General method to divide a circle into any number of equal parts

[@VideoFusco]

This construction is only a very good approximation for the division of the circumference into equal parts. Gauss and Wantzel have shown (and the mathematical demonstrations are irrefutable) that with straightedge and compass one can construct only regular polygons whose number of sides is a Fermat prime number (that is, prime numbers obtainable from the formula 2^(2^n)+1 but not all numbers obtainable from this formula are primes) or a product of powers of Fermat prime numbers and powers of 2.

[@pnintetr]

Galois theory 😎

[@kumoyuki]

but this is *NOT* a straightedge and compass construction. it is a *ruler* and compass construction. There's a ginormous difference.

[@VideoFusco]

@@kumoyuki it is an approximation even with a ruler: a ruler cannot measure irrational lenghts.

[@londonalicante]

@@kumoyuki Virtually everything done here can be done with straightedge and compass. Note that he did not directly split the diameter into 9 parts, he drew a random diagonal line and marked off 9 parts of arbitrary equal size, then transferred them using parallel lines to create similar triangles. He skipped several tedious steps in drawing the parallel lines (he mentioned in the video that he used the software to help mark off parallel lines), that is the only cheat used in following the constraint of only straightedge and compass. This IS a straightedge and compass construction, but it doesn't give the right answer. Try it with very small values (triangle and square) and you will find it doesn't work perfectly. It also doesn't work perfectly for very large values (over about 20 sides) but physical inaccuracies make straightedge and compass construction impractical at those sizes anyway. This is method is just a curiosity. Use a protractor.

[@chriguhof4470]

@@londonalicanteDo you know, how accurate this approximation is?

[@PedrinhoCruzeirense]

For those who criticize this method: this trick is useful for those who don't need perfect precision (like wood workers, on making n-sided tables, or masons on making n-sided decorative patterns on a big floor or on a big wall).

[@ArthurGeometry]

That's right!

[@elineeugenie5224]

Beautiful!! Using my 40 years old compass, it's pure joy

[@tono002]

Appreciate your timing to make this video, just like I learned in drawing school

[@eddiemorrone870]

This is a great and accurate approximation. One viewers comment pointed out that it’s only off by 2 degrees for a nonagon. Even with a spirograph you’d have to be careful of your margins for larger divisions.

[@5switch09]

It's much more accurate if you don't use a compass for the division. From point Q make lines as you did for line QB with the other numbers. That will give you the points on the circle dividing it much more precisely. Every second point is your main one while the others are your mid points. I found that this method is much more reliable for me because I don't have to pinpoint the exact point with compass every time while watching if the compass moved out of alignment or not.

[@5switch09]

You would have to of course make a second point Q on the other side

[@wizrom3046]

Yes, BUT to only use the even numbers

[@cristan9582]

Why point 2 is important?

[@Sim-q9t]

probably the point wanders in the paper or not placed right

[@sharonjuniorchess]

@@cristan9582 Because point 1 is where you divided the circle (i.e. point A) and so the next point you would need to find is point 2. Note: the 9 points define your scale the end of which is a line going back to the diameter line (i.e. point B). The object of this scale ruler is to determine the length of a single space which is then repeated around the circle.

[@carlaa.1617]

This is the best explanation I have ever seen, I love drawing mandalas and sacred geometry and this is most helpful! Thank you so much!

[@culmalachie]

... thanks, and now I know what Mandalas are! these rabbit burrows on youtube ....!

[@ginacaballero9521]

I'm into mandalas as well and this is a very thorough and helpful explanation. Thanks for sharing.

[@jacemandt]

A standard proof that trisecting a general angle with compass and straightedge is impossible, is to prove that a 20° angle can't be constructed that way, so if the general angle happened to be 60°, you couldn't possibly trisect it. IIRC, this is done by showing that the set of constructible angles is a field that doesn't contain 20° (π/18). But if this method were theoretically exact, rather than just a good practical approximation, you could divide each of the central angles of that 9-gon in half and you'd have an exact construction of a 20° angle. Therefore this construction can't be theoretically exact.

[@observersnt]

Beautifully done, crystal clear, superb graphics. Just thoroughly sensible. Thank you very much

[@joefranich4933]

Well done! My nephew and I are going to make decoder rings (ROT x) and I needed to know how to do this from scratch - manually. Going to give it a go now!

