The problem Euclid couldn't solve

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Welcome back! This is my second video now and I really hope you enjoyed it! Please leave me any feedback, questions, etc. in the comments.
===Chapters===
0:00 Introduction
0:29 Constructible polygons
2:06 Non constructible polygons
2:33 Constructing the 17 gon
3:42 Calculating with points
6:02 Constructible numbers
8:24 Why and how you can construct the 17 gon
15:04 Which polygons are constructible
16:27 Outro
===Acknowledgements===
At around 4:19 you construct the sum by translating the distances with the compass. I show the wrong distances. they're translated in parallel, not around the points.
At around 4:50, the distance is not called "argument", that's the angle
At around 5:30 I talk about the bigger and smaller triangles. It's more about the sides of the triangles and only in this case their relation is like that. But it doesn't have to be
===Made with===
Manim (www.manim.community/)
===Music===
Music by Vincent Rubinetti
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
open.spotify.com/playlist/3zN...
===Tags===
#geometry #17gon #heptadecagon #polygon #euclid #gauss

Опубликовано:

30 июн 2024

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Комментарии : 150

@mathkiwi Год назад

Hi, I hope you liked my video! Please leave your feedback, questions, etc. in the comments. Also, please read the description.

@cubicinfinity2 11 месяцев назад

it can be hard to follow in realtime. I need to come back to it later when I'm dedicated enough to follow along and really think about it. But it has already shown me a relationship between modular arithmetic and complex multiplication that I hadn't considered.

@mntrmntr 11 месяцев назад

7:36 "only addition, subtraction, multiplication, division and square root" - why only those? Somehow you skipped over the most interesting part. I can guess, that the proof that no other operations are possible with compass and ruler is hard, but you could have said at least something about it.

@acampoverdeify 11 месяцев назад

You really should use a black background with white lines, like 3Blue1Brown

@WaluigiisthekingASmith 11 месяцев назад

@@mntrmntr the thing is i believe the proof isn't even that difficult. Since the only objects you have a circles and lines you just need to show that their intersection can be represented as only square roots, and +,-,*,/ of the center of the circle, the radius, and two known points on the line

@buttonasas 11 месяцев назад

"Squaring the circle" is an idiom I've heard but I had no idea it was an actual thing in maths. I had to rewind like 8 times to realise you're not using the idiom and I should look up what that means.

@Bruno-cb5gk Год назад

Loved the video, it's really well done but I think you made a small mistake. You called the modulus/length the argument, when instead the argument is the angle.

@mathkiwi Год назад

You're totally right

@0ddSavant 11 месяцев назад

@@mathkiwiI appreciate you calling the modulus the argument as an Easter egg to see who was really paying attention. Nicely done. I love additive things like this. Just a few simple operations, but they hide incredible complexity and diverse application inside those deceptively simple steps. Cheers!

@p4vector 11 месяцев назад

Also I think zeta^35 should be zeta^1

@deserado11 11 месяцев назад

... say what? 🤪 (fastenated by mathematics but can't do it to save my life 😢)

@pseudolullus 11 месяцев назад

@@deserado11it's about complex numbers. The modulus is the distance from the origin on the complex plane, and the argument is the angle from the origin to the point on the complex plane.

@KinuTheDragon Год назад

For the nonagon, I had to think on it a bit to realize that you can "combine" two polygons like the pendecagon if the constituent polygons' side counts are coprime (since then you dont need to worry about accidentally using the same vertex twice). Great video!

@mathkiwi Год назад

Thanks!

@M4DA. 11 месяцев назад

You can probably extend this logic further and conclude that using n-gram and k-gram you can contruct m-gram where m=LCM(n, k)

@javierantoniosilva8477 11 месяцев назад

This video went from elementary to mind blowing and iluminating real fast, especially if the viewer knows its fair share of undergraduate math. I love when different branches of math are shown to be just different faces of the same dice.

