"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.
+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 :)
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.
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.
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.
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
***** 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.
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.
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 ?
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.
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?
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.
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 ?
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.
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
+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
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
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! :)
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.
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.
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.
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
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...
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.)
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!
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.
These videos are just amazing. Where else could you see such an influential mathematician like David Eisenbud explaining a fun little geometry project?
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.)
When I was a kid, my favorite number was 17. I couldn't explain why, but whenever I picked a "random" number, it was almost always 17. It was also my student number at least once. I am Gauss reincarnated: confirmed.
Omg I can make a perfect 17gon in my game euclidea. Update: I tried and failed ! It is possible but I'm lazy. Sorry Update: he made a mistake at 6.20 and I done it using the diagram at 6.45. Yipeeee!
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 .
Sees the thumbnail affter watching Great Big Story's Why the World’s Best Mathematicians Are Hoarding Chalk: Oh! It's one of the Hagoromo Chalk people! He really has a soothing voice. Wish I had this guy as my math professor!
Ρε μάγκες γιατί το λέτε 'επταδεκάγωνο'? Δεκαεπτάγωνο ή δεκαεφτάγωνο είναι το σωστό. Decaheptagonon should be the correct name. Νow, try that with 23 angles, the next prime, εικοσιτριάγωνο..
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
7th Grade, Math Club, Tully New York, 1972. "You can't construct a regular 5 sided polygon." Period. I said "That can't be" and started trying to figure it out on my own. I tried on and off for years. Last night I watched this video "... we know how to construct a 5-sided polygon..." Wait, What??? I agonized over it until tonight when I had to do it. I turned to Google. Yes, of course, it had to be a Satanist with tattoos and everything, but there it was. Easy as pie (pi?). Never believe "can't." Never give up.
Bad news everyone , i am using a very accurate sketching program... and this solution is wrong, it dose not work when you play it out with 0 tolerance for error... i tried it 3 times, sorry.
+mohadish1 Me too! Got a 20-21 gon. Followed his instructions to the letter using GeoGebra! Checked, double checked, triple checked! He made a mistake somewhere. Looks like the etching on the door is wrong too! Ooops!!! Where was his mistake? Please someone help!!!
Actually there is a mistake! I know it can be done, it has been mathematically proven by Gauss, but I'm saying this demonstration has a mistake somewhere. Several people have arrived at the same incorrect construction.
+Rick Skinner If you follow his demonstration mathematically you will see that it does indeed work if it is constructed perfectly. The angle between the first angled line and the diameter of the main circle can be calculated as tan^-1(.25) for example or 14.036 degrees.
odd numbers are hard to work with, but interesting when you find the trick, multiplication helps, here a example, if you want to make a 15 pointed star, you would draw a 5 star and divide it 2 more times, 3x5=15, you could start with a triangle also, coz 5x3=15 also, which makes a triangle and a pentagon appear in the same polygon or polygram
One day I'm going to create a book about this and I'll make sure to clean up all the unnecessary parts and explain why this is the way it is on behalf of the Bob Ross of math
Why does he feel the need to bisect the 2/17ths of the radius? 2 is a generator in the group 'addition mod 17', and thus using that length as a generator should suffice.
Pretty cool. I figured that you don't have to bisect the line that is 2/17 of the circle. Just use your compass with that width and go around the circle twice!
10:20 I don't know why you think a 21-gon is an impossibility. I can absolutely assure you that 21-sided, 2-dimensional regular shapes do, indeed, exist.
