Dividing a line segment into equal parts (Thales theorem)
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- Опубліковано 25 лис 2015
- This shows how to divide a given line segment into a number of equal parts with compass and a set-square aplying Thales theorem.
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#Geometry #HowtoDraw
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This is exact and clear way and very easy and beautiful
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Nice
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Sir, I tried by drawing parallel lines after drawing two end points of intial line. There will somewhat slight variations in adjesant division.
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I've got a question, what's the practical use of the Thales theorem? Can't I just divide the original line by using a ruler and dividing the length by the number of segments I want?
Making polygons, i think
It’s easier and more accurate this way in certain applications.
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is there any method to divide a line into 3 equal parts using divider
This videos are very important
Also called Intercept theorem, not to be confused with Thales other theorem.
Sir if we have to divide a line segment of 5.7 cm into 3 equal parts so we should take the measurements of compass at what cm
It should not make a difference. Normally you choose a length that is easy to measure if you are using a measuring stick, but so long as you use 3 equal measures you should be fine. See it as creating overlapping similar triangles (all corresponding angles are the same) so the ratios of the side lengths will also remain the same.
To convince yourself of this you may wish to try the following:
1. Draw a segment AB that you can divide into 9 equal parts (9cm or 9 inches, does not matter).
2. Number the division points D1 through D8 (A would be 0, B would be 9).
3. Draw another segment AC, of arbitrary length, let's use 5.7 (cm or inches) that sits adjacent to AB at an angle (exact degrees not important so long as its not 0 or 180, eyeball something from 30 to 45 degrees ).
4. Join B and C with a red coloured line (BC) to make a triangle.
5. Draw lines parallel to BC through points D3 and D6, you should have 3 divisions on AC.
6. Take a different colour, say blue, and join point D6 with point C, with the same colour draw parallel lines through D2 and D4, they should intersect AC the same points as the previously drawn red lines.
7. You can do the same thing with another colour, this time using point 3 as the new triangle (ACD_3).
Regardless how long or short AB is (in relation to AC), any point on AB will divide AC by the same ratio (on angles not 0 or 180).
You can even use a theorem (diagonals of trapezoids theorem) related to this one (basic proportionality theorem) to divide the space between two parallel lines by whatever ratios you desire.
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Super cool
Currently watching this the day before the final exam😁
Thank you
Nice
I realize this is a "how to draw" video, but the video misses the mathematical point completely: The mathematical point is to be able to divide an arbitrary-length line-segment AB into N equally long segments using ONLY a compass and a straight edge. Such a proper construction relies on first creating an arbitrary triangle ABC and then constructing N-1 additional smaller but similar triangles whose lower-right corners are at the segment boundaries. The construction of the smaller triangles can be performed by an initial compass-only copy-angle operation, followed by N-2 compass-only copy-length operations, or you can use N-1 compass-only copy-angle operations.
There should be no use of other measurement-generating or angle-generating tools (ruler, angle-protractor, set-squares). Hence, setting the compass to a specific 2cm gap is superfluous and confusing. And using an angle protractor as a ruler instead of a dimensionless straightedge is likewise confusing and superfluous. Then there is the operation of constructing the parallell lines, which should be performed via copying the angle ABC at the A-to-C intermediate and equidistant waypoints, and not via the computer calculating a parallel translation of the CB segment, nor by by using "set-squares" tools, which the narrative says.
Oh, and Thales Theorem is not at all required for this construction. Which is why I got started on picking apart this video and separating drawing technique shortcuts from the mathematics. I was looking for a video about Thales Theorem and landed here.
justmath how can you be bothered to write a comment that long when you know that nobody will read that because of how long it is and no I haven’t read it
i knew something wasnt right
I mean thats nice that you have a tool that stays parallel to precious lines. But the crux of the problem is that a human is going to be moving this tool and how you can maintain parallel with just a strait edge compass and your hands
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Nice vi2
When you started dont use the circle that conflused me
Wait.. How would we know that it is exactly fivided because we are randomly moving that set square upto some distance 🙄
😊😮
If you are dividing a line into 8 equal parts , do you use the same method ?
Yes, same method
Arthur u tried in the end u did
Graphics homework like this comment if it’s the same for you as well
dont use circle please because its became difficult to understand
What is your name?
Not clear at all how you achieve parallel lines after the first one. And what is the marking of the lines at the end "showing they are parallel" ? Missing too much here to be useful.
4 line tu de
What r u saying mate? So Thales knew set square, protractor in 3rd century BCE...first tell the statement, then interpretation of the statement and proof as given by Thales...I guess no one in here is better than Thales...this way of education is just stupidity....!!
tehe
I searched for this question and how to do it in Adobe Illustrator. How come your key wording includes that? Thank you for wasting my time.
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I don`t really understand .
This is not a good way, you can’t really control parallelism. This is questionable use Thales theorem while the theorem is correct
Kumuk 99 use two set square and you do it properly 👍