@MichaelRothwell1 11 месяцев назад

Here is my explanation of the construction of the pentagon in the video using the Carlyle circle for the appropriate quadratic (which turns out to be x²-(-1)x+(-1)=0), the key aim being the construction of the length cos(2π/5). The 5th roots of 1 are ζ⁰, ζ¹, ζ², ζ³, ζ⁴. As powers of 2 (mod 5) are 2, 4, 3, 1 we can order the powers of ζ according to the powers of 2 (instead of the powers of 3 used for the 17th roots of 1): ζ¹→ζ²→ζ⁴→ζ³ This time, the conjugate of each number is 2 places after the number. By symmetry, ζ⁰+ζ¹+ζ²+ζ³+ζ⁴=0 So ζ¹+ζ²+ζ³+ζ⁴=-ζ⁰=-1 and ζ¹ζ²ζ³ζ⁴=ζ¹⁰=1 Now split the sequence ζ¹→ζ²→ζ⁴→ζ³ in half, taking alternating terms: η₀=ζ¹+ζ⁴. η₁=ζ²+ζ³ Note that η₀, η₁ are real as both are the sum of a 5th root of 1 and its conjugate. In particular, η₀=2Re(ζ)=2cos(2π/5). η₀+η₁=ζ¹+ζ⁴+ζ²+ζ³=-1 η₀η₁=(ζ¹+ζ⁴)(ζ²+ζ³)=ζ³+ζ⁴+ζ¹+ζ²=-1 So η₀, η₁ satisfy x²-(-1)x+(-1)=0 This quadratic can be solved using the Carlyle circle construction (see en.m.wikipedia.org/wiki/Carlyle_circle ), with a circle having as diameter the line segment joining (-1,-1) to (1,0), so centre (-½, 0), and indeed marking this point is the first step in the pentagon construction in the video. The next step is marking the radius of the Carlyle circle, from (-½, 0) to (1,0), followed by marking η₀, the positive root of the quadratic (the roots are the points where the Carlyle circle, with centre and radius just found, intersects the x-axis) which equals 2cos(2π/5), and halving this gives cos(2π/5), the x-coordinate of ζ. Finally we construct the point ζ as the intersection of the perpendicular to the x-axis at η₀=cos(2π/5) with the circle in the 1st quadrant.

@garrettkajmowicz 11 месяцев назад

I have a degree in engineering. This is the first time I've had any real appreciation for how classical geometry and algebra can be connected. Thanks!

@xwtek3505 11 месяцев назад

This means that whether there are infinitely many odd-sided constructible polygons or not is still an open question because it's not known whether there are infinitely many fermat primes or not.

@alucs6362 Год назад

This is an amazing video, especially if the viewer is already mathematically minded and/or knowns at least some advanced highschool or undergrad level mathematics! It's challenging at points, but in the way all good maths is. I have a couple of suggestions from a didatic point of view, but feel free to take them or leave them: 1) It would be good if you showed at least a quick graphic method for each operation you talk about or at least the crucial non-obvious step to get there. For example, angle addition - it is really straightforward if you know how to copy angles, but if someone is new to the topic they might not have the intuition/technique necessary to know where to start. 2) I really like the bits where you encourage exploration! For more viewers to engage with these moments it might be worth giving those that are newer to the field a tip or direction about where to start. This can be done a couple moments after you pause, so that it doesn't spoil it for those who don't want tips. Once again, great video! Really surprised to see a video with such production quality and such good content in a channel with relatively few subscribers. Edit: Beautiful title by the way, it perfectly manages to make the video really enticing without feeling clickbait-y in any negative sense!

@mathkiwi Год назад

Thank you so much for the detailed feedback!

@Qermaq 11 месяцев назад

I agree with all the above. I found your pace somewhat rushed. I know a 20 minute video gets less than half the views of a 10 minute one. But what you're communicating is worth extra time. I think 3B1B has the opposite flaw, he tends to over-repeat things. I wish I could listen as fast as you think I can. ;)

@ygalel 11 месяцев назад

I actually learned this construction by Gauss when I first learned Geometry in college, and I was so amazed. Next year when I was learning Galois Theory it came up again and had a deeper understanding of it's constructibility. The fact that I couldn't share how amazing this is with my highschool students was the reason I couldn't continue as a teacher anymore 😂

@ultracreador 11 месяцев назад

No te subestimes, de todas formas, no es fácil explicar la construcción de esto:14:53

@danmimis4576 11 месяцев назад

Well-done video. Speaking of 7 and 17, did you guys notice that the year this video was published: 2023 = 7*17^2

@mocaothi7383 11 месяцев назад

Perfect timing

@ALEXANDERCHEWTIANYOUMoe 23 часа назад

Oh yes it is

@johnchessant3012 11 месяцев назад

9:15 zeta^35 would be zeta^1 15:39 it might be nice to explain that 2^k + 1 can't be prime if k has any odd factors, because x+1 divides x^k + 1 when k is odd otherwise, great video!

