Immediately on seeing the thumbnail I thought "I had no idea that's a thing" and "of course that's a thing!". It makes so much sense, but I'd never heard of a proportional divider before. And now I want one.
That's my channel's main essence to bring out forgotten pieces of stationery and engineering tools. If you take a look at other videos, you're going to find other things that have the same sense for you. Things that were usual and a must someday and as the digital revolution hit, they all buried under sands of time. People have forgotten them, but their lack is being sensed every day. Stay with me, and you gonna find dozens of these sorcery devices 😊 and by the way, many thanks for your attention and support 🙏
@@smizmar8 It's really a genius design 👌specially the one with decimal scaling. I severely suggest it if you are into geometry. Thanks for your attention
Thank you very much for the education. These dividers are amazing and I find it perplexing that such a thing is not common knowledge…. You have my like and subscribe with this first video 👍🏽
Glad it was helpful! Many thanks for your attention and support. There are some other educational videos in my channel you might find useful, so I really suggest taking a look 😀 good luck, buddy
I wouldn't have known you could use them to make all sorts of polygons... I had been eyeing a set prior simply for reducing/enlarging designs, but now I've even more reason to save for them!
@CSGraves And plenty of other applications, buddy. But remember, I really suggest the one with decimal scaling over the other. Its range of applications is almost unlimited, and with a little practice and experience, you can even be innovative and find other applications👌
@@sinashishehgarha3023 Been a while since I've used a vernier caliper or micrometer, so it'd be a bit of re-learning to read the such a scale again, but the increased flexibility seems worth the effort.
Hi, buddy 👋. Staedtler proportional divider with decimal scaling is one of the most practical and useful ones. It has a broad range of applications. Many thanks for your attention 😊
This video is very serendipitous! I have been researching proportional dividers heavily over the last week or so. What kind of compass and ink cartridge are you using to scribe your circles?
I'm really glad that it was useful 😌 it took me about a month researching and making this video, and it is a relief to see others enjoying it. The compass is Fabercastell equipped with a Fabercastel 0.1 technical pen , and the ink is a regular Rotring technical pen ink
@@sinashishehgarha3023 awesome! Thank you! I’m just getting into geometry and “constructing” shapes with simple tools. It’s really interesting! Thank you for your help!
So, what is the class of numbers for which pairs of line segments with the number as the ratio of their lengths, be constructed with compass, straightedge, and this tool? For compass and straightedge, my understanding is that it is something like, the rational numbers adjoin the (2^n)-th roots of integers, if I remember correctly? I know the square root of any integer is in there, but I don’t remember how to take the square root of an arbitrary given ratio… Oh, I think I vaguely remember the process. Ok. It sounds like this method allows constructing the sine and cosine of any rational multiple of 2pi? Does this allow for constructing any (real) algebraic ratio? If so: I’m surprised that one tool like this is enough to get to the algebraic completion of the rational numbers?? But maybe getting cos((a/b) 2pi) isn’t enough for that? Ah, wait, Yeah, just having the operations of n-th roots for positive integers n, and arithmetic, doesn’t suffice to get all the algebraic numbers from the rationals, because of (e.g.) the “unsolvability of the quintic”. Still, maybe this at least gets you everything expressible using just arithmetic and n-th roots? Like, there’s a correspondence between trisecting an angle and taking cube roots, right? Does that correspondence extend? Seems like it should. Ah, taking the cube root of e^(i theta), is trisecting the angle theta, but I want to cube root a ratio of lengths… If I have a ratio of lengths, I can find an angle which has that as its tangent, Uhh, tan(3 atan(x)) is probably a cubic polynomial in x or something like one? (a+b ı)^3 = a^3 + 3 a^2 b ı - 3 a b^2 - b^3 ı = (a^3 - 3 a b^2) + (3 a^2 b - b^3) ı, uh… Letting a=1, (1 - 3 b^2) + b (3 - b^2) ı , Hm… Can probably do it, not clear to me how to do it.
Funny enough that you release this video right on a day I was looking a good and detailed info on the proportional dividers! This is a very good video, I thought I knew these dividers, but I had no idea that it can solve proportions. How does one gets the tables though, is there a scanned manual somewhere?
Glad it was helpful! buddy. Yes, just search "Staedtler proportional divider pamphlet." There is a scanned version of it in a website. Actually, I don'tknow the site's name, but I found it this way. Many thanks for your attention 😊
Trace an angled from one edge of the line. Mark n units on it; where n is the number of units you will divide the primary line. Now, at the last unit of angled line join with the end of primary line. Draw parallels of this line at each unit and you will have the primary line divided.
@lpanades Bingo, that's a really fascinating geometrical method 👏 using divider only decreases the process and makes it easier 😀 but obviously, any of the applications mentioned in this video have a special geometrical method to be performed. Anyhow, many thanks for your attention and informative comment 👍
new to me, and amazing abilities!
@lohikarhu734 really amazing...and there are plenty of other applications if one is a bit innovative. Thanks for your attention 😊
Immediately on seeing the thumbnail I thought "I had no idea that's a thing" and "of course that's a thing!". It makes so much sense, but I'd never heard of a proportional divider before. And now I want one.
That's my channel's main essence to bring out forgotten pieces of stationery and engineering tools. If you take a look at other videos, you're going to find other things that have the same sense for you. Things that were usual and a must someday and as the digital revolution hit, they all buried under sands of time. People have forgotten them, but their lack is being sensed every day. Stay with me, and you gonna find dozens of these sorcery devices 😊 and by the way, many thanks for your attention and support 🙏
You explained everything completely and accurately👌
Wow, what an amazing geometric tool!!! I've never seen that before. Incredible!
