. Very accurate and useful in other ways. Also, I learned to find the center of a circle by using a square to inscribe a line as you began, but then you find the centerpoint of each of those lines and draw yet another perpendicular line from each of those centerpoints. Where they meet is the center. I like yours better. No measuring.
Brilliantly simple. I've tried a few of these techniques for finding a circle centre and this is probably the best. The beauty is that any piece of A4/letter paper with a square cut edge works: you don't even need a proper 'square'. JM
Beautiful, just beautiful.This should be the way it is taught in elementary and high school. Even university level, with actual application to the real world. And afterwards the students drill a hole in the center or try to balance it if it is the center of mass.
explained better than any math teacher i ever had. i finaly learned my geometry and trigonometry ones i was in the metal workshop. ones you see it aplied it becosme a delight to know and understand it =)
Excellent explanation. A similar way to find the center, the one I thought you might use, is to choose a point on the circle's edge, then with the ruler, measure a fixed straight distance to the side, in each direction away from the point. That defines an unmeasured angle. Then, using your square/ruler as a compass, use the compass technique to split the angle, and draw that line across the circle. That angle will be 1/2 of whatever angle you started with... but will necessarily be symmetric side to side and will go through the center. Do this again from another point on the circle and you've identified the center. Your way is nicer I believe.
Simple, beautiful and brilliant. I would have loved to see one more step before dividing both sides by two and that is extracting 2 from 2x+2y=180 which is a useful idea to present for thinking out proofs like this. The idea being to stop at each iteration and see if there is a way to simplify by removing any common factors. So it would have become 2(x+y)=180. In this way, the next step, the division by 2 doesn’t have to be an idea - the step becomes self-evident to divide by 2. It seems almost redundant but Ive found it to be absolutely critical when attempting to approach proofs for yourself.
Brilliant! Thank you. My daughter is always saying along the lines of "math is great and all, but what practical use is algebra". This is a perfect example of how you can use simple algebra to help find the centre of a circle (say for a woodworking project). I know there are other ways, but still I'm sure that this will help to convince her. 😄👍
I saw the soapstone and thought it was going to be a bit low brow, but useful. Then he said "Proof". I said, "You mean like a real geometric proof?" and looked at the time bar and realized half the video is for nerd proofs! Then my man whipped out a couple truths and made algebra of it!! 🤸🤸🤸 Freaking awesome!!
I was in high school when my brother wanted to find the center of a circle to install a speaker for an amplifier. I drew 2 cord lines then used a string to bisect the cords. Extending the new lines they both crossed at the center point. Same principle different tools.
From any 3 points on the circle you make 2 chords. Find the midpoint of each chord, draw a line from the midpoint in towards the center, then do the same for the other chord. Where they intersect is the center.
Excellent video Tex! Love your useful notso common knowledge videos like this finding center of a circle one as well as your knot vids, I’d like to see your description of where the guy is prefitting, a wall frame or rafters or some kinda framing but he’s in a corner or against a wall or something and hes using a scrap 2x4 at different locations to mark the cut lines but it seemed easy I’m just not proficient enough of a carpenter to tell ya what it was but thanks again for another good video
This is great 👍 as a guy, i wish i was taught this way, in a practical and useful way! If i had been taught this way i think i would have been interested in engineering instead of learning to pass an exam
There is a special kind of combination square that is custom made for finding the center of a piece of round material. It has two 45 degree angles coming together at a point as opposed to one single 90 angle, and the scale fits inside off to one side. The frame can be placed anywhere on the the side of the circle to draw a diagonal line through the piece. You make two diagonal lines through the piece and you're done finding the center. It's a fairly common measuring device in the trades and it shouldn't be too expensive.
This will always be the easiest method to find the center of a circle. No measuring and anything that has a sharp pointed corner like sheet of paper or a book can be used
@RickMason-yj7pv my point was that while you can use special tools, this method works using anything with a square sharp corner like books and sheets of paper which is more likely to be on hand to more people at any point in time when special tools are not in their back pockets waiting to be needed.
"But I don't have a square" the student replied. "Just grab a large piece of scrap foil or paper and fold it in half then make another fold at 90° by lining up the edges" the shop teacher responded.