@blacklistnr1 11 месяцев назад

Really nicely animated video! It also reminds of a puzzle game I used to play called Euclidea

@MichaelRothwell1 11 месяцев назад

This is an excellent video and explanation. I have known for a long time which polygons can be constructed with straight edge and compass, but now I finally know why. At least, I understand why the constructable polygons are constructable. However, I'm not sure that I can see why in all other cases the polynomials cannot be reduced to solving successive quadratics.

@mathkiwi 11 месяцев назад

The main focus was what polygons are constructible. For the other ones, their polynomial can't be reduced to a quadratic one. For n=7, you get degree 7->6->3.

@MichaelRothwell1 11 месяцев назад

@@mathkiwi I get that. BTW, this was an excellent practical example of field extensions by quadratic roots. I guess kind of heading towards Galois theory...

@izaactheberean6860 11 месяцев назад

Just make a ruler that has transcendental & irrational numbers on it, but the ruler is a fractal so it's not just an appromixation. Easy.

@zapazap 11 месяцев назад

The problem of constructing with 'compass and straightedge' is indeed easy of we change the definition of 'straightedge' -- hence changing the definition of the problem. Cheers!

@NoActuallyGo-KCUF-Yourself 11 месяцев назад

Step 1. Turn it into an engineering problem. Step 2. Solve the engineering problem.

@zapazap 11 месяцев назад

@@NoActuallyGo-KCUF-Yourself This works to solve the original problem only if solving the engineering problem helps to solve the original problem. Does it in this case?

@WaluigiisthekingASmith 11 месяцев назад

Really cool video. The way the roots of unity came up and the recursive quadratics are super reminiscent of FFT . My only wish is that you really dive into why nth roots are not constructible (except for n=2^k). Every time people talk about what constructible numbers are they explain how you can construct+,-,*,/,and sqrt but they don't explain why you can't get for example e^x or cube root(x)

@bandana_girl6507 11 месяцев назад

The question of what additional regular polygons could be constructed with gaining a method to trisect an angle is very open-ended as the method is not specified. Judging based on the one method I know of making constructable angle trisection possible (allowing for folds, folding points on to each other, and folding points on to lines, which other than drawing a circle or arc, also covers all of the possible constructions with straightedge and compass), though, you would also gain the possibility to solve cubics, meaning that you could have any prime n where n-1=2^a*3^b for some integers a and b. You'd also, of course, have an arbitrary power of 3 as an option in your polygons just like bisection gives you 2.

@pafnutiytheartist 11 месяцев назад

Beautiful animations!

@DrPhipster 5 месяцев назад

What a fantastic video. Keep up the great work! ❤️🥳🙌🏼

@MrRyanroberson1 11 месяцев назад

4:25 i don't know if anyone has mentioned it yet, but this animation is incorrect. it implies that the length OB is being conserved to BX while the length OA is conserved to AX, which would result in a kite, not a parallelogram

@MichaelRothwell1 11 месяцев назад

Yes. This error is acknowledged in the video's description.

@SheikhEddy Год назад

Underrated video!

@alphalunamare 11 месяцев назад

When I was a child I was shown how to draw polygons. Draw a circle, line out the diameter, and draw a line from left edge upwards anywhere so it hit hit perimeter. Divide that line into n segments where n was the number of sides you wanted. (It's easily done with a pencil, ruler and set square). Then you drew a line from the centre through the 'second' mark on the line and where it hits the circumference make a Cord from the left diameter point. You then have your side. Try it 🙂

@mjeffery 11 месяцев назад

This appears to be a constructible method for finding a chord on the circle given any n. Since an arbitrary n-gon is not constructible, it's not possible that it always produces the chord for an n-gon. But I was hoping that it produced a close-enough approximation for some range of n, so I wanted to understand the method to see why it might work approximately. Unfortunately, I wasn't able to follow your directions. I tried coming up with an interpretation of "draw a line for left edge upwards anywhere so it hit[s] perimeter", but didn't produce results that are even approximately correct. Here's my (failed) interpretation: Given a circle with center O and point E on the edge, draw the diameter line OE. Pick a point P on segment OE and draw a line perpendicular to OE at P and label an intersection of this line and the circle OE as T, creating segment PT.[*] Find point F on PT that is 2/n of the distance from P to T (so PF:PT :: 2:n). Find point C which is the intersection of the ray OF and the circle OE, making chord EC, which is supposed to be one of the sides of the n-gon inscribed in the circle OE. [*] This sentence corresponds to the part I couldn't interpret. The above fails not only because the choice of P is arbitrary and affects the size of the chord greatly, but because even a "reasonable" choice for P (bisecting OE) produces a chord that is way too short. Can you clarify and correct the above to describe the actual method? In particular: Is the "perimeter" for the circle OE? What is "upwards" mean here? What flexibility does "anywhere" describe? And what does "left edge" reference? NB: I interpreted the "perimeter" as being the perimeter of the circle, "upwards" to mean perpendicular to the diameter OE, "anywhere" to indicate the arbitrary choice for point P where the perpendicular is drawn, and "left edge" to be the left segment of the diameter, which I chose to be segment OE. Thanks