@@smizmar8 It's really a genius design 👌specially the one with decimal scaling. I severely suggest it if you are into geometry. Thanks for your attention
Please upload more un common tools like this.
@sumanprusty1173 Hi buddy, I'll do my best to research and find more innovative and yet simple tools like this one. Stay tuned.
Thank you very much for the education. These dividers are amazing and I find it perplexing that such a thing is not common knowledge….
You have my like and subscribe with this first video 👍🏽
Glad it was helpful! Many thanks for your attention and support. There are some other educational videos in my channel you might find useful, so I really suggest taking a look 😀 good luck, buddy
A useful and clear video, thank you very much.
Glad it was helpful! Many thanks for your heartwarming comment 😊
I wouldn't have known you could use them to make all sorts of polygons... I had been eyeing a set prior simply for reducing/enlarging designs, but now I've even more reason to save for them!
@CSGraves And plenty of other applications, buddy. But remember, I really suggest the one with decimal scaling over the other. Its range of applications is almost unlimited, and with a little practice and experience, you can even be innovative and find other applications👌
@@sinashishehgarha3023 Been a while since I've used a vernier caliper or micrometer, so it'd be a bit of re-learning to read the such a scale again, but the increased flexibility seems worth the effort.
Definitely, it is. Nothing you can't handle 👌
thank you. I have been looking at a second hand set of Staedtler proportional dividers, but unsure if they would be useful to me. Now I know.
Hi, buddy 👋. Staedtler proportional divider with decimal scaling is one of the most practical and useful ones. It has a broad range of applications. Many thanks for your attention 😊
This video is very serendipitous! I have been researching proportional dividers heavily over the last week or so. What kind of compass and ink cartridge are you using to scribe your circles?
I'm really glad that it was useful 😌 it took me about a month researching and making this video, and it is a relief to see others enjoying it. The compass is Fabercastell equipped with a Fabercastel 0.1 technical pen , and the ink is a regular Rotring technical pen ink
@@sinashishehgarha3023 awesome! Thank you! I’m just getting into geometry and “constructing” shapes with simple tools. It’s really interesting! Thank you for your help!
Any time, buddy. Any time
So, what is the class of numbers for which pairs of line segments with the number as the ratio of their lengths, be constructed with compass, straightedge, and this tool?
For compass and straightedge, my understanding is that it is something like, the rational numbers adjoin the (2^n)-th roots of integers, if I remember correctly?
I know the square root of any integer is in there, but I don’t remember how to take the square root of an arbitrary given ratio…
Oh, I think I vaguely remember the process.
Ok.
It sounds like this method allows constructing the sine and cosine of any rational multiple of 2pi?
Does this allow for constructing any (real) algebraic ratio?
If so: I’m surprised that one tool like this is enough to get to the algebraic completion of the rational numbers??
But maybe getting cos((a/b) 2pi) isn’t enough for that?
Ah, wait,
Yeah, just having the operations of n-th roots for positive integers n, and arithmetic, doesn’t suffice to get all the algebraic numbers from the rationals, because of (e.g.) the “unsolvability of the quintic”.
Still, maybe this at least gets you everything expressible using just arithmetic and n-th roots?
Like, there’s a correspondence between trisecting an angle and taking cube roots, right? Does that correspondence extend? Seems like it should.
Ah, taking the cube root of e^(i theta), is trisecting the angle theta, but I want to cube root a ratio of lengths…
If I have a ratio of lengths, I can find an angle which has that as its tangent,
Uhh, tan(3 atan(x)) is probably a cubic polynomial in x or something like one?
(a+b ı)^3 = a^3 + 3 a^2 b ı - 3 a b^2 - b^3 ı = (a^3 - 3 a b^2) + (3 a^2 b - b^3) ı,
uh…
Letting a=1,
(1 - 3 b^2) + b (3 - b^2) ı ,
Hm…
Can probably do it, not clear to me how to do it.
@@drdca8263 wow 👌 are you a mathematician or astronomer😅
@@sinashishehgarha3023 Mathematician I guess? Though I usually say just “math person”. (I don’t have a PhD quite yet.)
@drdca8263 If you ask me, you are already qualified as post PhD 👏👏👏👏 quite knowledgeable 👌👌👌👍👍👍
Funny enough that you release this video right on a day I was looking a good and detailed info on the proportional dividers! This is a very good video, I thought I knew these dividers, but I had no idea that it can solve proportions. How does one gets the tables though, is there a scanned manual somewhere?
Glad it was helpful! buddy. Yes, just search "Staedtler proportional divider pamphlet." There is a scanned version of it in a website. Actually, I don'tknow the site's name, but I found it this way. Many thanks for your attention 😊
Trace an angled from one edge of the line. Mark n units on it; where n is the number of units you will divide the primary line. Now, at the last unit of angled line join with the end of primary line. Draw parallels of this line at each unit and you will have the primary line divided.
@lpanades Bingo, that's a really fascinating geometrical method 👏 using divider only decreases the process and makes it easier 😀 but obviously, any of the applications mentioned in this video have a special geometrical method to be performed. Anyhow, many thanks for your attention and informative comment 👍
You explained everything completely and accurately👌
Many thanks for your attention and support 🙏 I really appreciate your comments 😊