The Amazing Heptadecagon (17-gon) - Numberphile
ฝัง
- เผยแพร่เมื่อ 2 มิ.ย. 2024
- More on the math behind this: • Heptadecagon and Ferma...
Catch David on the Numberphile podcast: • A Proof in the Drawer ...
More links & stuff in full description below ↓↓↓
Professor David Eisenbud - director of MSRI - on the amazing 17-gon and its link to Gauss.
See end of this video for a bit MSRI's address at 17 Gauss Way!
Support us on Patreon: / numberphile
NUMBERPHILE
Website: www.numberphile.com/
Numberphile on Facebook: / numberphile
Numberphile tweets: / numberphile
Subscribe: bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
Videos by Brady Haran
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanblog.com/
Sign up for (occasional) emails: eepurl.com/YdjL9
Numberphile T-Shirts: teespring.com/stores/numberphile
Other merchandise: store.dftba.com/collections/n... - วิทยาศาสตร์และเทคโนโลยี
![[Full Episode] MasterChef Junior Thailand มาสเตอร์เชฟ จูเนียร์ ประเทศไทย Season 3 Episode 1](http://i.ytimg.com/vi/Qs5zdBqLn_8/mqdefault.jpg)
Catch David on the Numberphile podcast: th-cam.com/video/9y1BGvnTyQA/w-d-xo.html
The most sides i know is the rhombicosidodecahedron it has 62 sides
Ok
@@elviraloiuselabas861 circle.
numberphile, what if i found something for hendecagon (11) ?
I've tried to follow your instrictions using Geogebra Classing and ended up with something close to a (20 1/8)-agon
This is like Geometry with Bob Ross.
+Ryan N haha, my thoughts exactly! He is just missing the "here we draw some happy little circles"-part
that's exactly what I was thinking.
+Bon Bon
It's not intended to be an art piece tho
Marcello Chua Nevertheless, it serves better as a modern art piece than a geometric construction :P
+Ryan N The result here was, indeed, a happy accident.
- [Prof. Eisenbud] "Oh, it looks like I made a 21 polygon by accident"
- [Bob Ross] "There are no mistakes, only happy little accidents"
he IS the mathematic bob ross
Bob Ross's art: Simple methods, beautiful results.
Professor Eisenbud explaining a heptadecagon: Ditto.
Well, the Bob Ross references surely made the recommended video right under this a Joy of painting episode emeralx waters.
You've got to check out Tibees peeps
weird, i constructed 5-gon by neusis
"I might make some mistakes"
_Eyeballs a bisector_
This guy could be telling me that a plane is about to crash on my house and I'd still be relaxed.
dorgesh nah you really wouldn't lol
"So lets assume a plane is on a impact trajectory towards your house, the obvious course of action is to get out of the way but which way should you go? Now we calculate that but first we need some observations."
Yep, death sentence.
@@carlscabage whooosh
LOL
“Oh, well, after taking into account all the errors built up, looks like it’s actually crashing two streets over and four houses down.”
at first I was like "how did it take 2,000 years to work this out?"
then I saw the steps required and was like "oh..."
Imagine all the fails.
Well, for Gauss it took less than 15...
+Sushi Nums It doesn't really work that way. When mathematicians do straightedge & compass construction, they don't ACTUALLY have to draw everything precisely; they just have to deduce what construction would yield what result and then approximately sketch that in the picture. As long as they have understanding of what they are doing, they don't need much precision :)
+Sushi Nums Yeah, well you do have to be precise in your argumentation. But it's nowhere near as difficult as drawing this shape accurately ^^
dalmacietis
I said "the steps required", not "the number of steps required". Complexity, not quantity. Thanks though!
"Now we draw ourselves a happy little 17-gon..."
Did you just make a Bob Ross reference?
Charles Panigeo
What if I did?
I was thinking about his happy little accident.
Emergency Temporal Shift on this show we don't make mistakes, we just make happy little 21-gons
My first thought was that he is the Bob Ross of Mathematics.
