Dope Tech Episode 2

<<@gauravpallod4768 says : Oh yes. Finally a valid use of converting to polar coordinates>> <<@rdmeena3938 says : Similar. Ward>> <<@_Baku says : Would be curious about how this problem changes when the triangle is drawn on the surface of the sphere (using great arcs) instead of inside it.>> <<@FrederickCorkery says : "promosm">> <<@nikhildugar_iwnl says : Hey im kinda confused if theta 126.9 degrees and the centre is in in green area doesn't that mean that some parts of green are red area as the triangle won't be acute?>> <<@MrConverse says : 6:44, outstanding video, but you said ‘odds’ when you meant probability. It’s in the title too. Odds is the ratio of winners to losers. Probability is the ration of winners to the total. Hope it helps!>> <<@fardinabrarsafi says : Man that's awesome. We can never get enough of these nerdy videos>> <<@nasimajosefi says : your explanation and animation are surperb, can you telle how you do your animation?>> <<@AzeddineHamich says : 👌>> <<@HollowDog5899 says : Sometimes I forget this guy is a genius>> <<@helphowdoinputusername3571 says : A curiosity I've had for a while is: how would a second time dimension work? Like a second spacial dimension allows us to move along two axes and occupy a higher level of space. It allows us to combine coordinates in axes to occupy different positions in the 2D/3D space. But how would that even work for time? Like would you be able to age in two directions? How would that affect processes that depend on time, or entropy? What would that even mean for measurements such as velocity? Or would time just be measured as the distance from O on the axes? Super weird. I can't even begin to think of what that would mean, unlike with spacial dimensions, for which it's at least possible to intuit some of it based off of flat land observations and comparisons.>> <<@GuagoFruit says : I watch these videos without really taking anything in to feel smarter about myself.>> <<@JosaxJaz says : The people in these comments are far smarter than me holy>> <<@leventaksakal5 says : U have to make a sketch like "If god was an engineer." where an atheist and god have a conversation in afterlife>> <<@doim1676 says : You do make interesting videos, but i find it hard to stay focused because of the many little pauses you make while speaking. Some of them may be a good thing, but for me it's too many. Just a suggestion for improving, but maybe it's just a me thing and the way you record you videos is fine 🤷>> <<@artificercreator says : Can you do a tier list of the hardest type of mathematics to learn that have real life applications? OR, or, what about a tier list about the most challenging fields of ingeniering? or mabye something more like, rocket science vs architecture or stuff like that. Thanks for your videos.>> <<@MichaelZankel says : 5:10 I disagree, it should be written as: 4pi*r*z- pi*R2d2 I cannot believe you didn’t write it that way, very disappointing.>> <<@stevenpike7857 says : Hey Zach, I was curious about your opinion. I would think that the laws of probability are independent of time. If this were the case, then if you could time travel you could never get back to your future. For example, if you traveled 10 years back in time and then traveled back to your future, all the events based on probability would be "re-rolled". Another example is say you memorized the lottery numbers that won in last weeks lottery and then traveled back in time. The odds of winning this particular lottery is, say, 1 in 350 million. Since the balls "have no memory" it would still be 1 in 350 million chance that those numbers would come up. There's no guarantee that those numbers would come up again. I don't know, it's just something I thought about, what do you think?>> <<@brandonmaldonado7008 says : Can you make videos on these topics. Architecture Systems engineering Biotechnology Quantum Computing/Engineering>> <<@jorgeespinal5591 says : Hey Zach, I’ve been interested in Aerospace engineering and I was wondering if you could recommend any specific YouTubers that give a similar experience as you, like giving their experience through college and such? Thank you so much😁>> <<@decoder01x says : Golden ratio is the fabric of the universe beyond metaphysics>> <<@RespecterAlexander says : 👍 👍 👍 👍 👍>> <<@josgibbons6777 says : Alternatively, use compound angles to write P(theta)=(sqrt(5)/2)sin(theta/2-phi)-1/2 (where the angle phi is an exercise), with maximum (sqrt(5)-1)/2.>> <<@netzaltali says : Sometimes I forget this is a math channel and I always think you are gonna butt in with a goofy punchline>> <<@JohnSmith-lf5xm says : Can you stop talking like a Kardahsan sis?>> <<@godfreypigott says : How is the 3rd point chosen 'randomly'? If it was chosen by picking from uniform distributions of latitudes and longitudes then this would not work.>> <<@johnchessant3012 says : 3:54 Really cool fact! I think you can link this to the 3b1b video on surface area of the sphere, specifically the animation that breaks apart the sphere and rearranges it into a cylinder>> <<@reidflemingworldstoughestm1394 says : Arctan? Yes.>> <<@roundpiano says : Where do you get puzzles like this from?>> <<@hatredlord says : Just for the record: is this angles of a 3D triangle, i.e. tunneling through the sphere? Or non-euclidean triangles along the surface of the sphere?>> <<@nevenazMadwrld says : more discussion of the golden ratio and speculation about how it is fundamentally related to this problem would have been interesting to add, give another 2-3 mins to the video>> <<@mrxylophone1 says : Burgundy>> <<@AnonimityAssured says : I discovered, quite a few years ago, that the bisector of the larger of the two non-right-angles in a 1-2-√5 triangle cuts the longer orthogonal side of that triangle at a distance of 1 / φ from the right angle. I'm sure many people had already discovered it, even centuries before me, but it was still satisfying. This problem reminded me of it.>> <<@theaxelr8r says : I'm not happy with the explanation from 3:05 onwards. You can't just say "these bits aren't red so they're green". I have no confidence that ALL the points in that section are valid>> <<@louisrobitaille5810 says : 6:57 "Out of nowhere." If there's one thing I've learned in maths and physics, it's that mathematical constants (not physics ones like c or α, afaik) show up in the most unexpected places… until you realize that most of those "unexpected places" have one thing in common: a circle (or sphere) can easily pop up if you play with the numbers a bit.>> <<@PedroMoratori says : In portuguese, Teta sounds like boobs>> <<@JR13751 says : You didn't justify why does only green area results in acute triangles.>> <<@Qermaq says : Man your math videos are really good. Would love more of these.>> <<@louishannett356 says : You should look at the construction of a pentagon. When you draw the 5-pointed star using the points of the corners of the pentagon the golden ratio shows up for the line segments that form the 5-pointed star. Also, the ratio of the side of the outer pentagon to the inner pentagon of the 5-pointed star is equal to phi squared. Also, the value of sin(54deg)=phi/2. The values of trig functions for angles of 18deg, 36deg, 54 deg and 72deg have phi buried in the expression. Have fun with it.>> <<@AzureFlash says : I picked a random video, it was Zach Star, he's a cute so I win>> <<@agrajyadav2951 says : Chef's kiss Phi and pi are two sneaky bois>> <<@Matthew_Klepadlo says : “Bro, here’s why you’re a fvcking m0ron!” “Now, do you like interesting math puzzles that utilize the golden ratio?” Zach Star in a nutshell lol.>> <<@rhashydramos7927 says : Can I use this to defeat the United States president?>> <<@zayyeyint027 says : Omg..., I have been waiting for your video:)))>> <<@no_name4796 says : 0:23 yeah the triangle is very cute I WIN!!!>> <<@cycklist says : So why do many video titles start with an unnecessary 'so' at the moment?>> <<@Wargon2013 says : Does Bertrand's paradox play a role here given that the selection method for the 3rd point hasn't been specified further?>> <<@archangelazrael8090 says : I wish Zach is my Math teacher>> <<@ultrainstinctgokuhope7442 says : So your saying I can unlock tusk 4, got it>> <<@Haiticoulers says : Boring.>>