Always enjoyed math. Thought About becoming a mathematician. I can see how also how you can use trig to find the lengths and angles along with pathagoreum therom.
you could just measure the mid-point of the hypotenuse of the first triangle. or you could just draw a line anywhere on the circle through 2 points of the edge of the circle. Then find the midpoint of that line, use the square to make a perpendicular line from the that midpoint, through 2 points of the circle, that gives you the diameter, then find the midpoint of that line for the center of the circle.
Many moons ago, I studied technical drawing. Place your pencil tip on one point before sliding the rule to that point, then you can eyeball the second point. A lot more accurate starting position.
Whilst it is good to know the proof, knowing how to do this in practice is just brilliant, nearly six decades of building things could have been somewhat easier, every day is a learning day😊.
Draw line on (somewhat) two sides of the circle, then draw a 90degree off mid point of each line toward center, where they intersect, that is the center of the circle
You can also find the center of the circle by constructing the perpendicular bisector of two non parallel chords. Where they cross in the center of the circle.
From my survey days, the sum of interior angles of any polygon = (n-2)180 (n being the number of sides) for a triangle=180 for a pentagon=540 a nonagon (9sides)=1260 The polygon does not have to be regular, it could have obtuse interior angles.
It's very strange to see that such a famous Greek name as "Thales" is linked to totally different theorems in the latin world (France, Italy,...) and in the anglo-saxon world (US, Germany,...). For the French students, Thales theorem is related to parallelism and proportion of segments, never used by US scholars obliged to demonstrate the similarity of triangles. In France, we also apply the property of a square angle inscribed in a semicircle but without giving any name to such theorem...
Is it not the converse that you need to show (that is, you have to show that if you inscribe a right triangle in a circle, its hypotenuse is a diameter: you showed if one side of an inscribed triangle is a diameter, it is a right triangle)?
This is all very well . But I'm a model maker and need to find the center of small rods, say 1/4 of a inch ( 6.35 mm ) .How do can I do that without the use of a lathe ?
I tried to reason this myself before watching and came up with drawing any two non-parallel cords. Measure and mark the midpoint of the cord, and draw a line perpendicular to the cord through the midpoint. Definitely not as simple as this video, although I guess you could say it achieves it in only 4 lines drawn instead of 6.
I am curious, since you need a square tool to do this, and the square will have measures on it so you can just measure the diameter and half it, what is the practical benefit of this approach over simply measuring and halving?
Measuring and halving the diameter is often times less reliable than you would imagine. This is easily set up by a simple experiment. Draw out a large diameter circle on a flat surface. Around 2 feet. Then try both methods. I think you’ll find the first method is much less reliable. On the other hand, you can replace the square with a laser, and then use the second method to find the center of circles that are in excess of 50 feet in diameter.
Of course, with the framing square that you used at the beginning, you do not actually need to draw the second right triangle. As you point out, the hypotenuse of the first right triangle passes through the center of the circle, so it IS the diameter. You can measure the length and mark the center of that diameter. But I get the point, it is more fun to not measure. I used to love the old compass and straight edge geometry problems in high school.
Another method: draw a line segment having two point (point c1 and point c2) anywhere on the circumference of the circle. then draw a perpendicular line with three points: points d1 and d2 on the circumference, and point d3 being the midpoint of line segment c1 to c2. Therefore, the center of the circle is the midpoint of line segment d1 to d2. Why: because line segment c1 to c2 is parallel with a tangent line of the circle, and all tangent lines are perpendicular to the diameter of the circle
I am a millwright/welder. I work in commercial construction. I have owned my own business for 18 years now. Generally I work on installation of equipment for the feed mill industry, as well as commercial paint and blast booth installations
@@txtoolcrib Millwright = the Macgyver of the construction world. My father and I are civil engineers. We both have best buds who are welders. I've also been welding for 3 years now and really enjoy it. Tinkering and building stuff is life!
I have always enjoyed repairing and/or designing something in my head, then make it come to fruition by actually constructing it. In a nutshell, that is pretty much what millwrights do. I had considered pursuing an engineering degree when I was young, but it’s just not me. I don’t have the patience required to deal with office politics. Instead of being the guy, I like being the guy the guy counts on to make sure it’s done right.
