It Took 2137 Years to Solve This

COMMON COMMENTS AND CORRECTIONS! 1. At 44:30 I say: "the next one is 257 which is one more than 256, 2^7" but of course 256 is 2^8. Terrible mistake on my part! 2. A few have asked whether I should be saying "primes of the form 2^(2^m)+1" when discussing Gauss's method. This is right but I deliberately omitted this to address it in the sequel -- I say that the method works on primes of the form 2^m+1 which is correct, it just happens that m must be a power of 2 for it to be prime. 3. 41:39 alpha_2 is incorrect: the coefficient of root(17) should be negative. 4. Regarding "transferring lengths" because the compass is supposed to "collapse" when picked up: Euclid proves (Book 1 Proposition 2) that you can move a line segment wherever you want. Originally I was going to show this, but I cut it to avoid an awkward complication so early in the video. It's proved so early in Elements that a collapsing compass can be treated as a non-collapsing one that it isn't worth worrying about! 5. Regarding the 15-gon, many have pointed out that since 2/5-1/3=1/15 we can just draw that arc and we're done. All who point this out are correct but I was presenting Euclid's proof. Like I said about the square, there are easier ways but that's how Euclid does it! 6. Regarding "2137": My patrons and I had no idea about the meme in Poland when we named the video! It's a fun coincidence -- the number comes from Elements being written ~300BCE and Wantzel publishing his paper in 1837. Obviously only an estimate as we don't know exactly when Elements was written!

2137 is a very special number indeed

It surprised me how long that problem took to solve, didn't realize you were THAT old

So many Poles in chat, it's like the ℘-function up in here.

Ah yes, 2137. Number of the beast.

Imagine my disappointment when I clicked on the video an realised the 2137 number was chosen just randomly, without acknowledging it's holiness

JPII Moment

I'm imagining Euler going back in time and explaining complex numbers to Euclid and only hearing "wow, I never thought about it this way, this is so wrong yet so intuitive"

John Paul II joined the chat

Jan Papież mentioned!!!

Watching this at 21:37

I didn't expected the Pope Number in non-polish video

Another Roof has managed to harness the power of polish memes to bring in more people to learn about math.

jan paweł drugi konstruował małe wielokąty

16:34 funny to me that diophantus accepted that rational numbers exist, and we use his name to refer to equations with integer solutions.

You should play "barka" as background music and eat kremówki

Pan kiedyś stanął nad brzegiem Szukał ludzi gotowych pójść za Nim By łowić serca słów Bożych prawdą O Panie, to Ty na mnie spojrzałeś Twoje usta dziś wyrzekły me imię Swoją barkę pozostawiam na brzegu Razem z Tobą nowy zacznę dziś łów Jestem ubogim człowiekiem Moim skarbem są ręce gotowe Do pracy z Tobą i czyste serce O Panie, to Ty na mnie spojrzałeś Twoje usta dziś wyrzekły me imię Swoją barkę pozostawiam na brzegu Razem z Tobą nowy zacznę dziś łów Dziś wyjedziemy już razem Łowić serca na morzach dusz ludzkich Twej prawdy siecią i słowem życia O Panie, to Ty na mnie spojrzałeś Twoje usta dziś wyrzekły me imię Swoją barkę pozostawiam na brzegu Razem z Tobą nowy zacznę dziś łów

46:41 "You may now perform a poly-gone" that pun coming back at the end cracked me up

toż to papieska liczba!

Only 12K views for a video with this quality of content is outrageous, great work.