@alphalunamare 11 месяцев назад

@@mjeffery Sorry about my sloppy language. Also my memory was clearly a bit foggy. I google and found this video of what I so poorly described. I'd be very interested in seeing your results, perhaps a bound on the error? Best Regards ... ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-SBdSHOiMJS4.html

@mjeffery 11 месяцев назад

@@alphalunamare OK, interesting. This method takes the diameter of the circle AB and picks point X on 2/n of the way from A to B (so AX:XB :: 2:n). It also picks point P to form equilateral triangle ABP. Point C is formed by intersecting the line PX with the circle so that P and C are on opposite sides of the diameter AB. This is clearly exact for a square, and with a small amount of work can be shown to be exact for a triangle, which immediately implies that at works for a hexagon, too. It does not work for any other regular n-gon. For a pentagon, it undershoots the angle by about .065%. For a heptagon, it overshoots the angle by .17%. For an octagon, it overshoots by .42%. By the 25-gon, it has an error of 4.4% and overshoots enough that it doesn't manage to even get 24 sides. (These errors were found numerically.) As a physical method to draw a good approximation of an n-gon with a small n, it's pretty good, but as expected it isn't a correct general method for constructing one. Nor does it do a good job as n grows larger.

@alphalunamare 11 месяцев назад

@@mjeffery I am impressed! :-) Here's a question:- If you plot the error as n grows far greater than 25 do you notice a cyclicity in its graph? Another consideration is to make an adjustment to the 'second' point through which the penultimate construction line is drawn, but that smells of epicycles. :-)

@Geek37664 2 месяца назад

I think a video on angle trisection would be a wonderful one for you to make. There’s a plethora of great math there and it can explain why you can construct the heptagon and nonagon and still remain in the complex plane.

@puccid 11 месяцев назад

Good video! I just find the music a little distractive, I think it is a little too high in volume

@123pok456ey 11 месяцев назад

Why do we choose the way to split the zetas into the etas and then the mus? Not quite know where these comes from, and don't know how those summations (the 3^(nk+i) ones) comes about

@calvinjackson8110 26 дней назад

Gauss figured out how to construct a regular 17-gon when he was 19.

@disonaroaurelo 3 месяца назад

Ultra easy level - Quickly solving Euclid's 7-sided polygon problem using angles xD Just imagine the lines as edges that are rectangles and have corners. Now take and make a transversal square inside another square, the more you increase the number of edges in the polygon, the more the open angle between the two edges of the fold of the initial transversal square will be divided between the other 1st corner/corners added. Sides 0°, 90°, 180°, 270° subtract an element from the division as 2/4=0.5, removing 0.5 from 2 becomes 1.5. However, this wouldn't make sense, so let's use the open angle of the corner in difference to 0° and see how much it is equivalent in terms of divided values of degrees on the other corners, using a rule of three We have a 0° side which here will be the top of the seven-sided polygon if you only take the straight side of the figure which is what we will do. Taking the cosine of 60° which is 0.5 as a reference, just find how much the difference between other non-homogeneous degrees is worth. Come on, now it's easy to find how many degrees there will be for each by dividing the degrees in half and this way we will have our 7-sided polygon perfectly made using degrees.

@ultracreador 11 месяцев назад

Ahora, un vídeo de los polígonos que se pueden construir con el método Neusis.

@Pikachulova7 11 месяцев назад

Love the video

@phenixorbitall3917 11 месяцев назад

I love derivations like this.

