Welcome to the Texas Tradesman, my name is Ben. This channel is dedicated to metal working tips and tricks as well as welding projects (both useful and for fun). I had the great benefit of having some very good teachers in my life in my profession as a millwright. My goal is to pass some of those useful tips, tricks, shortcuts, and skills onto the next generation through the wonders of social media.
You can get all of the 30 degree lines without changing your compass radius. Once you get the first one by bisecting the 60 degree angle, you can then put the point on of the compass on the 30 degree line to get 30+60 aka 90 and then again on the 90 to get to 150. then after you get the 15 degree line, you can get do the same thing to get 75, & 135, then you only need to reset the compass once to get the remainder of the 15 degree lines.
DEFINITION FOR INDENTION (1 OF 1) noun 1. The indenting of a line or lines in writing or printing. 2. The blank space left by indenting. 3. The act of indenting; state of being indented. 4. Archaic. An indentation or notch.
I would suggest that the next time you feel so inclined to attack someone based on your ”perceived” intelligence, you might want to have a clue about what you’re talking about first.
1. Thales's _Thales_ is not a plural word, so it takes _'s_ like every other singular noun. 2. /TAL-ess/ It's a Greek name. Initial _th_ is plosive, not soft, and the _a_ is flat, like in _flat._ The _e_ is also flat, as in _bet._ Amazing how you can rack up so many errors in just one word, but there ya go. I guess how they do teacherin' in Taxes. And you spend almost nine minutes wittering on about something that's fully explained by the diagram on the Wikipedia article. Just amazing.
As an applied mathematician I sometimes slum it by watching this type of video. Machinists have all sorts of hacks they use but could never prove in any rigorous way but they do work and are based on proper Euclidean geometry. A carpenter once asked me about a rule of thumb he used fo arches and I derived it from basic ellipse properties and it made sense. 17th century mathematics was highly geometric and Newton's Principia is almost unintelligible to modern readers. Indeed, Nobel Prize winning physicist Richard Feynman once tried to replicate Newton's highly geometric proof of his inverse square law of gravitation and it defeated him because Newton relied on obscure geometric properties that we simply don't learn these days because of analytic geometry etc. Newton did a geometric derivation of the shape of minimum resistance in a fluid and althougn it was obscure he got the same answer a fluid dynamicist would get woth modern techniques. Geometry is really powerful and only involves simple tools.
Cool. I think this would be great to show to my geometry class. One pedantic note. I believe you are using the converse of Thales Theorem: if you have an inscribed right triangle in a circle, then the side opposite the right angle is a diameter. (In other words, Thales' theorem says "diameter implies right triangle" while you need "right triangle implies diameter.")
Very interesting discussion of geometric principles. In your story: considering that the unfortunate structural engineer of record on this project actually thought that builders could construct the roof to within 4-mils of design elevation is both quite amusing and quite distressing at the same time! To construct it to within 1/2" of design would be impressive.
Draw any inscribed triangle in a circumference, then Trace the 3 mediatrixes. The point where they meet is the center of the circle! The prthocenter!!!
Thank you for the very direct route to explaining this! The paint story is so believeable in that I heard my father talking about how his days at nuclear sites- everything was so technically right yet painfully expensive when two surfaces did not meet because of such things.
At 0:56 you could have used the endpoint of one of the existing two lines, to draw the third in a right angle, of which that third is parallel to the first. The diagram becomes simpler and easier to understand.
Thale’s theorem is just the inscribed angle theorem in reverse. The right angle used is an inscribed angle, and the inscribed angle theorem states that the angle AVB is equal to half the angle AOB, where O is the origin, and A, V, and B are points that lie on the circle. So given three points on the circle and the angle 2ø between two radii, you know the inscribed angle at the third point is equal to ø. But you can also go in reverse. Given an angle of 90° inscribed in the circle, the other two points form an angle of 180° with the center, so drawing a straight line between them must intersect the center. Then you just do that twice to find the intersection of the two diameters.