I learned the Pythagorean Theorem in the 7th grade about 1966. How is it that they never taught us this one? And, that I never heard of this until now?
Nice! But isn't there an implied third statement in that method? We are taking it as truth that the line connecting corner B to the center forms two isosceles triangles on each side. That was sort of mind blowing on its own 😅
No, it's not taking anything new. All radii of a given circle are the same length, so if you connect the ends you form a triangle with two sides of the same length, thus by definition you've created an isosceles triangle.
@@keith6706you're right. I had to watch that part again, and I saw then that the A-mid and C-mid segments were the other radii in question. Well I guess there's the implied statement then 😅
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This is what RUclips is supposed to be , passing on skills that we may need . Great video.
There are way more videos on the internet that cause humans to become even more idiotic, depressed, and mentally ill. They are what youtube or online platforms should remove. But they won't do that, because idiots watch other idiots do idiotic things. And almost all people are idiots, hence idiot uploaders get millions of subscribers / followers
Is that what the creators of RUclips said it was meant for?
This is what grade school math teachers teach you by about grade 3 - but just using a sheet of paper.
Yes. Great video. The angle inscribed at the center of a circle is equal to its arc length, while an angle inscribed on the rim of the circle is half of that. The total length of a circle is 2pi radians, so the half of it will be 180 degrees at the center, which means 90 degrees at the rim of the circle. But I must mention that it is not Thales’s theorem. That theorem is about parallelism and proportions.
@CristianSuciu-t3w there are several proofs attributed to Thales, this is definitely Thales’ Theorem, a special case of the Inscribed Angle Theorem.
Well done and thank you! As a retired high school math teacher I loved your geometry! Technically you proved that "if an angle is inscribed in a semicircle, then it is a right angle." What is really needed is the converse statement, "if a right angle is inscribed in a circle, then the endpoints of the chords form a diameter." The proof of that converse statement is actually much easier than the one that you did. (A true statement does not automatically guarantee a true converse. They both require independent proofs.) But enough of that! Please forgive me for the math lesson. But I really enjoyed it!!! ;-)
Thank you sir. I'm actually a bit out of practice. I kind of kick myself sometimes for as often as I have to look up old formulas again. One that I have to look up all the time, because I don't do it enough, is cone volumes. I have always loved math, especially geometry. It is the universal language.
Math Teachers unite.
@@vanessakitty8867
Dyslexics untie!
@@txtoolcrib
Math is the closest thing to a universal language that can be achieved. But, significantly, it is not a universal language. There is no universal language.
I take "universal language" to be a means to communicate anything to anyone. But Kurt Godel's incompleteness theorems demonstrate that any nontrivial language can express propositions whose correctness cannot be determined by means of that language. In other words, the proposition can be communicated but the proof of its correctness cannot.
Therefore the language fails the criterion of being able to communicate "anything." It's not in fact universal. This is true not only of mathematics but of any nontrivial language, so it's not as if we've failed somehow to formulate mathematics correctly.
My 37 yr old brain just imploded trying to decide your words lmfao...
I like how you included that in reality, you want to do this 3 times to be sure that your point is actually the center. As once said by Adam Savage, (and probably many others) : anyone can draw a pair of lines that cross, it's only when the third line also crosses that you can be sure it's the center of your circle.
As a Pipefitter I learned this many years ago. But, when I saw this video pop up, I chuckled and had to watch. God bless you brother.
I’m sure you have a ton of tips and tricks for working with pipe.
@@txtoolcrib I've worked with plenty of pipefitters, and can assure you... that's what she said.
I love these videos Ben.
But after you teach them they're generally so simple that I'm ashamed of the ignorance beforehand.
As always, thank you for sharing. You're an incredible teacher and I am grateful you continue to do so.
I generally find, that most things are quite simple if you have the right teacher.
@@txtoolcrib The right teacher is the one who teaches you how to learn.
Nifty. I had heard that BCE Greeks had invented the Carpenters' Square, but I had not known of this clever use. Well done and thanks.
I loved that you added the math at the end. I was working on a quick project, but stuck around to learn more about it. Thank you!