[@baxbanni2226]

Amazing. Thanks for sharing.😊😊

[@davidbrown6295]

This is NOT an accurate method. You get a nonagon, yes - a 9-sided polygon, but it is NOT a regular nonagaon as claimed - a 9-sided polygon with all sides equal and all angles equal. The first 8 sides are all equal in length, but the 9th is different from the rest. It is definitively proven (long ago now) which regular polygons can be constructed via Euclidean geometry and which cannot. This is the content of the Gauss-Wantzel Theorem as has already been mentioned elsewhere in these comments. If you are interested to know more about this, you can look up "constructible polygons" in wikipedia. Pulling a quote from that article: "a regular n-gon is not constructible with compass and straightedge if n = 7, 9, 11, 13, 14, 18, 19 ..." Notice that the regular nonagon is not constructible. The method presented in this video is not a neusis construction, it's just wrong. There are neusis constructions that extend Euclidean geometry sensibly and allow solutions to some classically impossible problems - that's not what's going on here. We have a false and deceptive claim that is misleading people.

[@andreash.6175]

What a pity ! But Arthur is wrong with this construction ! First i thought i was messing arround with my compass, but then i tested it with a CAD program and now i understand, thats not my fault ;-)

[@davidbrown6295]

@@andreash.6175 Not your fault at all. I applaud your use of a CAD program to check this out more carefully. It is one of the perrenial flaws in geometric "arguments" to rely upon the accuracy of manual drawings - the accuracy of such drawings degrades very quickly with the increasing number of drawing steps. It is this kind of flaw that allows people to believe that they have achieved something that they have not. CAD is far better, but every CAD "drawing" has its limitations also. There is no substitute for the rigor of mathematical proof, which Arthur's construction is not. As I noted already, it is difinitively proven which regular polygons can be constructed in Euclidean geometry and which cannot. The ones of many sides that are "interesting" have constructions that are quite complex. They are beautiful in their own way, but not simple and not achieved by any "general method". An interesting subject, but quite non-trivial.

[@Alkis05]

It is an approximation and it has it's uses. It has reasonable precision, since the error is that it devides the circle in 40.3º instead of 40º, which is just as good as one can do with a protractor. And if want to be precise in the langugage as well as the drawing, although the method is accurate, it is not perfectly precise.

[@andreash.6175]

@@Alkis05 Yes, but it should be mentioned, thats only an approximation. IF using this way here, it is advisable not to use the compass measuring a side length around the circle, but the lines throu the diameter where the cros the circle... By the way: you always can also use the formula a = 2 * r * sin(180/n) by your pocket calculator and to measured and transferred as side length with your compass. This would be exact....

[@Alkis05]

@@andreash.6175It wouldn't be exact because "sin" is a transcedental function. Shouldn't you mention that? No you shouldn't, because the people that don't know about it don't care for that degree of precision and the people that would need to know probably already does. Besides, this requires a calculator. There are some situations where you can't use one, most notably when you just don't want to. Also, you would need some kind of protractor too, which you might not have, at least one that is appropriate to the scale of the drawing.

[@deepakagarwala3664]

I was looking for this exactly. Thankyou ❤❤❤

[@venantiusjpinto]

Awesome, and truly appreciated!

[@neillawrence4198]

This takes me back to the 60's when I worked in the drafting room, laying out templates for fabricated parts. 4" x 8' drafting table, pencils, triangles, compass, and a huge eraser. And not a computer in sight. I can remember one of the engineers came in with a Texas Instrument calculator that only did basic operations (+-*/) and everyone was amazed. The rest of us used a sliderule, or pencil and paper. I think he paid something like $300.00 for it, which would be $3000.00 in today's money. Sure is a whole lot easier with my CAD/CAM program. Can make any n-gon in about 30 seconds.

[@KenFullman]

How long before you discovered what 5318008 was upside down? (or is that just a British thing?)

[@manishbairagi3006]

Sir should i always use 2nd point as intersecting point? And why only sir 2nd point not any other?

[@TheAggromonster]

And why do I have to draw all the other points and connect them back to the diameter line? Method works, but no explanations.

[@JavierSalcedoC]

Because this is fake af​@@TheAggromonster

[@zwgrafakhsandrianos7784]

I thought i was smart untill i saw this video.Thank you so much.

