 don't really have anything planned so this is kind of filler content it would just really be me messing around I might be I'm looking into conic sections I'm not really making any progress I'm gonna ask about this in the end right now I just want to show you my crack at the at the Colatz conjecture and if you don't know what that is basically you insert a seed number let's call that number n and you multiply it by three and add by one if it's odd then divide by two if it's even divided by two if it's even and you repeat this process till you get to a loop or see if it grows infinitely who knows but what but the conjecture states that it will always reduce to one and it'll get into a loop with between one and four okay so my attempt at solving a problem involved not looking at it from inserting numbers and checking but generating numbers that will always reduce to one so for example let's say we got the first generation I like to call generation zero and that's equal to one one will always reduce to one because it's one and then the next generation this is generation one you take generation zero multiply that by two to the end that gives you an infinite list of numbers and then and then you fit those numbers let's call this n1 we subtract by one and then divide by three and an interesting note is that four to the n minus one will always be divisible by three there's a proof for this I don't want to get into it right now but it's an interesting proof I think it's used as an introduction to proof by induction anyways now you have an infinite list of numbers between between one and zero okay after that the next generation you do the same thing g2 equals the previous generation times two to the n I'll put that in n1 minus one over three if you if you notice something that when n equals zero you get you get the original list of g1 so it so the next generation will always include all the numbers in the previous generation now it looks something if I'm going to generalize this it would look like g I already used energy let's just call it uppercase n because gn minus one play that by 2n I don't know though I don't know how I would do this in formal notation I don't really know a lot of math notation okay I would know that this is kind of union but anyway doesn't matter the the way there are two ways you could you could prove that this that all of this will eventually lead to every number if you if you conduct this process infinitely one of them I think would be impossible which I'm gonna discuss that one first which would basically basically asks you to prove that it will read it will reach every single every single number that has prime factorization with every single possible combination with each n which I think would be impossible firstly because it involves prime and a lot of the problems that involves finding predictability with primes are usually impossible to solve or at least really hard to solve like the goldback conjecture which it would try to which states that every even number is a sum of two primes can be described as a sum of two primes but that's getting off of topic the point is primes are really random and it's really hard or impossible to find any order in them the next one which I think has more promise is what you take take let's say a gap between two to the four and two to the five and the conjecture is that for every every gap you know between every power of two there is a finite number of generations that will that will cover every single integer between those two numbers or maybe an infinite who knows but so long as you could as you as you can establish a rule improve that n amount of generations will cover every single number like you could say you could say it takes it takes three three to the end with n being that amount of generations will fill all the numbers here it doesn't matter just so long as you could establish a rule improve that rule you could prove you could prove that every single number is covered or you could always say that you could say something like between every single one every single one of these you could always say that oh at some point you will always have one more number that fits between these two or these two and so on so I guess I think that one has a lot more promise I don't know if it's been tried before the only the only video I've seen on this problem is the one by very tassium I don't know how you pronounce that I thought this problem is really cool but anyways here's the here's the thing I want to make a video on but I can't because first of all it's too hard and second of all I just don't know how to I just don't really have time so it involves conic sections you still haven't really reached conic sections but basically you take you take like two two cones and put them in like a 3d coordinate system like that like their tips like their tips on top of each other so it makes this like hourglass figure and then you have a general you have a general function it's a times x squared it's going to take forever plus b times x y x times line plus cy squared plus dx plus e y plus f equals zero let me finish reading this what I want to find out is if you can insert all of the six numbers into a function and get a plane we get three points of the plane which would be the origin of the y-axis you know first unit of the y-axis and the first unit of the x-axis let me just give an example real quick so a parabola a parabola would be like a equals negative one and e equals one because it would be y minus x squared and f would equal zero y minus x squared equals zero that gives you y equals x squared and you get a parabola now a parabola would basically be a plane it's had like a 45 degree angle so that this goes on forever but this never touches anything down here there's also there's also circles but you but you could have like x y squared plus x squared equals one and you have a plane that crosses right here and that gives you the unit circle and you can also have you could you could also have hyperbolas which is y squared minus x squared or x squared minus y squared I don't know I don't know how they do but basically you have a plane crosses like that so that it hits both the top and bottom cones and if it's zero it gives you this it intersects it perfectly where where it touches that point it just gives you these two these two lines if it's something other than zero let's say like two you get you get something like this I don't know what it's like in that case or it would be something like this now what I want to figure out is if you can again input and put all these values into a function maybe a matrix of some sort and get back at these three points the origin the x the x the unit x axis and then the unit y axis if you could like send me a video that does this I would really appreciate it because I really want to understand how conic sections work I don't know if they teach this in precalculus this specific thing but I'm hoping they do that's all thanks for watching