Відео

@@jeromeglick old digital video camera technology would auto truncate the video files at 33 minutes and I was too old, dumb, lazy to do any editing, so I just put the videos up in parts.

@@Legotyres P is arbitrary with coordinates (x,y), so PE = √(x²+y²). But not sure how that helps.

@@dodecahedra thank you so much for the replying I’m still learning and as it was for a bit of something to do, it’s ended up being a lot more complex than I thought it was going to be

Massive thank you! It worked perfectly, those are the numbers I was looking for. I has been calculating F1 to P1 , not x and y 😃 I’ll say, your my hero as I’ve spent a number of days playing with the ellipse (which has been really cool) and got so far, but this was the last hurdle for my needs and I hadn’t been able to find the answer 😃

Yeah, I started out referring to n as a natural number out of simplicity, but the algebra works out better if you let n be rational. If you want, you can just set n to be "the next natural number" by rounding up. That's just adds a step or two to the argument.

same. I felt like I was watching an important scientific announcement

Or just use the teleporter.

to suggest that there is no solution to your plight indicates a lack of understanding of the geometry of hallway traffic. as we are all well-versed in the technique of weaving in and out of the traffic of individual moving students, let us focus on the greatest obstacle of the hallway hustler: the Small Set of Stationary Scholars. to simplify, visualize this SSSS as a closed circle. the first step is to enter the circle as a member, forcing it to expand slightly to accommodate the increased circumference. then, treat the SSSS like a spinning wheel. WLOG, let clockwise be your direction of travel. irritate the person to your left until they step away from you, causing a clockwise turn (birds-eye) of the SSSS. repeat this step until you are on the other side of the circle, then make a quick exit and continue down the hallway.

/gamemode spectator

@@VeenaKailad ah, your solution appears familiar. hath your ears set upon the "roundabout"? one of humanities most grave mishaps? well, allow me to bestow knowledge upon you. a roundabout, according to Oxford Languages, is "a road junction at which traffic moves in one direction around a central island to reach one of the roads converging on it". appears to be of a similar concept to that of which you have mentioned, hm? doesn't this sound impressive? NO. a roundabout is a barbaric free for all and a disgrace upon roads everywhere. have you considered the thought that one person does not move, and thereby causes a major crash? and how would you even infiltrate the SSSS in the first place? your "solution" would simply inflate the problem!

@@adithisathya4165 i see you have conceived of the enormous amount of personal effort needed to make this maneuver possible. having conceived of it, endeavor to commit yourself to its actual completion, and you will have no further problems. any student who puts in effort to make themselves sufficiently irritating to those around them need not fear the one person who "does not move"; though we cannot guarantee much about this arbitrary member of the human race, their instinct for self-preservation may be depended on. the developed capacity to irritate induces all those in the vicinity to step away, enabling the student to also force a gap in the SSSS for initial infiltration, as a pebble dropped into water creates ripples outward. of course, being this annoying is not a skill to be taken lightly - therein, the personal effort.

Based on this elaborate showcasing of your analytical faculties, us older folks can rest assured that you young people are obviously more than capable of handling the unforeseen complex problems that the rest of the 21st century will undoubtedly thrust upon us all.

nah for real that was a blistering place

Agreed if it's 5:45 without traffic, imagine students that just stand in little groups blocking half the hallways or students with their arms linked that move slowly and you can't pass them. You can try to speed walk, but the crowd only moves a certain speed and it usually isn't fast

@@gghollen6933I guess if you went outside and then entered on the far side of the school you might be able to avoid the traffic. Also this doesn’t consider the affects of weather

@@justinian1453 that’s true and they said they are also assuming you can leave right when the bell rings, but that is not the case

@@gghollen6933 astute observation, fellow peer. i admire your ability to observe the environment around you and classify common obstacles on the great journey to room 309. your ability to relay information through these "comments" is truly remarkable. i especially relished reading the section on "little groups". i, too, find myself in this peculiar predicament in which i am unable to surmount these circles of scholars for the duration of their assembly.

@@adithisathya4165 Sounds very familiar; reminds me of my youth.

Maybe not to you, but they’re wonders to me. Why are they in the courtyard? Why did I not realize this sooner?

⁠​⁠​⁠@@eriklodal8882Mr.Kaluta’s Material Science class used to make them. They’re supposed to all be to scale. In theory one of the concrete slabs in the courtyard is a model of Blair that my year made.

Yes, I chose not to address this for simplicity since these arguments are intended to be only at the level of rigor of Euclid, who is often a bit sloppy with these things. Since ∡1 + ∡2 < 180, the lines have to meet on that side. The adjacent angles have to sum to > 180 and so the lines can't meet on that side since we can't have a triangle with two angles that add to more than 180 (see Prop 17).

@@dodecahedra Thanks. Your comment explains to me the missing part of the proof.

@@patrickwithee7625 No deep and principled reason. It's just the syntax of the Fitch system I inherited from the Barwise and Etchemendy Tarski's World. Many variants are possible, of course.

I talk about this a bit in the beginning. Yes, you can consider Dedekind cuts a model. Then, since we can show that the cuts satisfy all the axioms of the real numbers, something out there exists that acts exactly like the real numbers should act. So that's good enough for most. Or you could make the stronger claim that this is what the real numbers REALLY ARE.