[@divyam3.1415]

Absolutely amazing. Loved it dude !!!!!!!

[@vulcanfeline]

i like drawing mandalas in M$paint (since my drawing skills suck) and find your methods wonderful. a little finagling to get them to work with no compass and they're not perfect, but they're fun. thx for all your work :D

[@Drew_Hurst]

Try using the software called "gimp", has more tools.

[@waqasarshad7904]

@@Drew_Hurst can you tell me which software the author has used in the video?

[@GiantSnipe]

This is great - no use for it currently but good to know and I will try to work out the maths behind it

[@the_luminary]

So whats the point of drawing ALL 9 parallel lines after drawing the 2nd line which intersects "Q"?

[@joshuaschiffman624]

Did you ever find out?

[@Ani-yt4nf]

It must have been to divide the straight line into n parts equally. After getting the length from the intersect point to B, the parallel lines are no longer needed. They were just used to equally slice the line into 9 parts

[@M05tly]

I also wonder what the purpose of this is. The needed points seem to come from the center line, with the preceeding line not needed? Is this the most accurate way to divide the circumference of a circle with only a straight edge and a compass?

[@borislum1998]

@@M05tly that is a geometric trick to make equi-distance divisions on a line. in this case, just trust the geometry and you really only need that location of the second division on the vertical diameter. then follow the steps as described. so if you want to draw a clock, ie twelve division. use this trick to mark out 1/6th of the vertical diameter line. draw the line from Q and this point to the edge of the circle. use that compass trick to mark out the other 10 divisions to get 12 lines of the clock. easy peasy

[@M05tly]

@@borislum1998 I don't understand on first reading but looking at my comment it's been over a year since I watched the video. I'll rewatch it and let you know when it's clicked. Thanks for the info.

[@peta1001]

Thanks!

[@MikeAG333]

Excellent tutorial, and very clear. When naming things (anything) by letter, "I" and "O" are traditionally omitted because they can be mis-read as numerals. "Q" is generally omitted too. So your list of points on the circle should have been A, B, C......H, J.

[@ArthurGeometry]

Great tip!

[@kentmumar2901]

thank you so much sir

[@christianeb8494]

Génial.

[@Chucktender69]

Love this so much and thanks you for posting this. I’m about to put in a spiral staircase into an uneven semi circle one piece at a time and I believe this will answer all my troubles.

[@cyclingroanoke4837]

1:50 this doesn't seem to jive. What is the second reference point when connecting the diagonal lines to centerline? Especially if done by hand these could be all over the place. And the placement of the second diagonal line seems critical. 3:07

[@GabrielMarinescu-k5p]

Yes, indeed! The deviation between the part calculated with the approximative method above and the exact parts is approx 0.646944 ...%

[@paulss8503]

I am stuck, I’ve been trying to use this method and I’m always slightly out ie when I measure around using the compass it doesn’t return to the origin it’s off -I’m measuring and remeasuring in fact it’s more accurate if I just measure 36 with a protractor (I’m dividing the circle into 10 equal parts) I’ve even tried drawing from QB every 2nd point instead of a compass and it’s still slightly out!!!

[@Tavussatwaossi]

How do you demonstrate, rigorously, that the point B is *exactly* at 1/9 th of the circumference ? (Angle AOB exactly equal to 2 * *π* / 9 ?)

[@El_papa_de_Rambo]

Now I can cut the cake in the office accurately

[@daljeet247]

Wow man ,

[@etyrnal]

is this an approximation? is there any 'imperceptible warpage'?

[@akmurthy2938]

There is approximation. The magnitude of error will be revealed in the last arc and the error will be magnified by increasing the size of the circle!

[@Unemployed12333]

✌👌

[@user-eb4iq2jw3y]

Great video-thank you

[@svenkamog2232]

Very helpful thank you

[@keithwiley7122]

It's clear that this method is only approximate, since it's famously impossible to construct a regular 7-gon using only a compass and straightedge. However, I can't seem to find a resource that discusses this approximation in more detail (e.g. how approximate is it? When is it no longer wise to use it?). Is there a particular name for this approximation that I can search?

[@MrStudent1978]

It's not an approximate method, however the accuracy does depend upon how accurately you draw points, arcs and lines etc. The method is based on "Thales theorem ".

