Maths Paths || Big Internet Math Off

Big Internet Maths Off! aperiodical.co...
All the pitches so far have been so well thought through and awesome, do check them out!
But if you'd like to vote for something a little more chaotic then my round will go live at 8am on the 6th July :)
Me on Patreon, one day I will post something there / ayliean
Stay nerdy, stay awesome, enjoy this video whilst its up cos it genuinely was a half hour edit and I might take it down.
Felt nerdy, might delete later ;)

[@cooluisdean]

LIKE THIS COMMENT IF AYLIEAN IS COOL

[@Ayliean]

Thanks bro! Self like 😏

[@bretscofield]

I like you just casually mentioning you were spending time thinking about the platonic solids.

[@davidsteinhour5562]

Happy birthday! I platonically solidly love you! And as an American and aspiring emigrant, I thoroughly enjoyed voting for you over an almost -as-good second option! 😉

[@trucy1337]

Happy birthday to the most colorful mathematician of all :D

[@lightninbolt986]

Happy birthdayyyy to one of my favourite maths communicators out there!!! I hope you have a great day

[@akaelalias4478]

+

[@Chewxy]

Eulerian paths are interesting and all, but how are you freehanding 33×33 grids on white paper and still getting straight(ish) lines.

[@Ayliean]

Oh, that is not a skill I have! There are little grid dots :) I should try a fully freehand one on one of the days though!

[@emilyyyylime-]

​@@AylieanDo note that thanks to the nature of powers of two all you need to do is draw lines in the centre between two previous lines and you'll end up with 32 equal width segments

[@Nazgul3001]

6:47 did not expect such a splendid political joke! Happy Birthday

[@stiofanmacamhalghaidhau765]

there was (probably) another a few seconds earlier too

[@JellyMonster1]

Hooray it's Ayliean! Those fence posts, ha. I might vote for you but will have to see what the 'others' are like first. Good luck.

[@Ayliean]

Yes, informed voters ftw! The other piece of Maths is a very nice classic, and thoroughly explained - so I think it’ll be a tight margin!

[@JellyMonster1]

@@Ayliean Seriously, making an octahedron with a balloon wins on the spot.

[@sampert2010]

I missed the chance to vote, but my heart is full watching your video and seeing you did a win!

[@homeopathicfossil-fuels4789]

32? Its a 2^X number, and thus one of my countless favourite numbers. Congrats on still being one of my favorite numbers! Also you are already one of my favorite youtubers because every video you do is a healing moment to counter how most women in my local community squick out at any mention of math.. As if I lose my girl card from ever dealing with anything math. But here you are making math cool and girly

[@MatSmithLondon]

You're an inspiration, even to little old not-that-mathsy me.

[@Blindastronomer]

Happy Birthday Ayliean! :D

[@Ayliean]

Thank you! You're about a month early but I will keep it in the birthday wishes bank. I still have quite a few more grids to draw :)

[@user-gd9fq7od8u]

​@Ayliean Is there any way to reach you aside from youtube comments? I found your channel a couple months back and have been fascinated by you since! Keep posting videos and ill keep watching!

[@rotflmaopmpqxyz]

So there’s 33 * 31 vertical lines, and 31* 33 horizontal lines, so there’s 2046 total lines. So the total number of ways to draw should be 2046!, or 2046! * 2^2046 if you consider that each segment can be drawn in one of two directions

[@nahla_nee]

I'm so glad I've found your channel! This was a really cool video, it got me to start thinking about a puzzle that I abandoned a while ago (trying to write a program to find the longest path in a word ladder game for N letter words in a somewhat reasonable amount of time) so thank you! Also sorry it's hard for me to hear the name of the author(s?) you were talking about at 5:25 would you mind sharing the paper's title and authors name? P.S. i love your nails! what do they say? I can make out the first two words but the third is a bit blurry.

[@Ayliean]

Ooooh I play a daily word ladder game, but where you’re trying to get there in the shortest time! The paper is by Demaine & Hart and if you follow the link in the description it’s there. The nails say F* THE TORIES! I was trying to use my other hand as much as possible to keep them out of shot, but I stand by what I said.