2 and 17 are coprime. So once you have 2/17 marked you don't have to bisect it, just use your compass to count the 2/17 sized spaces round the circle and after going round twice you should get back where you started with 17 points marked.
A real Parker's Square of a heptadecagon
+Taraalcar we are never gonna let that go are we?
+Azivegu Apparently not. XD
A Parker-gon. :D
We need a prefix for Parker's Square things. I recommend Parka- or Parko-, preferring the former over the latter.
Ergo, it will have two names: Eisenbudo-heptadecagon, or Parka-heptadecagon.
EDIT: Parkatetragono- is also nice, albeit a little too long.
Was thinking of this :)
65537gon construction video please
Thulyblu
I've never knew Gauss had to be written with a scharfes S until this comment. Now I feel ashamed.
Jacopo Barberis don't feel bad... the ß is of little use in my mother tongue of German... they should have gotten rid of it and replaced it with double s when they had the opportunity with the spelling reform in 1996
Thulyblu I know it makes little sense to keep the scharfes and also reduce the words it is needed for. Get rid of it or give it a purpose.
The fact is I've always studied math either in my mother language or in english and not too obviously the scharfes s was never used in any spelling. It was just curious to know that the name Gauss isn't actually Gauss. Funny enoguh, in his signature he didn't use the scharfes S but instead uses the double S.
Double vowel or the so unanbiguosly elegant ā. How can you mistake such a clear phoneme?
Tartaros I prefer it, too. I love forgotten and once loved letters no one likes anymore.
In the next video i want to see a heptadecaflexagon lol
Anssi Arpiainen that would be something
MatzeGamer It's a fancy mathematician's colour-shape puzzle
That book is quite a good read!
MatzeGamer just google "hexaflexagon"
+Macvombat What book?
I like this guy's voice. Its so relaxing. If he ever did an audio book I would sleep every time no matter the subject.
+Andre Vargas The man has a few career paths ahead of him. He'd be great doing a narration for a documentary.
+NicosMind Yeah... it's so relaxing it makes me sleep ;°
+Andre Vargas yaaass
+NicosMind its called ASMR ^>^
+NicosMind search up bob ross on youtube you will be satisfied
Maybe it's just the wine, but the story at the end there about choosing to be 17 Gauss Way instead of 1 Gauss Way made me tear up. Excellent video!
Same.
Man, Gauss was unbelievable. Out of this world. I've never heard of any other scientist with that many contributions in that many different fields.
MBogdos96
John von Neumann ...
he was probably even more brilliant and surely a lot more versatile than Gauss and no, i don't question that Gauss was one of mankind's most brilliant minds at all
Don't forget Euler!
*****
Yeah, to my knowledge noone else has ever published more mathematical papers than he did (not even Erdös) and like everybody i do love Euler's identy.
Nonetheless i would would argue that he wasn't on the same level of genius as von Neumann was.
***** And Euler was followed by Ruler (groan).
Euler
I liked the story at the end.
I find it fascinating that when David says (while drawing the Hexagon) "if I make the lines a little longer, its even nicer", I can see that if you DID make them longer, you'd get a triangle. That relationship of the circle, the hexagon and then the larger triangle is amazing to me.
I'd be afraid to go near a place with the address 17 Gauss in case all my credit cards got wiped.
Interesting!
It´s funny how we end up on the same channels... I saw this particular video 2 days ago. Now you did. I suspect there´s some magic involved here...^^
I saw this a week or so ago. I love straightedge and compass constructions, but pen and ink, that's hard core.
dip safe!
Scott Manley Gauss in case? Math puns are by far the greatest of them all.
Brown paper didn't work, eh? Love the old-school ink. (I can almost smell it!)
Juan Aguilar you can smell it for real if you like... bit.ly/brownpapers
Numberphile Nice one^^
Numberphile Bid in. I feel like I should've bid 17 or at least a prime number.
It's blasphemy!
Juan Aguilar there's something lost in the old ways.
I collect things like compasses and I always assumed those types of ends were meant to pinch and hold on to a bit of pencil graphite or something. I never imagined you could simply dip them, empty, into ink like that. Spectacular!