I've seen the same theorem used in reverse for laying out or verifying right angles for, say, erecting walls, plotting gardens or marking boundaries for sports. It uses a long stick with pointed ends of length L (length relative to the scale of the project) and a shorter pointed stick of length L/2 (plus a bit) that pivots dead on the midpoint of L such that when folded, the 2 tips meet exactly at either end. So when you splay it out, you get your 'diameter' of an imaginary circle, a radius, and a perfect 90º angle. It can be used in the horizontal or vertical plane.
Where does the 90⁰ angle cone from?
Many many years ago I took geometry in high school. I had passed algebra by the skin of my teeth (read a D) and hated the course. Then I took geometry and fell in love with proving theorems. I had not heard of this one and find it so interesting. I have been a woodworker my entire life (now 76 and still practicing my craft) and finding the center of a circle was easy. Well easy as long as my centering square was long enough. But finding the center of something beyond the 12" tool was a bit of trial and error. You have solved that proble in as little as 3 minutes and in 6 minutes told me how it worked. FANTASTIC!!
I did really well in algebra and struggled with geometry. but, watching this video renewed my interst in geometry…thanks to the algorithm that brought me here.
Now, if you only have a ruled straight-edge, you can draw any 2 chords* and mark the midpoint of each. From each end of one chord draw an arc with the same radius ( greater than 1/2 of the chord, but the longer the better) so that the arcs intersect inside the circle. Connect the midpoint of the chord to the arc intersection with a straight line and extend that line if necessary to be clearly closer to the opposite side of the circle. Repeat with the other chord. Those two lines intersect at the center of the circle and each of them is perpendicular to their chord as well as coinciding with a diameter of the circle.
*A chord is a straight line segment whose ends are also on the circumference of a circle.
It is probably the most accurate method. But it is not the most practical on a circle that has already been cut out. Consider that most of the time on a construction site, you will find a slew of squares, but not a lot of compasses.
This is amazing. I learned something new today. I always used rulers to find it by keeping the edge fixed and moving the inner one. This is way easier
You brought back a lot memories....and offered a lot of useful tips today.. Geometry was the only math class I ever actually liked and at least for me, beyond the basic add/subtract/multiply/divide, the most useful.
I made a tool (from a youtube video) called the Thales Square, for checking corners for square. Worth looking up. Makes sense when watching second part of your video. The tool is basically a stick (line AC) with a stick (line BO) pivoting at the center of AC. If all 3 points touch (one at the corner, the other two on the "walls", then the corner is 90 degrees. Very accurate and useful in other ways.
Also, I learned to find the center of a circle by using a square to inscribe a line as you began, but then you find the centerpoint of each of those lines and draw yet another perpendicular line from each of those centerpoints. Where they meet is the center. I like yours better. No measuring.
Brilliantly simple. I've tried a few of these techniques for finding a circle centre and this is probably the best. The beauty is that any piece of A4/letter paper with a square cut edge works: you don't even need a proper 'square'.
JM
But you need a 'writing instrument'. Lol.
Most people only have markers.
This is the most brilliant thing ive learned this year. How have i not known this... Thank you for this knowledge
I hope that you find it useful going forward.
Cool. I'm an older man but never knew this. Much appreciate it, including the explanation of Thales' Theorem.
Beautiful, just beautiful.This should be the way it is taught in elementary and high school. Even university level, with actual application to the real world. And afterwards the students drill a hole in the center or try to balance it if it is the center of mass.
explained better than any math teacher i ever had. i finaly learned my geometry and trigonometry ones i was in the metal workshop. ones you see it aplied it becosme a delight to know and understand it =)
Nobody’s going to mention how good that freehand circle was?
Truly incredible.
All I can draw freehand is a wobble🤔
I thought exactly the same thing!
@@jakelilevjen9766 Yeah, he must've used that handy pinhole in the paper as a guide, when he drew the circle freehand off-camera...
Dude!!
Excellent explanation. A similar way to find the center, the one I thought you might use, is to choose a point on the circle's edge, then with the ruler, measure a fixed straight distance to the side, in each direction away from the point. That defines an unmeasured angle. Then, using your square/ruler as a compass, use the compass technique to split the angle, and draw that line across the circle. That angle will be 1/2 of whatever angle you started with... but will necessarily be symmetric side to side and will go through the center. Do this again from another point on the circle and you've identified the center. Your way is nicer I believe.