[@nahla_nee]

@@Ayliean Oh cool, that'd be a fun variation to solve as well. I'll have to give it a shot myself, thanks for sharing! I scrolled past your section when I checked out the website cause I thought it would be just your video, but it seems that the link is in fact there and there's a bonus video! I'll be sure to check both out ^-^ And hell yeah, f the tories!!! I understand why you'd want to keep it out of the shot, but I'm right there with you on that :]

[@makaiev]

Who knew math had baloons... gues you learn something new every now and then

[@OneTrueBadShoe]

I love your videos and you. I'll definitely vote for you. I got distracted, though, by something. Do you think platonic solids are aromantic? I just joined your patreon, too!

[@quillclock]

hair and nails on point. i thought those were sheets of acid XD

voted ☺️

[@likebot.]

Schlegel loves solidses. My Platonic solidses

[@stiofanmacamhalghaidhau765]

congrats on winning this round!

[@willemvandebeek]

Happy birthday! :) And first!

[@Ayliean]

Thanks you very much for the premature birthday wishes (and always being first!) but strap in because we still have another month of drawing this 32x32 grid to goooo!

[@willemvandebeek]

@@Ayliean oops, I seem to have triggered a wave of premature birthday wishes in the comments. Sorry for that and sorry for always being first... have I always been really first? I don't mean to be creepy that way, I just want to support you via the KZbin algorithm as much as possible. :)

[@Ayliean]

Voting is now live for the next 24 hours! If you liked this video, consider voting for it in the Big Internet Math Off :) 💗✨ You just click a button, no logging in or anything like that! aperiodical.com/2024/07/the-big-internet-math-off-2024-round-1-match-6/

[@taylormanning2709]