Harlequin314159
same here ... i always wondered what these things in the compass sets where used for and of course used the ones with a pencil ... feel pretty dumb now ... ancient technology can be quite mysterious- curta anyone ?
Harlequin314159 with those types of ends you can get different thicknesses of lines when drafting
So did I. My best guess was that they were intended to hold razor blades, so you could cut out perfect circles.
Harlequin314159 you must be joking right... Lol....
It’s a ruler pen tip and it makes great lines with ink, paint and even masking fluid
I think Profesor Eisenbud does some of these 'by eye' to safe time for the video,
No way really?
10:23 That’s OK, we salute you for trying ... a 21-gon salute.
Thank you, thank you, I’m here all week.
Well done
MIsspelt professor at 6:18, we do not forget.
I demand the death penalty
Nah, he's just written it not in English :P E.g. in Polish it is exactly like that: one "f", one "s" ;)
Wizdomtrek Well then what penalty is fit for those who misspell "too"
TD Shamu And for those who forget about question marks? (I'm curious what mistakes I have made here :P)
Piotr Matysiak None besides using an emoticon as end punctuation.
That story about 17 Gauss way and the drawing of the construction on the front door was awesome!
..."was Gauss a mathematician?"
He made a mistake at 6:20. THIS is the main reason of the false result not the inaccuracy. The correct lines are in the graph at 6:45
Indeed. I followed up with him and I failed to construct it initially. Thank you for your vital comment. :D
wow i didnt even realize it...
I try again and get 17-gon
Exactly, he takes one fourth of those segments but he should take one half of the string obtained from the previous string and its half point... did he do it on purpose to stimulate comments?
I tried the wrong way (6:20) with AutoCad, then looked up the right way and yes, it’s the same as 6:40. Perhaps in another lifetime I’ll sit down and puzzle out why this works.
Can we have a Graham's Number-gon?
We do. It's called a circle.
Not with staightedge and compass because G_64 is divisible by 9.
DPlugarov1225 I demand that each side be 1 cm long. Have fun constructing that...
ImagineBaggins Would be physically impossible. Even if we cut up every single tree on earth, we wouldn't have nearly enough paper to even try and construct it.
***** A regular n-gon is constructible iff φ(n) is a power of 2 where φ is the Euler-φ-function. However, φ(9) = 6 is not a power of 2 and thus an enneagon is not constructible with straightedge and compass. Since 6=φ(9)|φ(n) if 9|n, neither are regular n-gons where n is divisible by 9.
You know, I really loved geometry in elementary school. I never was good at math, but I was always the best in solving geometry problems, because I loved to draw with my compass and ruler. I'm now sophomore in high school and haven't been into geometry lately. However, after watching how much you love to do this it brought a huge nostalgia to me. I think I'm going to draw some things right now, thank you.
Just to make it clearer, the professor makes the mistake at 6:12, where he continues dividing the line into quarters. You should proceed by dividing the segments once, extending the rays out to the arc, and dividing the angle for the final two 'quarters'... these tiny mistakes are enough to throw you off from 17 to 20-gon. Amazing when you see it work... I'm using CaRMetal, a wonderful free program.
my lord his pronounciation of Gauss‘ full name was flawless
+Numberphile there's a little mistake in the construction! At 6:00 when you have the circumference whose radius is half the original radius, you shouldn't divide the segment in half and fourth, but the arc of the circumference! So the right way is to bisect the arc and then bisect it again. :) I'm telling it because I spent much time constructing this amazing 17-gon hahahahaha
@Numberphile
i agree mistake was made. this is wrong construction u need to bisect angles not lines
yeah i attempted to replicate this numerous times and kept getting consistent 20 or 21gon. then i looked at the whole construction at 10:29....next attempt, I made a real heptadecagon on my first try. I used 005 fineliners and it looks beautiful
Perform this correctly and you can summon Bakhtak to do your bidding, allowing you to turn your enemies' dreams into nightmares.