@jocabulous 11 месяцев назад

12:21 new pokemon lore just dropped

@xXJ4FARGAMERXx 11 месяцев назад

I never realised Mew's name was just a single letter

@BramCohen 11 месяцев назад

My guess with having trisection would be that it expands to cubics so you can find any n-gon where n is a prime and n-1 is a power of 2 times a power of 3. Also can multiple by 3 in addition to 2 of course.

@BorisNVM 3 месяца назад

really cool

@beatrizkarwai6763 11 месяцев назад

I think it would be possible to construct any regular polygon if we were allowed to move the "compass" in three dimensions. it would be similar to the process of dividing a line segment into equal parts. a tridimensional compass should be able to divide any angle in an arbitrary number of equal parts, so through a similar process it could also create any regular polygon

@flameofthephoenix8395 11 месяцев назад

I don't know what the rules are, I've somehow managed to go my whole life without being familiar with the basic graphing tools like compasses, and even rulers.

@awindwaker4130 11 месяцев назад

This video is not introductory at all, you can't follow it if you don't already know it.

@peterdavis9403 11 месяцев назад

Probably breaks some rule , but N-secting could be done by making a long strip with a line and compass marking N successive points, then bending the strip into a full circle and transferring the points to a planar circle. The angles could then be copied to the angles needing dividing.

@bandana_girl6507 11 месяцев назад

Though then you have introduced a new tool. Also, the mathematical construction would have to first lay your strip on an arc segment of the angle then straighten it out, n-sect the line segment on your strip which is now a line (a rather straight forward process), and then moving the strip back to the arc to n-sect the angle.

@albert12798. 11 месяцев назад

this is how to catch my attention

@capnabulel 11 месяцев назад

This video proves that you can definitely construct a polygon as long as it is a multiple of some power of 2 and some fermat primes. But I don't think it proves that others cannot be constructed for sure, does it? I guess that will require a proof that you can't exponentiate with a rational number unless the denominator is a power of 2. Since |cosine of the angle|

@mathkiwi 11 месяцев назад

The compass solves a quadratic equation and the straightedge a linear one. That might be an answer

@capnabulel 11 месяцев назад

yea that makes sense. Just wanted to point out that it wasn't explicitly stated in the video why cuberoots or higher order roots aside from powers of 2 are not constructable

@Qermaq 11 месяцев назад

@@capnabulel I think it comes down to we can bisect arbitrary angles but we cannot trisect or more-sect arbitrary angles.

@columbus8myhw 11 месяцев назад

@@capnabulel It has to do with the 'degree' of the constructed points. The degree of a constructible point is always a power of 2, but the degree of the cube root of 2 is 3. To fully define degree and prove its properties requires a little bit of linear algebra.

@Toxic__rl 11 месяцев назад

u can do 7 side polygon. i had to do that sh*t on my engineering drawing class lol O.o

@DascooleSchaf 11 месяцев назад

Gutes Video mit musik

@ken_q 11 месяцев назад

Lmao I accidentally set the playback speed to 0,5 and i thought he was on drug at the start of the video 😂

@yiannchrst 11 месяцев назад

very good Greek letter pronunciation! (i am Greek)

@davidgillies620 11 месяцев назад

I've never seen the neusis construction as any more artificial than the compass and straightedge. Neusis-constructible polygons then include the heptagon, nonagon and tridecagon for example. It's an open problem whether the icosipentagon is neusis-constructible

@brummi9869 11 месяцев назад

The video is really good, but I think you made the music too loud, it seems to be at an equal or higher volule than your voice

@accuratehvacr 11 месяцев назад

Try different speakers or sound settings.

@Nicolas-ld3eq 11 месяцев назад

There were two pints created with green intersections at exacly 2:58 and 2:59. What are they constructed after ? what method was used to obtain these two points?

@edoardodaurelio4102 11 месяцев назад

Those are just the midpoints between the origin and the previous points. Their construction is actually shown at 13:02, and explained (although a bit rushed) in the few seconds before. Cheers!

@morgengabe1 11 месяцев назад

Contradictions are underrated!

@Trizzer89 11 месяцев назад

Does the 17 sided polygon use the 8-15-17 right triangle? That would explain it

@ultracreador 11 месяцев назад

Me parece que utiliza un triángulo rectángulo donde aparece la raíz cuadrada de 68 68=(17)(4)

@mokhlisstsoulifaroukh1704 11 месяцев назад

What kind of music is played in this video? Who is the band ? Thanks so much

@gaopinghu7332 11 месяцев назад

In the description there are some links for them.