Once I heard the problem I wanted to take a stab at it before listening to your solution: Assuming any segment (side of a square) can be drawn at any time, there are 2112! ways, 38,463,989,151,604,811,720,760,881,743,776,208,704,072,164,595,104,073,343,251,640,236,255,483,071,536,829,336,768,844,768,154,335,415,648,499,893,752,720,243,142,574,901,572,646,547,162,851,018,721,239,048,473,420,139,533,582,736,665,885,515,697,046,887,297,757,221,251,579,075,317,848,458,269,881,646,720,059,557,673,791,787,824,402,648,359,781,187,155,552,330,573,506,815,107,664,091,869,096,263,724,644,215,099,101,947,314,231,160,307,783,294,688,355,827,138,563,463,723,848,002,303,259,058,476,378,463,587,770,056,534,639,089,715,112,345,467,528,746,568,905,063,209,204,477,568,932,244,454,296,400,245,853,998,388,885,837,853,148,527,833,637,532,217,670,538,805,843,698,075,083,755,692,469,089,151,017,233,311,765,513,234,790,868,886,762,506,109,067,123,584,882,061,806,875,303,032,398,512,552,932,019,085,515,179,619,574,719,434,367,631,342,108,762,055,337,532,531,818,358,629,743,521,362,631,902,451,779,202,567,665,053,888,273,122,769,892,565,948,740,312,222,763,129,107,082,898,959,280,812,556,225,209,108,374,921,684,851,822,869,414,451,107,733,299,332,522,949,512,761,968,725,474,087,178,956,043,709,194,092,513,463,587,322,310,710,216,563,595,590,909,835,762,685,668,178,403,386,418,128,561,238,665,642,802,011,091,511,988,020,752,382,696,353,366,690,243,915,350,676,883,780,972,205,110,236,026,419,379,286,007,780,836,344,407,365,567,374,603,989,573,273,540,128,350,983,438,360,259,670,245,023,454,625,401,326,404,105,837,448,355,962,716,468,337,814,594,901,484,776,847,737,955,310,096,432,833,612,829,981,316,554,162,005,079,802,154,804,415,855,447,962,906,111,199,157,173,176,437,444,594,947,130,813,220,335,273,091,393,358,061,386,680,243,326,206,204,609,800,816,669,805,402,016,288,139,753,247,158,710,705,802,001,281,993,929,337,028,430,445,996,971,710,638,992,966,378,626,794,595,003,761,036,002,794,988,272,297,154,297,118,268,599,525,405,501,092,660,604,763,506,040,171,072,189,469,489,424,300,948,093,091,916,987,970,617,608,849,509,092,327,519,987,045,848,899,688,646,242,048,780,785,850,675,371,341,646,266,170,904,457,252,300,637,878,373,221,875,259,888,692,952,592,037,627,097,576,376,656,163,473,069,638,587,058,549,693,094,045,105,512,490,623,026,722,007,641,993,403,785,143,025,678,353,980,335,863,258,235,701,238,860,031,584,602,255,782,785,908,081,906,648,844,834,258,854,169,027,389,050,107,132,319,289,123,680,908,860,608,267,747,416,758,070,156,198,480,828,437,065,528,073,604,013,037,034,141,019,057,812,963,642,483,381,857,001,485,588,328,893,802,290,174,324,441,356,582,047,729,681,992,046,882,457,150,396,898,408,137,306,599,309,617,096,754,224,722,475,541,399,414,662,409,169,240,551,752,871,890,762,147,422,712,700,372,614,110,735,030,182,199,142,268,158,461,905,407,387,887,004,812,873,958,799,064,953,703,688,894,220,545,569,871,898,088,942,439,093,381,555,461,123,208,231,516,490,310,255,248,226,557,400,929,759,899,381,193,314,527,245,294,452,678,433,974,388,364,302,747,862,760,118,071,122,932,840,960,231,550,685,787,132,118,167,405,371,971,528,425,294,856,952,769,632,856,312,308,461,450,592,741,695,914,007,242,404,858,210,106,034,463,290,040,608,668,467,709,279,877,881,248,401,355,662,731,017,747,246,605,297,764,827,858,252,356,721,045,936,057,725,126,873,427,587,235,498,224,272,862,027,558,247,671,814,213,420,931,687,139,448,809,539,622,474,404,718,743,648,721,413,850,977,035,508,182,357,915,416,938,240,407,511,424,536,527,533,863,050,201,843,046,845,077,439,761,432,619,072,832,628,464,850,147,445,844,250,139,181,598,243,848,502,985,974,403,562,279,152,046,240,178,970,111,383,552,689,099,007,909,641,229,142,408,094,213,801,963,741,107,166,195,974,292,878,998,231,242,475,500,452,858,506,158,717,560,334,071,597,896,375,430,780,283,286,182,594,901,826,652,490,963,543,106,288,825,349,283,227,919,550,821,961,844,748,084,320,763,599,061,581,463,137,807,493,804,414,463,204,663,430,570,613,849,372,982,866,097,450,233,637,291,865,267,689,842,687,173,644,284,750,554,837,920,890,954,711,805,323,713,234,325,932,177,503,318,899,644,756,158,328,284,659,910,912,052,684,152,286,499,269,496,384,719,711,758,876,979,620,834,750,333,120,690,192,696,337,038,250,794,647,513,746,393,476,733,403,334,399,466,796,993,808,112,919,701,154,143,310,625,864,832,170,329,410,301,763,747,404,420,545,306,789,888,470,113,420,878,599,926,552,228,189,074,223,219,166,470,685,556,372,953,935,218,743,684,850,656,471,144,898,373,187,308,153,831,533,185,634,964,980,069,169,282,637,925,475,388,654,157,833,470,208,051,423,911,346,410,605,127,771,563,073,816,415,169,960,378,236,668,259,957,889,187,138,792,528,060,272,565,956,351,246,366,096,860,929,039,777,947,278,659,621,674,556,819,046,343,387,022,576,173,237,347,500,788,616,842,563,734,978,869,776,250,089,432,607,702,496,001,205,500,170,718,860,720,067,073,266,037,403,298,532,545,311,635,705,842,141,594,977,706,424,494,046,212,935,625,134,526,852,722,000,433,871,346,781,910,290,949,425,249,927,520,845,658,158,044,198,603,072,933,498,078,094,863,095,291,780,672,323,463,093,460,771,538,212,090,758,020,045,889,892,060,018,016,556,143,750,689,989,260,079,635,366,127,221,245,399,867,403,744,201,348,512,186,489,690,910,315,221,487,004,285,182,604,009,350,708,486,749,053,988,073,183,085,701,258,090,293,619,053,033,551,371,863,260,735,266,586,363,662,670,846,745,204,774,204,467,089,733,599,646,188,360,626,651,562,818,418,805,831,049,478,912,013,756,260,371,638,754,555,398,673,970,237,442,732,338,527,347,838,082,999,310,614,897,648,789,252,022,226,977,282,898,769,384,673,946,489,211,403,831,988,079,702,532,072,449,064,731,502,688,123,472,759,556,188,093,806,305,918,217,460,239,256,888,663,678,819,321,655,846,376,437,718,327,603,678,460,675,903,107,665,809,070,053,857,400,645,536,796,693,500,342,068,740,694,789,830,988,194,780,757,043,738,697,942,307,515,923,578,577,071,822,506,992,132,471,059,646,387,632,803,536,785,490,601,467,934,220,194,824,225,798,825,656,244,711,436,292,072,296,629,960,807,209,309,015,241,294,444,904,936,237,440,877,302,424,944,277,307,164,887,079,759,964,101,178,038,860,969,709,917,935,937,131,604,477,767,182,024,786,379,334,293,179,147,020,091,128,957,529,219,117,388,661,725,369,873,210,024,473,302,692,690,965,608,009,484,047,580,231,268,287,832,002,538,377,450,179,791,370,734,038,934,370,760,716,546,846,180,158,356,212,757,800,465,460,953,481,835,353,859,623,612,460,463,788,539,392,334,980,717,157,227,768,939,205,593,464,324,675,437,806,134,368,007,150,929,856,117,812,742,227,772,817,865,890,271,831,452,324,839,997,200,801,297,283,591,235,980,398,846,846,059,830,769,246,343,338,714,844,097,619,785,673,226,329,134,388,486,490,134,959,867,235,672,773,946,410,384,205,541,932,194,241,130,351,074,066,509,664,508,644,353,264,593,064,253,687,400,999,930,499,108,062,080,705,305,890,897,513,111,851,032,874,660,632,426,895,260,429,713,605,174,173,378,166,623,891,304,091,613,900,985,821,100,245,105,698,413,823,662,090,982,757,977,174,412,058,549,528,204,452,096,186,369,184,472,694,596,160,940,077,708,470,683,975,191,429,404,881,830,113,554,788,156,518,949,168,716,830,385,400,533,415,530,166,678,085,117,717,999,818,712,294,680,081,238,000,696,170,365,650,109,243,573,940,131,824,578,436,816,512,477,027,702,036,278,317,327,002,584,618,404,856,893,813,471,220,303,466,099,385,444,985,808,351,587,416,942,403,674,998,218,602,273,257,350,507,505,697,602,079,510,123,394,081,259,555,596,340,885,348,042,950,402,791,915,605,656,146,105,025,334,958,898,879,224,525,338,299,211,807,917,338,485,133,255,114,752,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