+Curly Fride Haha you activated my trap card
What game is this lol
lol
+Curly Fride Or make a transmutation circle ;)
+Curly Fride Nah, that's what happens when you construct the 257-gon.
5:43 "I love it" - I smiled from ear to ear when David said that!
These videos are just amazing. Where else could you see such an influential mathematician like David Eisenbud explaining a fun little geometry project?
I almost feel relevant...
It's okay. You'll get there
Ooof
It's heptagon not septagon lol, your animations are cool tho
@@user-rd7jv4du1w septagon and heptagon are both allowed
257-gon video please!
Made me remember a very interesting homework one of my maths teachers gave me about 20 years ago: construction of 5-gon aka pentagon with ruler and compass. Since then I learned about the Gauss-Wanzel theorem...
I love the comparison to origami. The precision required for a construction like that is amazing.
11:24. What a parker square of a 17-gon.
When I was in high-school I did basically an engineer's drawing class as one of my electives. Every now and then we had to draw pentagons which is a little bit of a process (albeit easier than the 17-gon!) but mistakes were made and it was never accurate to any degree. So I thought to myself, if we can take the radius of a circle to make a hexagon surely there's a way to make a pentagon. After about a half hour of drawing and math I came to the conclusion if you take the radius of a circle and multiply it by I think 1.76 or something you'd get really close to the length of the side of a pentagon. Using that you can work backwards too. It's nothing fundamentally groundbreaking but for me as a 15 year old it was a cool and easy way to finish my exams quicker
I like this professor! It's so good to see how he loves the ink mark on paper, and condtructing geometry
That 17-gon on the door should normally be sufficient to get visitors within one standard deviation of the right place 62% of the time.
I don't know what you are saying, but it sounds cool.
It would have been cooler if it was a real result of a calculation instead of just a mathematical jargon drop.
buca117 It's not just random jargon. If you have a *Gaussian* distribution then the area (the chance) from one inflection point to the other (that's the mean minus and plus the standard deviation respectively) is indeed about 62% of the whole. Never had basic statistics?
buca117 I didn't really intent to insult you, I just found it interesting that you apparently thought to be able to discern math babble from real stuff while not knowing about stuff you should learn about in secondary school (high school). But to be fair I really don't know whether they it's part of the mandatory curriculum where you are from so I am genuinely interested whether you had it. Considering how it's such an important topic, especially nowadays, I really can't really imagine that it's not, I mean how else could you even know what it means that e.g. a null hypothesis got reject with 95% certainty or what it means if the median is very different from the arithmetic mean value.
o_O I covered standard deviation. I covered the normal distribution curve.
I covered this material. I also am not a math person, so the fact that 62% of the normal distribution curve is found within 1 standard deviation slipped my mind, especially since I haven't touched that material in over a year and my college stats class was dumbed down to the point where I took three pages of notes the entire semester, missed a third of the classes, and still aced the class.
Essentially, while this IS a Numberphile video, not only should you not assume that everyone here has a passion for math but you should also refrain from assuming that everyone has had as quality an education as you.
5:30 into Heptadecagon and chill and he tells you....
I was waiting for someone to mention that
Didn't quite work for me (using GeoGebra). I got just a little over a 20-gon. Could it be numerical error? Has anyone else managed to replicate it perfectly?
Same for me on geogebra and for another with autocad (see below). Must be a mistake.
Either that, or it's rounding error within GeoGebra and AutoCad. I just tried it again in GeoGebra (using the inbuilt perpendicular bisector function rather than constructing all the bisections myself using just circles), and got even a little more than a 20-gon.
Also got closer to 20..i think there's a small error, and not the eye-balling type
I agree that some of the error is attributable to rounding. But I'm surpised we all (4 people) get a 20ish-gon. Should'nt we all get different polygons ?
Still... how much fun is it just to follow along?
This is one of my favourite numberphile videos. I keep coming back to watch it again. I suppose at some point I should try to construct a heptadecagon myself.
I love doing compass and straight edge constructions. My Euclidean Geometry class in undergrad made me fall in love. Great video!