[@keithwiley7122]

Gurpreet Singh but if it weren’t an approximation, then all polygons would be constructible polygons, and that would contradict the Gauss-Wantzel theorem, no?

[@keithwiley7122]

For those also interested in this question, this method seems to be referred to as "the Bion method", and is mentioned in Chapter 1, Use 17 of 'The Construction and Principal Uses of Mathematical Instruments' by Nicolas Bion, though he refers there to Johann Christophorus Sturm's 'Mathesis Juvenilis' as a source for the method. He also discusses the (very small) error fundamental to the method.

[@MrStudent1978]

@@keithwiley7122 thanks Keith! I intended to say that theoretically this method is not an approximation but as the number of sides will increase, the manual error accumulated may become appreciable enough.

[@samisiddiqi5411]

I always thought it was called the Neusis construction, and that's what the Wikipedia on this topic is called but even then I'm asking the same question about the method...

[@spudnickuk]

looks good to what you have done, but how did you come up with using the number 2 and what are all the other numbers for so why is it needed to draw al the other divisions Please explain :)

[@davidmcgrath9581]

Brilliant!!!☘

[@Co-uy4mi]

Hello, I have a question Is there a formula to divide a circle into n equal parts? Like using pi or sin or cos Something like that?

[@abdellahbellafqi3357]

No there is not

[@Alkis05]

Yes there is: ___________________ ╱ ╱ ⎛ ⎛2 ⋅ π⎞⎞ L = R ⋅ ╱ 2 ⎜1 - cos ⎜───⎟⎟ ╲╱ ⎝ ⎝ n ⎠⎠ L is the side of the n-polygon inscribed in a circle with radius R

[@teeeff5179]

actually there is (sort of) : "chord length" = 2 x R x Sin (theta / 2) where 'R' is the radius of the circle and 'theta' is the angle subtended at the center of the circle by the chord. This is useful when you are dividing a circle into N equal segments: the formula simplifies to "chord length" = D x Sin (180 / N). So here you'd set your compass to "chord length" in order to mark off N equal segments of a circle with diameter = D.

[@jamilrahman5960]

if we needn360 divisions then?

[@AngelobOfficial]

Great video!! So well explained! Could I ask you for a formula, or a written source like if n*6 x(distance)=… . My question is coming for a musical purpose. From Geometry and music theorised my EUCLID, in music we call them euclidian beats or patterns. The idea is, no matter the number of beats/hits they are always spread evenly around a circle. So I was looking around but never found a formula to put it in code form. Thanks in advance!

[@elleeo1495]

You would need to do that mathematically. It is not possible to divide a circle by any given number. Look up "constructible polygons" for proof.

[@johnrobertson93]

@@elleeo1495 Yes. It simply can't be done for anything other than 2^n number of arcs (i.e., 2, 4, 8, 16, etc.) or 3 x 2^n number of arcs (i.e. 3, 6, 12, 24, 48, etc.), and certain other specific numbers including 5 x 2^n, 15x 2^n, 17 x 2^n, etc. or p x 2^n where p is the base number of sides of known constructible polygons.

[@chotafallen8390]

Remember that 40 years ago in school. ^^ but why do you use Nr2 not 3 or 1? explaination is missing

[@constablecomfortable]

Omg. That's just blown my mind box. Is this how they did the 56 Aubrey Holes at Stonehenge perhaps?

[@c848]

I am trying dividing the circle into 11 equal parts with this method and I am not succesfull. One division is much smaller. Why is not working?

[@pauljs75]

This didn't work well with n=7 either. So off to try something else...

[@harryjega5643]

Very good video.

[@teekaesthete]

I tried to divide 13 parts. This method did not work there...

[@mark2tech]

Whoever figured this out first had to be a genius

[@mglenadel]

For some reason I can't find it anywhere but in Portuguese-language sites and videos, but the method is known as the "Rinaldini Method", and I believe this to be the name of the guy who invented it. Link in Portuguese Language Wikipedia: pt.wikipedia.org/wiki/Divisão_da_circunferência_em_partes_iguais_(processo_geral) I have found references to the Bion method, and the Tempier method, which seem to be the same thing, somehow.

[@kazparzyxzpenualt8111]

Not a fully functioning math type. I read the comments and watched the demonstration. Using 360 ° as a starting point can one not just divide that by the number of desired sections? Marking enough of the circle by enough degrees should provide something as approximate. Someone said this drafting method did not work for 11 and someone else said the same for 13. I got 32.72 .....and 27.69....and will try to make a drawing to see if I can learn how much of a fudge needs to be worked in between the lines to " Look" good enough. I don't get enough time with my compass anymore.

