directrix

anonymous asked:

*bows lowly* My Liege, can you tell another near-death experience that happened in theater?

I’m starting to think you guys want me to die. 

Anyway. 

Once upon a time I was in the world’s worst production of Hamlet. I’m not exaggerating–our Hamlet was a ginger who didn’t know his lines, our Gertrude had food poisoning, our Ophelia had never been in a play before, our ghost missed his entrance more than once and I had to ad-lib blank verse until he came back on, and in the midst of all this clowning around, I was the world’s most exasperated Horatio.  

Now, for those of you who aren’t familiar with the play, there’s a scene where Hamlet and Horatio talk to a friendly gravedigger, who makes a lot of jokes and just generally alleviates the uninterrupted sense of suffocating tragedy–and in our case, suffocating fucking boredom–that is Hamlet. And for some reason we’d blocked out this like slapstick Three Stooges bit where the gravedigger tosses the Yorick skull to Hamlet, who talks to it for a bit like an absolute fucking loon, and then tosses it to me to catch and hold until the end of the scene because, in case you haven’t noticed, HORATIO IS HAMLET’S BITCH, EVEN WHEN HAMLET DOESN’T KNOW HIS FUCKING LINES AND HORATIO HAS TO BE ONSTAGE FOR AN EXTRA FIVE SCENES TO MOUTH THEM TO HIM WHEN HE FUCKING FORGETS. WHY FOR THE LOVE OF RICHARD BURBAGE DIDN’T THEY JUST MAKE ME HAMLET???

But, uh, that’s beside the point.

Anywhoo, I’m standing around like a piece of fucking furniture like Horatio usually does while Hamlet is chatting up the gravedigger, and because this dude is a comedian at heart (BAD CASTING CAN YOU SAY BAD CASTING) he decides to change the blocking. He catches the skull, kisses it smack on the teeth, says, “Alas, poor Yorick, I knew thee well!” and just fucking flings that motherfucker over his head. Now, what you have to know for the rest of this to make sense is that we borrowed this skull from the fucking anatomy school at a local university and if we broke it we owed them like $500, and let me tell you, this whole damn company wasn’t WORTH $500. So, in retrospect, giving Hamlet free reign to toss the skull all over the fucking stage just maybe wasn’t the most genius plan, o Herr Directrix. But nobody ever listens to Horatio. 

So Hamlet just fucking chucks this very valuable skull over his head and I’m completely unprepared for it because this is not where he usually throws it (probably because he forgot the rest of his goddamn lines) so I hurl myself across the stage and fall and slide six feet on my knees like I’m Zac fucking Efron in High School Musical 5: Disney Destroys Shakespeare, BUT YOU HAD BETTER BELIEVE I CAUGHT THAT GODDAMN SKULL BEFORE IT HIT THE FLOOR. WHAM Yorick lands smack in my outstretched hands and I’m relieved for all of two seconds before I realize oh right, human skulls have fucking TEETH, which sank straight into my palm when this thing fell from the sky like a ballistic missile, and I am now bleeding everywhere. (There’s a hand-injury theme happening this week apparently.) And it all happened so fast that Hamlet hasn’t even fucking noticed, because Hamlet is a self-centered twat, so he’s still talking with the gravedigger and I’m just staring at the friggin’ skull in my hands like Wtf Yorick you fucking BIT me–and the audience is beside itself because this is a travesty tragedy and they don’t even know what to laugh at.

But I still have lines, I can’t leave the stage, so for the rest of the scene I’m just kind of sitting on the floor, holding a skull, casually bleeding all over it, waiting for Hamlet for finish his fucking tea party so I can wash my hands and soak poor Yorick in bleach so the anatomy school doesn’t have to deal with any actual human anatomy (i.e., my blood). But this is a long-ass scene, so I had to get up and stand in the back for the whole fucking funeral while Hamlet and Laertes are fighting over who loves Ophelia more (like it matters now, you morons, bitch be DEAD). Eventually Hamlet has his tantrum and storms out and everyone turns around and looks at me like they’ve forgotten I’m there, because everyone always forgets Horatio is there until Hamlet has a tantrum, and I’m standing there, looking sketchy as hell, still clutching a fucking skull with blood all over my hands. And Claudio gets this really confused look on his face and just goes, “Horatio…?”

And I swear, it took every ounce of my self control not to just yell, “That’s right, ‘twas I that killed Ophelia! Plot twist, motherfuckers!” and spike Yorick on the floor and swan the fuck offstage. 

And that is the story of the time Hamlet sucked and Yorick almost bit my fingers off.

The hyperboloid

“In geometry, a surface S is ruled (also called a scroll) if through every point of S there is a straight line that lies on S. The most familiar examples (illustrated here in three-dimensional Euclidean space) are the plane and the curved surface of acylinder or cone. Other examples are a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space.” - wikipedia

A ruled surface can always be described (at least locally) as the set of points swept by a moving straight line.

Origami axioms

Origami, the art of paper folding, can be interpreted as an intriguing geometrical model. Folds represent lines, and intersections of folds, points. Now, to model origami, we need to know which new folds one can make from a given configuration. The most natural model uses the axioms of Huzita-Hatori-Justin, describing the operations that can be made when folding a piece of paper.

Humiaki Huzita discovered and reported the first six axioms in 1991. The seventh independent construction was discovered by Koshiro Hatori in 2001. Jacques Justin, however, already published the complete system with seven axioms in 1989, but his work remained unnoticed.

  • Axiom 1: one can fold a line through two given points.

  • Axiom 2: one can fold a given point onto another given point.

  • Axiom 3: one can fold a given line onto another given line.

  • Axiom 4: one can fold a given line onto itself, while folding through a given point.

  • Axiom 5: one can fold a given point onto a given line, while folding through a given point.

  • Axiom 6: one can fold two given points on two given lines.

  • Axiom 7: one can fold a given line onto itself, while folding a given point onto another given line.

The first two axioms don’t seem that exciting, but they are needed for basic constructions. Axiom 3 states the construction of bissectrices, axiom 4 the construction of perpendiculars. Axiom 5, interestingly, provides a method for solving quadratic equations by origami; the new fold is in fact a tangent line to a parabola (with the given point and fold as focus and directrix, respectively) through a given point. Axiom 6 even allows us to solve cubic equations, which is in general not possible using only straightedge and compass!