[@skyethebi]

Well you can do it without lifting your own off the paper if you allow yourself to go over the same line multiple times. Also is that a trans flag in the background?

[@Ayliean]

This is true, I should have made the distinction that we can't go back over lines more clear. And yes, I spray painted it myself! Trans rights are human rights :)

[@OrganicAlkemyst]

Happy Birthday on the 12th!! For the different ways to draw the grid, are you also taking into account symmetry?

[@BooBaddyBig]

Given that there's 2^66 ways to draw or not draw the edges, so I think it's going to be QUITE A LOT of ways to sequence them.

[@sohampadwal6134]

Paige from YS got older 😮🤩

[@sweetmesaJS]

what country is that flag in the background from? 🏳️‍⚧️ seems like all the cutest girls are from there :3

[@sehabel]

I noticed that, too! I'm from there :3

[@leibniz9834]

Yooo, you and I are very close to the same age! I’ll be 33 in September! Between that and you being so cool and interesting, can we be besties?? (Although I live in the States, sadly 😭)

[@annesortland3947]

amazing video, like the trans flag in the background btw.

[@eaglewolf404]

The number of ways to draw a 32*32 grid by doing one edge piece at a time would make ((33*32)*2)! = 3.846398915*10^6106 different possibilities. Safe to say you're not gonna run out anytime soon. Explanation of calculation. 32*32 grid makes 32*32 edge pieces both horizontal and vertical + 32 on the last edge to "close" the boxes. so 32*33. To find out how many possibilities if you draw them one at a time you do factorial. 10^6106 is a stupid big number. For comparison: there are between 10^78 to 10^82 atoms in the observable universe.

[@noobtracker]

pretty sure it's 33*33 rather than 33*32, and you can't just multiply that by 2 to account for the fact that lines can be drawn in two directions cause that implies that every line is drawn twice, once in each direction