[@brentbuckley285]

Why did we divide AB line by the number of spaces we want and not use it? Also, Thales's theorem requires a 90-degree angle if I'm not mistaken. Why did you use cm's? I've tried this to make a 26-part circle 5 times, and it hasn't worked. It seems like you're leaving something out.

[@sunflowerbadger]

I think this method relies a lot on being really accurate. I tried this for 13 points and the first time ended up with exactly 12! The second time I got 13 but the final gap was smaller than the rest. I shall persevere, but any hints on doing this by hand would be appreciated. My ultimate goal is to make a massive circular calendar with 365 or 366 divisions... has anyone tried this before? I wanted something about 1 meter diameter.

[@zarau01]

I had the same results when trying to divide into 13.

[@DonaldRipper-m1b]

Just use any competent drawing or CAD software. You can enter any number of points. Then print the result.

[@celticcreations4856]

If you only used the second marker, what was the point of drawing the other segments?

[@johnchristian7788]

If you search "set square" in KZbin, you will find videos on how to draw parallel lines (which is useful for finishing this diagram.)

[@plranisch9509]

How did Gauss constructed a polygon with 17 sides?

[@waygonedon]

What am I doing wrong? My hash marks don't meet up at the apex of the circle, and they are skewed by a few degrees.

[@lukasfilipsky31]

You expect correct results while using incorrect method. That is what you are doing wrong. Use trigonometry, you will see.

[@borislum1998]

you have to be very accurate with hand drawn compass lines. here is a tip. draw with a bigger circle. your error in the angles will be smaller. good luck. or use a CAD or computer aided drawing program

[@Jedidiah07]

How to solve across flat if only diameter is available?

[@廖勇坤]

Great Video!But i still don't now how it work😃

[@alexzuma2025]

mark the inclined line as many times as you want divisions

[@pivocopii8254]

Using this for building a roulette

[@jaghook]

HELP. HELP HELP,,,,A normal circle has 360 degrees,,,,,,how can i create a circle with 147 equal arcs of degree. Or to put it another way, How can i create a 360 degree circle, with a 260 mm diameter, divided into 147 segments of arc, each with an angle of 2.4489795 of a degree. Any help will stop me breaking down, regards Jim

[@Alkis05]

With the following formula _________________ ╱ ╱ ⎛ ⎛2 ⋅ π⎞⎞ L = R ⋅ ╱ 2 ⎜1 - cos ⎜───⎟⎟ ╲╱ ⎝ ⎝ n ⎠⎠ L is the side of the n-polygon inscribed in a circle with radius R. That being said, unless you are using a computer, it is very hard to make a polygon with so many sides by hand.

[@kksphilomath384]

Why we have to join Q to 2 only, why not any other point ???

[@mr.jayeshrangwani]

Same question

[@mr.jayeshrangwani]

Any idea? Or any ratio is this? Can this possible for other polygons?

[@WXTF369]

I believe 2 is always used because the person drawing already knows the first point as 'A'. Since they're trying to find the second point on the circumference, they walk the line from Q through the second point on diameter to the circumference to find where the next point is for even sides. After 1 is 2 so they always pass the line through 2. Hope this helps.

[@etyrnal]

because the metered line represents the WHOLE circumference... but your mark is only for half that circumference... as you are projecting the points out only to one side of the circle

[@Goofayball]

Why use 2 if you want 9 segments?

[@wirebrushproductions1001]

You should start by saying that this produces a very good approximation, not an exact division..

[@jamesrobson820]

When I look at the division E-F it appears shorter than F-G ,just an optical illusion I guess.😊

[@derekwilkinson7939]

Why did I get ten divisions?

[@ArthurGeometry]

kzbin.info/www/bejne/rJPHmYONZsanq5Y

[@Must_not_say_that]

(Pi x D) divided by n. Much easier.

[@BariumCobaltNitrog3n]

Random width parallel lines, yeah good luck wit dat.