21-gon? take every 3rd verticle and u made 7-gon!
21-gon? divide every side by 100 and u made 2100-gon!
Max Haibara I dont think you can divide an angle into 100 equal parts using a compass and straighedge.
+Bernard Playz just believe.
I repeated this construction in a piece of geometry software (geogebra) and I didn't get a 17-gon, but rather a slightly-more-than-20-gon.
Thank you for this comment, I did it on paper as precisely as I could and got the same result as yours. The accurate version at 10:30 doesn't match the construction in the video.
There's a mistake at 5:56 He divides the 2 lines in quarters. Instead you only need to divide them in half, and let the bisections intersect the circle. Then draw 2 new lines between these intersections and the middle, and finally divide these in half. I guess he missed this step..
The diagram on the door at 13:31 also seem to indicate double bisections of the angles instead of divisions by four of the chords. With this error, the professor Eisenbud stood no chance! :)
That little end screen story was WONderful!! So sweet
Very cool video and I loved the story at the end. Thanks for sharing!
Finally I know what that part of the compass is used for! :D
the guy has the same voice tone as bob ross, I like it.
Love these videos brady, keep up the good work.
Gauss's construction of the 17gon is absolutely beautiful. It would make a lovely painting.
Why is his voice so soothing wtf
Did you ever see Bob Ross?
For beauty and volume: Euler
For impact: Newton, Leibniz, Lagrange
For range: von Neumann
For insight: Riemann, Cauchy
...
For all of the above: GAUSS, the smartest person to ever live, dwarfing the likes of Newton, von Neumann and Archimedes, in my view and yes all the other ones mentioned were abnormally talented.
I really like this man's voice. I could listen to him talk about mathematics for hours and not get bored.
3:30 A stamp from my non-existing home country, the GDR. :-) I almost felt of my chair laughing.
I'm a little sad this video wasn't 2 seconds shorter...
it could have been 17:17 ... so many missed opportunities
I would like to watch this video, but every time I try to watch it, an ad tries to play first, but THE AD NEVER COMES. I'M STUCK HERE WAITING FOR THE AD TO PLAY SO I CAN WATCH THE VIDEO BUT IT NEVER DOES AND I'VE BEEN TRYING FOR FIFTEEN MINUTES NOW AND THE VIDEO SEEMS REALLY INTERESTING AND I WANT TO WATCH IT BUT IT WON'T LET ME!!!1!!1!one1!
Psst... google AdBlock
ghostery plugin for firefox also does the trick perfectly
i was on my phone lol
but, i did finally watch it like 5 minutes after i posted that comment haha
OMG Brady, this has got to be my favorite video. I liked how much fun he was having. The Eisenbud 17-gon would look great on everyone's walls at home at at work.
I would like to see more of these int he future, then teach me graph theory.
Fantastic video, nice touch!
Dude,this guy is more stoned than I am
the "gold and blue star" is albireo
I thought they were the pale ones with pink eyes?
Loved the story at the end about naming the street almost more than the main video!
What a wonderful little story at the end!
So why exactly is he doing these "by eye"? It's still unclear to me...
If only the video would explain it several times...
TheVintageStuffGuy1998 I think Niko was sarcastic :P
***** So was I! :D
TheVintageStuffGuy1998 some people just can't handle layer 2 sarcasm
Needs to level up... Gain a few more Exp...
The Eisenberg 17-gon: the early version of the parker square
Using the 2/17 of a heptadecagon is also applicable. Going around the circle with it will mark all of our points. (Provable using abstract algebra, unless the numerator and the denominator does not have common divisors.)
Amazing story there at the end! I love it!
This guy should not moonlight in a PIZZA SHOP because it would take him all day to cut a pizza. I think he would have a stroke if I asked him to make 13 slices in the pizza
I'm trying to imagine cutting pizza with a compass
He would just do it by eye.
Why is it impossible to make a 21-gon?