Simple, beautiful and brilliant. I would have loved to see one more step before dividing both sides by two and that is extracting 2 from 2x+2y=180 which is a useful idea to present for thinking out proofs like this. The idea being to stop at each iteration and see if there is a way to simplify by removing any common factors. So it would have become 2(x+y)=180. In this way, the next step, the division by 2 doesn’t have to be an idea - the step becomes self-evident to divide by 2. It seems almost redundant but Ive found it to be absolutely critical when attempting to approach proofs for yourself.
I follow exactly what you are saying. I will definitely keep that in mind in the future.
Smart clips!!! I just learned a lot here. Thank you very much!
Brilliant! Thank you. My daughter is always saying along the lines of "math is great and all, but what practical use is algebra". This is a perfect example of how you can use simple algebra to help find the centre of a circle (say for a woodworking project). I know there are other ways, but still I'm sure that this will help to convince her. 😄👍
I knew of Thales' Theorem but hadn't seen it used in reverse to find the circle center. Very clever!
FINALLY ! WHY WAS THIS SO HARD TO FIND? (I mean a really practical center finding method. There are SO MANY that are too convoluted.)
Yes sir! Done many a shade tree fab job laying out like that. That geometry lesson at the end took me back 30 years to HS!
I hear ya. Simpler times back then.
Man, I love circle geometry. The proof is always so eligant and evident. Also, that's very useful. I can use this in the workshop, thank you.
You’re very welcome.
I saw the soapstone and thought it was going to be a bit low brow, but useful. Then he said "Proof". I said, "You mean like a real geometric proof?" and looked at the time bar and realized half the video is for nerd proofs! Then my man whipped out a couple truths and made algebra of it!! 🤸🤸🤸 Freaking awesome!!
I was in high school when my brother wanted to find the center of a circle to install a speaker for an amplifier. I drew 2 cord lines then used a string to bisect the cords. Extending the new lines they both crossed at the center point.
Same principle different tools.
You can draw two chords anywhere on the circle, bisect them and where the lines meet is the center.
Brilliant.. !!! Much appreciated.
Can you tell me what brand and model your first blue with white lead drawing tool (pen.. pencil) might be.
Thanks.
From any 3 points on the circle you make 2 chords. Find the midpoint of each chord, draw a line from the midpoint in towards the center, then do the same for the other chord. Where they intersect is the center.
👍👍 Excellent step by step crystal clear explanation.
Excellent video Tex! Love your useful notso common knowledge videos like this finding center of a circle one as well as your knot vids, I’d like to see your description of where the guy is prefitting, a wall frame or rafters or some kinda framing but he’s in a corner or against a wall or something and hes using a scrap 2x4 at different locations to mark the cut lines but it seemed easy I’m just not proficient enough of a carpenter to tell ya what it was but thanks again for another good video
Thanks! I will try to do more videos like this.
Love it!! Not how ive always done it with a square but i like learning different ways
Another method is to draw a couple tangents, bisect them at 90degrees. Where the lines meet is your center.
This is great 👍 as a guy, i wish i was taught this way, in a practical and useful way! If i had been taught this way i think i would have been interested in engineering instead of learning to pass an exam
I should have payed more attention in geometry class. I have often struggled to find center of circle. Now will be a little easier. Thank you sir.
There is a special kind of combination square that is custom made for finding the center of a piece of round material. It has two 45 degree angles coming together at a point as opposed to one single 90 angle, and the scale fits inside off to one side.
The frame can be placed anywhere on the the side of the circle to draw a diagonal line through the piece. You make two diagonal lines through the piece and you're done finding the center. It's a fairly common measuring device in the trades and it shouldn't be too expensive.
This is the most excellent superior method I have seen. Thank you!
This will always be the easiest method to find the center of a circle. No measuring and anything that has a sharp pointed corner like sheet of paper or a book can be used
Or you can use a centre finding square.
@RickMason-yj7pv my point was that while you can use special tools, this method works using anything with a square sharp corner like books and sheets of paper which is more likely to be on hand to more people at any point in time when special tools are not in their back pockets waiting to be needed.
Thanks!