@jurajvariny6034 11 месяцев назад

Can't we construct cube roots in 3d space? Trying to use compass in space is awkward in practice, though.

@mumujibirb 11 месяцев назад

isn't there a method to draw any polygon with arbitary sides?

@koushikdas925 11 месяцев назад

Regular heptagon can be construct by compass and scale

@zetetic9 11 месяцев назад

I'm having a really hard time figuring out how you got your starting point for the line that creates the 90 degree angle for the square. 0:49 .

@2010ngojo 11 месяцев назад

Yeah, that wasn't really explained well, or at all, on how you can get a 90 degree angle with the tool mentioned in the very beginning. Edit: eventually I was able to make a square. It's a lot of steps though. Maybe I did extra steps, but it's possible.

@markhughes7927 11 месяцев назад

A Vesica Pisces allows the bisection of any base line at 90° and an identical circle to those used for the Vesica and originating at that intersection of the base line gives four equi-distant points on the circumference of that circle….(from a non-mathematician). Probably irrelevant.

@xXJ4FARGAMERXx 11 месяцев назад

You can divide a line in half, I think.

@pierreabbat6157 11 месяцев назад

How do you construct a hexamyriapentachiliapentacosiatriacontaheptagon?

@GaneshAher1729 11 месяцев назад

How did you used 3b1b music? I thought that was copyrighted.

@BenjaminGoldberg1 11 месяцев назад

Wonderful video, but you might want to replace the auto generated transcript with a hand written one... every time you said Fermat, it guessed something utterly wrong.

@Tom_Shepperd143 10 месяцев назад

This was something

@AstroTibs 11 месяцев назад

I think many of your yellow line segments change length during the rotation animation. Just a heads up.

@leofun01 11 месяцев назад

16:26 - I will try to guess : 2^m * 3^n * p1 * p2 * ... * pt

@skylardeslypere9909 10 месяцев назад

I have a small question which I might know the answer to but I want to confirm. In the end, we concluded that any polygon with (2^k)p_1...p_t sides, where k,t > 0 is constructable. But why is 4 also on this list? My guess at an answer is simply that we don't use the same method of constructing a square than we do for the others? Another question, but that might be because it's 2AM and I'm way too tired: are these numbers the only ones we can construct? Are there others that we may be able to construct in a different way?

@mathkiwi 10 месяцев назад

4=2^2. And yes, these are the only numbers you can construct. That is because a line solves a linear equation and a circle a quadratic one.

@skylardeslypere9909 10 месяцев назад

@@mathkiwi but 4 = 2² doesn't fit the pattern of 2ⁿp_1...p_t. I guess it's just an exception?

@Potoaster 11 месяцев назад

Why would you be allowed to bisect a line but not trisect it with this setup?

@MichaelRothwell1 11 месяцев назад

You can trisect a line segment or indeed divide it into any number n of equal parts. What you can't do with a straight edge and compass is trisect an arbitrary angle (you can trisect some angles, like 90°).

@Kirillissimus 11 месяцев назад

@@MichaelRothwell1There actually is a way to trisect an angle! You just bisect it, then bysect the section, then you bisect the section of the previous section and so on. Then you just add up the parts like digits in a number until you grt close enough. In fact you are only limited by how much time you are willing to waste and by the compass and paper you use. If you allow for infinite bisections then dividing any angle by any value even including irrational ones immediately become possible at least in theory.

@MichaelRothwell1 11 месяцев назад

@@Kirillissimus It's true that you can approximate the trisection of an angle as closely as you want, but when one talks about a construction using a straight edge and compass what is meant is an exact construction requiring a finite number of steps (and not the limit of a procedure with an infinite number of steps).

@X_Baron 11 месяцев назад

@@MichaelRothwell1 Angle trisection is also possible if you allow the paper to be folded during the construction, but that's cheating of course. 🙂

@MichaelRothwell1 11 месяцев назад

@@X_Baron Yes indeed, using the Beloch fold :)

@KlaudiusL 11 месяцев назад

Nice vid. Just a note: music is a bit loud and distract from what is important: the voice. For intro/outro is ok, but for an entire video hasn't meaning.

@FoxDog1080 11 месяцев назад

I'm interested as to whether or not 360 is divisible by 17

@xXJ4FARGAMERXx 11 месяцев назад

360/17 has a lot of digits, it's probably irrational

@HatterTobias 11 месяцев назад

@@xXJ4FARGAMERXx 360/17 is still rational Examples of irrational numbers are stuff like √3, π and e

@Kirillissimus 11 месяцев назад

@@HatterTobiasEven though 360/17 is rational its precise decimal representation still requires infinite amount of digits.

