Ok

You still around? Whats the name of this program? Nice work. I'm very impressed.

@@chrisbova9686 These frames have been individually created by old programs I wrote myself - so ancient they used screen 12, so can't run any more.

@@aldoaldoz Im looking to have someone help me do just that, create a program that intersects different radii. Have you continued to do more with geometry?

@@aldoaldoz hey how to make the 17-gon (heptadecagon) it was like humanly impossible

infinity is 5 minutes! .-.

casually skips 9 and 11

and 13 and 14

+ Gabriel Davis Well then, he also skipped 7, didn't he? OK, he doesn't come out and say so, but what he's covering are all the regular polygons that are *constructible* by classical methods (straightedge & compass) - up to n=51, anyway. The next one would have been 60, then 64, 68, 80, 85, 96, ... The rule for generating these possible n's is: n = {2ᵏ (for k=1, 2, ...) or 3 or 5 or 17 or 257 or 65,537} or any product of two or more of these factors - repeated *odd* factors not allowed (2ᵏ, when k > 1, is a repeated "2," but *is* allowed). So the outcasts from that list are {7, 9, 11, 13, 14, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 35, 36, ...} In case you're wondering where the (odd) numbers in that list of factors come from, they are what are known as Fermat Primes (see Wikipedia for a nice treatment of these), which are all numbers of the form F[k] = 2^(2ᵏ) + 1 that are prime. F[0] = 2¹ + 1 = 3 (P) F[1] = 2² + 1 = 5 (P) F[2] = 2⁴ + 1 = 17 (P) F[3] = 2⁸ + 1 = 257 (P) F[4] = 2¹⁶ + 1 = 65,537 (P) and above this point, all of them are either known to be composite, or are too big to determine whether they are. F[5] through F[11] are all known composite, as are several larger ones. F[5] = 2³² + 1 = 4,294,967,297 = 641·6,700,417 F[6] = 2⁶⁴ + 1 = 18,446,744,073,709,551,617 = 274,177·67,280,421,310,721 F[7] = 2¹²⁸ + 1 = forget it!

I love geometry

Yes, that's a heptadecagon. The rule for constructibility involves the Fermat primes, which are of the form 2^(2ᵏ) + 1 when that's a prime. The only such numbers currently known to be prime are when k = 0, 1, 2, 3, 4: {3, 5, 17, 257, 65,537} [Curiously, you can also get 2 if you're willing to set k = -∞.] If you think *that's* insane, check out the construction of the 257-gon! And, yes, there was a guy who spent ("wasted" according to the writer of the piece I read about this) 10+ years of his life composing the construction of the 65,537-gon!!!

ffggddss lol Obviously he was insane and probably in even worse mental condition after he finished.

Where can we find that article?

@@ffggddss Yeah no one cares

@@iCore7Gaming stop projecting your pathetic ignorance onto everyone

It was Gauss but he's dead now

You can always kick his corpse.

@@theviniso calm down there Satan

@@theviniso talk about beating a dead gauss

@@joeyhardin5903 most underrated mathematician/intellectual ever. People talk all the times about Einstein and Newton, a few people talk about Leibnitz, and Euler but in my opinion Gauss was the true mad-man.

I’m reply

Who's mama?

MaThS aRe EaZy!

Can't believe how gauss managed to pull that off

Yay, Gauss

L Martinson And at 2:37, we shall create an eye.

And just a previous video I saw was about the most liked post on internet which is an egg 🥚 🤔 🤔🤔🤔🤔🤔 ⚠️🔼👁‍🗨 Is it .. is it eggminati?

Our egg will fully bloom starting at 3:09

2:15 don't forget the bird that layed the egg.

PRESHOT COMMENT FAM !

A line with exact length for this to work.

That line was a work of Gauss...

A very precise line

A curvy line

Ze D

Come on Euler, out of all people, you must be able to understand.

Sit around with a pen paper a compass and a circle and think. Now go my child and find another infinite! There's infinite more to find!

@@brienmaybe.4415 *draws a circle* I HAVE MADE INFINITEGON!!!

Reverse engineering maybe

@@theM4R4T no haha

11 feels the same way about it

Theres also the ducking 256-gon and 65537-gon

There is a proximation method credited to Albrecht Dürer you can find online

7, the number which ruins geometry in every way possible

The way you suggest gives a perfect construction too - but it liked to draw a square with the sides parallel to the axes.

In that case, just bisect one of the 90-degree angles to get a 45-degree diagonal. That locates one of the vertices of the square you want. You already have the side-length. Alternatively, turn the paper 45 degrees.