No sir, Thank You!
"But I don't have a square" the student replied.
"Just grab a large piece of scrap foil or paper and fold it in half then make another fold at 90° by lining up the edges" the shop teacher responded.
Always enjoyed math. Thought About becoming a mathematician. I can see how also how you can use trig to find the lengths and angles along with pathagoreum therom.
you could just measure the mid-point of the hypotenuse of the first triangle. or you could just draw a line anywhere on the circle through 2 points of the edge of the circle. Then find the midpoint of that line, use the square to make a perpendicular line from the that midpoint, through 2 points of the circle, that gives you the diameter, then find the midpoint of that line for the center of the circle.
I’m aware
Finding the midpoint of a line segment is not as easy nor as quick as striking a couple of lines with a square.
Many moons ago, I studied technical drawing. Place your pencil tip on one point before sliding the rule to that point, then you can eyeball the second point. A lot more accurate starting position.
Tools and Math in the same video? Subscribed!
I do templates as part of my job and love these videos. Big time savers!
Whilst it is good to know the proof, knowing how to do this in practice is just brilliant, nearly six decades of building things could have been somewhat easier, every day is a learning day😊.
Draw line on (somewhat) two sides of the circle, then draw a 90degree off mid point of each line toward center, where they intersect, that is the center of the circle
That was really cool. I learned a different method years ago where you bisected two chords of the circle and their intersection was the center.
Which also works. In fact there are several ways to find the center of a circle, this just happens to be my favorite.
You can also find the center of the circle by constructing the perpendicular bisector of two non parallel chords. Where they cross in the center of the circle.
What pen are you using? Thanks
Now that's cool right there 💯
I learned something new today!
From my survey days, the sum of interior angles of any polygon = (n-2)180 (n being the number of sides)
for a triangle=180
for a pentagon=540
a nonagon (9sides)=1260
The polygon does not have to be regular, it could have obtuse interior angles.
Thankyou this is very practical and hepfull in my making things
It's very strange to see that such a famous Greek name as "Thales" is linked to totally different theorems in the latin world (France, Italy,...) and in the anglo-saxon world (US, Germany,...). For the French students, Thales theorem is related to parallelism and proportion of segments, never used by US scholars obliged to demonstrate the similarity of triangles. In France, we also apply the property of a square angle inscribed in a semicircle but without giving any name to such theorem...
Great instruction video. If anybody objects you just turn the disk about the marked point on a lathe and scrape off the circumference.
Thank you sir. For welding applications, this method works quite well. Now if you are machining, that is a different story.
I used to love doing plane geometry proofs in high school (50+ years ago). I think Pythagoras may have still been alive then. 🙂
He was my locker partner.
Is it not the converse that you need to show (that is, you have to show that if you inscribe a right triangle in a circle, its hypotenuse is a diameter: you showed if one side of an inscribed triangle is a diameter, it is a right triangle)?
I love how triangles are so intertwined with circles
This is all very well . But I'm a model maker and need to find the center of small rods, say 1/4 of a inch ( 6.35 mm ) .How do can I do that without the use of a lathe ?
I tried to reason this myself before watching and came up with drawing any two non-parallel cords. Measure and mark the midpoint of the cord, and draw a line perpendicular to the cord through the midpoint. Definitely not as simple as this video, although I guess you could say it achieves it in only 4 lines drawn instead of 6.
I am curious, since you need a square tool to do this, and the square will have measures on it so you can just measure the diameter and half it, what is the practical benefit of this approach over simply measuring and halving?
Measuring and halving the diameter is often times less reliable than you would imagine. This is easily set up by a simple experiment. Draw out a large diameter circle on a flat surface. Around 2 feet. Then try both methods. I think you’ll find the first method is much less reliable. On the other hand, you can replace the square with a laser, and then use the second method to find the center of circles that are in excess of 50 feet in diameter.
Clear and concise, excellent video.
Thanks!
Wow; I learned something new today!
Very informative for the new tradees
Squared center points of the two original chords will also give you the center point of the circle with moving the square one fewer time.