@HatterTobias 11 месяцев назад

@@Kirillissimus sure it does need infinite digits, but those infinite digits are just a pattern of a finite amount of digits repeated infinitely many times

@mihaleben6051 11 месяцев назад

7+10 3+4 I constructed it. Well it is in conatruction.

@rogercruz1547 11 месяцев назад

brasilian schools were not good for me, most of it flew way over my head

@askcaralice 10 месяцев назад

that's a nice video but why can't one construct a cube root or pi?

@kevinbyrne4538 11 месяцев назад

11:29 -- the so-called "Carlyle circle".

@donaldhobson8873 11 месяцев назад

Slight pedantic point. With a compass and straight edge, you can also take complex conjugates.

@danielsouzamatias7283 11 месяцев назад

feedback: the background music is too loud

@andreasfr1 10 месяцев назад

@mathkiwi ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-3tqwPJsyRqM.html&ab_channel=ArthurGeometry

@noblox2092 Месяц назад

uh i actually managed to construct a heptagon

@benedictsforester7045 11 месяцев назад

Didn't origami artists cracked splitting angle in 3?

@Auroral_Anomaly 11 месяцев назад

Couldn’t you just rotate the sides with an interior angle of 158.82°?

@metalim 11 месяцев назад

What I dislike about current state of math most - is goddam Eta, Theta, and the rest of the Zoo, that for some reason is still kept alive. Let the dinos die out, they are history

@miloradtomic 11 месяцев назад

Dear friends, thank you very much. You have opened spaces for me, that I haven't been in, for long time. Theoretical mathematics superb poetry. The lofty flight of our mind. Severall of your posts prove, that the same mind has quantumnes, and that regardless. Srodingers electron, and that there can be more space simultaneously ontologically condensing them. Your animations are perfect. I subscribe you, with pleasure.

@Treviisolion 11 месяцев назад

3:07 it’s unclear how you determined where these points should lie. Plus if you’re going to talk about constructing polygons, it may be a good idea to show the basic techniques, such as how to construct a perpendicular line. Very few people ever have to construct geometric constructs manually these days, so few will remember it if they’re even taught it at all.

@bandana_girl6507 11 месяцев назад

Those points seemed a bit arbitrary to me, too, but when he goes over the proof at the end and where the construction comes from, the construction of those points is actually shown. Steps are still skipped, though.

@YoutubeModeratorsSuckMyBalls 11 месяцев назад

Wdym we cant construct 7 gon? We can

@awli8861 11 месяцев назад

heptagon

@ejrupp9555 11 месяцев назад

There is a method to construct any number of of angles ... with just a compass and a straight edge. What are you talking about?

@ejrupp9555 11 месяцев назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eaKOyI9Srxc.html

@kremenskiyjr 11 месяцев назад

the f....

@erroos 11 месяцев назад

Very interesting but ain’t understandable

@blablabla7796 11 месяцев назад

Using a 90deg angle is kinda cringe. If you want to draw a right angle ABC where point B is the vertex, A and B are the original points on the line, just construct a point D using a compass and a ruler on the the same line as AB but on the other side, then construct two circles with the same radius on A and D with any length greater than AB, then use the two intersections of the circles to draw a line which is 90 degrees with line AB. That way you only need two tools.

@martinstubs6203 11 месяцев назад

Nach dem Akzent zu urteilen sind Sie Deutscher. Hier ein kleiner Englisch-Tip: „not constructible as well“ ist falsch. Es heißt „not constructible either“.

@farklegriffen2624 11 месяцев назад

Dude! Please slow down! I'd much rather watch a 30 minute video where you explain every step than a 15 minute video where I get lost every 2 minutes

@MonitorMichael 11 месяцев назад

Unwatchable because of the intrusive music

@zapazap 11 месяцев назад

Unwatchable to whom? Cheers!

@monitorcomputersystemsltd2375 11 месяцев назад

@@zapazap Unwatchable to anyone who can't block out the background music, which adds nothing to help the content and plenty to distract from it, Chhers!

@zapazap 11 месяцев назад

@@monitorcomputersystemsltd2375 I a cannot block but I could watch it So again: unwatchable to who?