@@rosiefay7283 That's exactly what the video did. It bisected the upper right angle first and the rest followed. In order to bisect accurately you'd need to do what it did.

Though the octagon was off-axis? Wow

Because this is only the polygons that can be drawn with a line segment and a compass

@DRAGEN RAID eh it was a weak r/woooosh

@@kirbs0001 well you can split all of them into more and more halfs so yk

@@fensti7917 non-trivial polygons, i guess

Technically yes, it would be more practical in reality but the the method shown flr 5 is the one with the least amount of steps

Underrated

most underrated comment I've ever seen

Well y'know. You can just draw a circle.

The more the sides the more negligable is the difference from the polygon to a circle so there's really no point unless you have a paper the size of a building :/

Fair enough, but these constructions were never studied because they were useful (we'd use a protractor then). People studied them because they were mathematically interesting, and the breakthrough that proved the constructibility of the 257- and 65537-gons also laid the ground for huge advancements in algebra - ultimately leading to proofs of the unsolvability of the quintic polynomial and the three-body problem.

Danny Are those the only two provably constructable polygons that large?

Thomas Jones *that aren't just trivial 2^n-tuples of other polygons

I hate when it happens

how

7: commons.m.wikimedia.org/wiki/File:Approximated_Heptagon_Inscribed_in_a_Circle.gif 9: commons.m.wikimedia.org/wiki/File:Approximated_Nonagon_Inscribed_in_a_Circle.gif 11: commons.m.wikimedia.org/wiki/File:Approximated_Hendecagon_Inscribed_in_a_Circle.gif 13: commons.m.wikimedia.org/wiki/File:Approximated_Tridecagon_Inscribed_in_a_Circle.gif

If you read above, you will see those are approximated. It's actually IMPOSSIBLE to construct a regular 7, 9, 11, 13-gon using a straight edge and compass.

Scott Wallace 65537 gon is constructible as it is a fermat prime. Search for it (Especially Numberphile.)

Wow, very cool. Thanks, Bernard! One reason I asked is that I do polymetric music, and 17 is one of my main rhythms. Check it out if you're interested- soundcloud.com/scott-wallace-189088488/lydia-ventures-into-the-jungle Cheers from cold Vienna, Scott

I think someone found the method for 257 but I don’t think the method for the 6553$ is known lel

Is a Heptadecagon

@@TunaBear64 ok what is the term for a 2d shape with 97 sides? Also is there a system by which I can correctly name any number of sides without a lot of memorization?

I just google circle.jpng

I also was puzzled about that radius, the first time I watched this construction. Well, it can be... any radius, because the related arc is needed only to determine angles (nothing about distances).

i believe the problem is "divide a segment in 7 parts"

There is a way to divide a segment with a strait edge and compass. I learned it in geometry class, it involves copying angles.

@@kat-oh3hx Phales' theorem, as we call it in Russia, could do.

Who hás 17 friends?

Tim M Random length

I worked also on 257 and 65537 regular sides polygons, which in theory can be constructed with a strightedge and a compass. I did also some tries with all the regular polugons up to 20-gon. You can find all of them in this italian page of wikipedia, where the linked animated gifs are all my works: it.wikipedia.org/wiki/Poligono_regolare#Tabella_riepilogativa

+Andrew Becker only five Fermet Primes are known. To date, no one has been able to find a sixth one, or prove that a sixth one cannot exist.

Yes, exactly.

The arc at 2:39 can be drawn whatever radius you want, as it is only needed to define some angles (not lengths).

aldoaldoz Good afternoon and thank you for your reply. After reading your helpful reply I tried to draw the heptadecagon again step by step and managed to get far as drawing the 'egg' at 3:05. However when it came to constructing the segments (3:05 onwards) my sheet of paper just became a total mess and everything got muddled. I don't know how the Ancient Greek mathematicians pulled it off!

Well, this drawing method is not so ancient! It cames after Gauss: he (at the age of 17!) understood some polygons could be drawn in addition to the classic series of polygons, those with an odd number of sides (triangle, pentagon, 15-gon). The "new entries" were 17-gon, 257-gon and 65537-gon. Look at wikipedia: you'll find many explanations, as well as my own animated gifs.

This circle is needed only to determine some angles, no distances. So it can be drawn any radius

P99AT If you do it in a small book it seemed is but it's not because if it is it will make a 16 gon

That circle can be any radius, as it is needed only to deterine an angle

The only possible constructible polygons have sides of Fermat primes (and their multiples). It's great look it up anw, it follows 1,2,3,5,17, etc