I am an older wood project guy. Thank you for your help.👍
Glad to help
Of course, with the framing square that you used at the beginning, you do not actually need to draw the second right triangle. As you point out, the hypotenuse of the first right triangle passes through the center of the circle, so it IS the diameter. You can measure the length and mark the center of that diameter. But I get the point, it is more fun to not measure. I used to love the old compass and straight edge geometry problems in high school.
Yes, that would be more efficient, but there is definitely something satisfying about using two triangles instead of a tape measure.
Very good proof. I had forgotten this law from high school geometry. Thanks!
Glad I could help refresh your memory!
What's the writing instrument you were using at the start?
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What type of sorcery is this?! I don´t understand how I have not known about this method. Thank you!
How about the old horizontal and vertical measurement using a ruler or tape measure?? 🤔 🕳️
You can also measure and split the difference on that first diameter line
You can.
Great info. What is the pen you used
SilverStreak by Markal
Another method: draw a line segment having two point (point c1 and point c2) anywhere on the circumference of the circle. then draw a perpendicular line with three points: points d1 and d2 on the circumference, and point d3 being the midpoint of line segment c1 to c2. Therefore, the center of the circle is the midpoint of line segment d1 to d2. Why: because line segment c1 to c2 is parallel with a tangent line of the circle, and all tangent lines are perpendicular to the diameter of the circle
So basically you're saying to find the centre of a circle with a square you need to triangulate it?
Another excellent presentation. Thanks!
You are very welcome.
Its really cool to see the connection with framin square
I really like these types of videos.
in an irregularly shaped but closed figure, how do you find the maximum diameter circle and it's center which falls entirely within that shape ? ;)
Im terrible at math but also mesmerized by it at the same time. God definitely has a sense of humor.
In my experience, most people are way better at math than they believe themselves to be. A lot of it boils down to the teacher.
Really enjoying your content...if you don't mind sharing, what is your background and/or what do you do for a living?
I am a millwright/welder. I work in commercial construction. I have owned my own business for 18 years now. Generally I work on installation of equipment for the feed mill industry, as well as commercial paint and blast booth installations
I have a couple of different videos that highlight the type of work that I do.
@@txtoolcrib Millwright = the Macgyver of the construction world. My father and I are civil engineers. We both have best buds who are welders. I've also been welding for 3 years now and really enjoy it. Tinkering and building stuff is life!
I have always enjoyed repairing and/or designing something in my head, then make it come to fruition by actually constructing it. In a nutshell, that is pretty much what millwrights do. I had considered pursuing an engineering degree when I was young, but it’s just not me. I don’t have the patience required to deal with office politics. Instead of being the guy, I like being the guy the guy counts on to make sure it’s done right.
Thank you for your excellent video
Thank you for taking the time to watch.
As a nerdy woodturner, I loved this!
Glad to hear it. I appreciate you taking the time to watch.
I learned the Pythagorean Theorem in the 7th grade about 1966. How is it that they never taught us this one? And, that I never heard of this until now?
What sort of pencil is that?
The white one.
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This is the only place (prisons, Jails) that I disagree with filming, all your other videos are great.
I've worked as a tin knocker for 19 years i can find the center with a tape measure in 10 seconds.
Same here but I'm a steamfitter
Nice. There are lots of ways to find the center of a circle. This is however a way to prove that it is the center :)
Should it be any given "right angle triangle" because you did use a square ruler to do this.
Yes, any right triangle. You could use a sheet of printer paper if you wanted.
Pretty cool that will come in handy. Thanks for that.
You’re very welcome.
U can measure the diameter and mark the radius which will obviously give the centre, easy way I believe
Terrific, thank you!
Great to know. Practical geometry. 😊
Nice! But isn't there an implied third statement in that method? We are taking it as truth that the line connecting corner B to the center forms two isosceles triangles on each side. That was sort of mind blowing on its own 😅
No, it's not taking anything new. All radii of a given circle are the same length, so if you connect the ends you form a triangle with two sides of the same length, thus by definition you've created an isosceles triangle.
@@keith6706you're right. I had to watch that part again, and I saw then that the A-mid and C-mid segments were the other radii in question.
Well I guess there's the implied statement then 😅
Great use of a writing instrument.
Good job,geometry is useful stuff.
The first part is how my brain works if I can see it in practical use I get it . On paper and calculations I’m lost . Thank you