Yes. The most stunning practical demonstration of this is to draw a line AOB through the center of a circle. Then put a pencil on a third point, V, anywhere else on the circle. Even as you move that point V around the circle, the angle AVB remains exactly 90 degrees, always exactly half of AOB.
Even easier then that is take any ruler and hold one edge at 1 inch and diagonally angle the other side of the ruler at some other inch mark as well on the other side of the board. The center will be half the distance of that diagonal length... Example, start the diagonal line at one inch on one side of the board and say 5 inches on the other side. The center will be at the three inch mark of the ruler...
The other way I have heard this is that if you start with a semi-circle and draw a line from one end to any other point on the semi-circle and then from that point to the other end of the semi-circle the angle between those lines will allways be a right angle. You are using this property in reverse by putting the vertex of a known right angle on a circle. The intersection of the right angle with the circle will be a semi-circle which lets you draw a diameter line, which by definition goes through the center of the circle. Do this a second time to prodoce a sevond diameter line and the intersection of the two diameters is the center of the circle.
Stonemasons who built cathedrals and fortresses in the Middle Ages began by establishing the unit 1 by driving two studs into the rock or into a flat stone. A firm, level floor was then built around the site. Ruler, caliper, string, chain (rigid), spirit level was all they needed. Their knowledge of how to make circles, ellipses, 90 45 degrees from a line was their magic and secret. In a few places, the studs are saved for repair work. Saw a French documentary about this, if I find it again I will link it. I apologize for the language error, this is written with google translate.
Here is another tip - how to create a right triangle when you have no rulers or levels or any equipment - only a long string and a knife. Use anything as a yardstick, and arm, a leg, a branch. Heck, stick two pegs in the ground, or use two rocks and define the distance as one unit length. Cut the string into three cords: 3, 4 and 5 units of length. Tie the ends of the cords together (3 to the 4, 4 to the 5 and 5 to the 3) and when you pull on the knots to the maximal extent, you got yourself a right triangle with the hypotenuse is the 5-units length cord. Of course, any multiple of the Pythagorean triplet would work: (6,8,10) , (9,12,15) etc. Pythagoras was a complete cultist loon, but a smart guy nonetheless.
Here's a handy add-on. To quickly get your cord lengths, take your string and anchor it on the corners of the 3-4-5 triangle you just layed out. Pull tight and mark at the corners. Cut at the marks and knot the ends. Now you're ready to lay out your triangle.
Angles are named with Greek letters, in a triangle with the corner points A, B and C as α, β and γ. The sides are a, b and c. That’s 5th grade stuff. Naming the angles with Latin letters seems very odd to me. Thanks for your explications!
I would like to see if there’s a way that if you had like an empty oil drum and you wanted to find the center at the bottom of it, how the center could be determined
The kind of set square he's using is particularly well-suited for inscribing right angles on the inside of a bounded circle, but you're right that you won't simultaneously reach both points on the diameter unless you have a set square of exactly the right dimensions. You'd have to mark your inscribed right angle first, and then construct the proper extensions on each side to reach both points on the diameter. You can do that with another, longer straightedge. If you're uncomfortable with the potential for imprecision when continuing a short line segment with a straightedge over a long distance, you could alternatively draw any two wide chords across the bottom of the drum, and then construct perpendicular bisectors of each. They'll both be diameters, and will thus meet in the center.
@@saranevillerogueart9627 Your geometry is correct, but the method in the video is easier. (I suggest that you actually try it both ways.) Constructing your square makes your suggested method harder.
I think is easier and only needs compas and ruler is to trace two different chords, then trace the perpendicular line at the middle to each chord using compass and ruler (open compass slightle more than half teh chord then trace two arcs pivoting one from each point in the circle in the chord, then unite the two crossing points with ruler and extend it as necessary into the inside of the circle), then the point where they cross is the center of the circle.
😂An easier solution using origami based on my high school teacher's mantra of "Keep it simple, stupid.": Fold the circle into quarters, where the 2 diameters intersect would be the center of the circle.🎉