[@ArthurGeometry]

Better use your 45º and 30 set-squares

[@Simon_Jakle__almost_real_name]

Carl Friedrich Gauss (en.wikipedia.org/wiki/Carl_Friedrich_Gauss ) was so proud of having found a way to divide a circle into 17 (equal) parts (as in en.wikipedia.org/wiki/Heptadecagon ), "claiming" this to be his greatest discovery in the year 1801 as far as it's told, so he might used calculus, but this must have been a rather/mostly analog(ue) way.

[@stephenroberts7459]

Errors accumulate! ---- on a 13 division exercise, a 0.5 mm error on the first division leads to a 5mm error on the last one!

[@davebashford3753]

Cool, but showing the derivation would've been *much* cooler.

[@modernworld3685]

YES THIS GOOD, BECAUSE, STUDENT WISE FOR KNOWLEDGE NEED TO HAVE THAOUGHT, HOW TO MAKE DRAW CIRCLE AT ANY ANGLE OF DIGREE , LIKE 5 DEGREES , LIKE 10 DEGREES, LIKE 45 DEGREES, LIKE 90 DEGREES. IS THIS GOOD GIVEN KNOWLEDGE.

[@stick1hun]

Is there a proof to this somewhere? I am really interested

[@simonpenny2564]

Mathematicians vs artisans - practical vs theoretical - symbolic reasoning vs geometric construction. Its an age-old debate. The point of geometrical construction is that no numbers or numerical reasoning are involved. And this is the way people built things for millenia - and in many places still do. The method isn't mathematically 'true' (40deg vs 40.3deg) but good enough if you are laying out, for instance, a 9 sides dining table. High precision measurement and precision marking is crucial, as errors accumulate - moreso for more sides obviously. At page scale, the thickness of a pencil lead introduces error - that's why machinists use scribes. And why medieval cathedrals and hindu temples were marked out full scale - as sails used to be in a sailmaker's loft. Manual accuracy is a lost art in the age of CAD

[@neepashah4351]

No its notworing. I tried taking 25 parts but it didnot.

[@alpha9526]

Followed your instructions and it didn’t work.

[@pcelarskisokak]

😅

[@JavierSalcedoC]

Unbelievable this video is considered true😂😂😂

[@erickarmigos1486]

T

[@renesperb]

Of course this construction is not correct .If you would measure the angle that you construct you would get 40.28 ° ,which is not bad in this case .Try your construction for a pentagon ,then you would see that you don't get a correct construction. It has been known for a long time already which regular n-gons one can construct with straight edge and compass (e.g. n=17,n=257 ), but e.g. not n = 7 or n=9.I have tested a few cases , and one can see that it is often a very good aproximation. So, for practical purposes it is in many cases sufficiently close.For n=9 this construction is off by 2.5° for point 9,for n=15 the last point is off by 8.63° ,for n=20 it is off by 12.7° . Hence for this approximation n should not be more than 10 for good results.

[@tomclarke1768]

Highly inaccurate if you wish to divide your circle into anything above 10 sections.

[@ArthurGeometry]

Totally agree, for 10 better use this one kzbin.info/www/bejne/rJPHmYONZsanq5Y

[@ploumtagada2]

Le gars qui a fait cette vidéo ne comprend pas ce qu'il fait, il lui manque donc une partie du traçage.

[@luisarmandogarzareyes752]

Ok it is fake but, I learned how to divide a line by n equal parts 😅

[@Etothe2iPi]

Why are you lying in the title? Your "equal" parts are NOT equal.

[@PatrickDepoix-r3v]

False! Don't work. I tested with my CAO application and it's false.

[@stephanieburton5677]

Rfje

[@D.E.P.-J.]

It's not exact. It doesn't work.

[@misa-g3o]

in constructive tasks of Euclidean geometry, it is allowed to use only a ruler and a dividers. Nothing that is 1 cmm.

[@horacerumpole6912]

Let's see you draw those parallel lines by hand using that triangle...

[@MariamAbdelshafy-g4p]

Yes😭😭😭

[@thomassheppard5369]

Drawing parallel lines with a set square is standard drafting practice. You just use another straight edge or second set-square butted up against one of the other edges on the first set-square and slide the first set-square into it's new position, drawing the parallel line. It's a technique that has literally been used for hundreds of centuries. Mostly because of its accuracy. The divisions are as accurate as your pencil is sharp. This was a great video, well made and informative. I tip my hat to the creator for their interest and effort. It is much appreciated 👏.