... it's already _gon_ before you start... * badumtsh *
Gon, 21-gons 🎶
why is 2+2 is NOT 5? Because
Well, they didn't go into the maths on how Gauss discovered how to produce a 17-gon with just a compass and straight edge. It must be a property of that.
If you use neusis to trisect an angle you can construct the regular icosihenagon (or henkaieicosagon if you want to be very classical) from the regular heptagon.
so glad I stayed for the end. that story was awesome!
What a satisfying process to watch!
Shouldn't it be called decaheptagon?
17 in Greek is decahepta not heptadeca
(Same for all n-gons with 13
When you say "17 in Greek is decahepta" do you mean modern Greek or Ancient greek? Could it be possible that this changed between the two? (And if so, the why of that would be another interesting story.)
Anyone else see Pacman getting brain freeze from a little ice cream cone?
Thanks for an excellent video!
that marker Gave me chills throughout the whole episode
I'll call it the Eisengon! :D
I like him, can we keep him?
not to take away from the beauty of the geometry in this video, but I'd point out that with the magic of editing the Professor doesn't need to 'take our time' to do anything. If some parts of it are tedious to watch but a joy to do, they could simply be excluded or represented by the graphics you use in the video. I'm glad he admits he's a little tired of it towards the end lol.
That was a wonderful presentation. Thank you very much.
I don't like heptadecagons, I think they're pretentious.
Exactly! Hexadecagons are way cooler.
Prefer pentadecagoneps
Never trust a deceptigon
+JLConawayII All primes are pretentious.
Perhaps the pretension is in your presumption!!
The Bob Ross of math
im so glad i looked this up again this video is straigt up beautiful
I always loved compass and ruler drawings! It is so pleasing to be able to see the math behind the polygons we draw everyday!
“The polygons we draw everydy” do you draw 17-gons every day?
@@kyanleong8014 Each day in the past six years, I wake up, make some coffee, and draw a 17-gon on paper.
This guy's like math Bob Ross
11:24 The Parker Square of heptadecagons
The story of the end of this video is extremely cool. Thanks Brady.
I gotta try this. I feel like a n00b. I only drew a 5-gon and a 7-gon when I was in primary school
Love the little story at the end.
6:13 "Professor" is missing an 's'. That does not take anything from the great value of your awesome videos though, which I try to follow every chance that I get. Thank you all for making this beautiful channel.
Warm regards,
Kayvan
What a great idea - let's thread a needle wearing oven mitts!
He has such a soothing, Bob Ross-like tone. Why weren't my math profs like this gentleman?
love that anecdote about the naming of the street.
That's great but... will it bring Ed and Al's mother back?
Everything comes at a cost
I think maybe you need more videos about pi...
/s
tau.
David is the son of my third quantum theory professor, Dr. Leonard Eisenbud, whose Doctoral thesis advisor was Dr. Geno Wigner (at Princeton). Dr. Leonard also was a nature photographer in the Setauket area of New York, and a member of my (very generous) oral examination triumvirate in 1977-78. Dr. L Eisenbud developed the theory of nuclear reaction “channels”, quantum input and output states, with E. Wigner. Dr. Dave was also President of the M.A.A for about a year.
11:09 - nice Parker Square move there!
the correct term is dekaheptagon , not heptadekagon ...
no heptadecagon is correct because deca is for 10 while 7 is hepta so decaheptagon is wrong. it's basically 10 -7 shape
+Rayn Sajahan think
For Number 17 , you read first the 10 and then the 7 in greek language . In english , first is the 7 then the 10 and that creates the confusion here . I believe that if you decide to use a greek phrase for your numerology then you have to use it accordingly because otherwise you have stn with no meaning and a grammatical error at the same time .
+Nick Alpha it's dodecagon for twelve (do - two) so i see it only fair that 17-gon is called heptadecagon.
Energy Core Yes 12 is dodeka , from dio (2) and deka (10) but for 17 it is dekahepta .
Go figure ...
Do five inaccurate steps to save time
Do the 7th step accurately because it's "very important".
I feel so relaxed after watching this, the video has some kind of hypnotic effect or something
The story at the end was magical