 What is the story of Pai versus new question? Pai is this, right? Let me give you a quick intro to Pai. Let me read the speed of God's ask. Disney, suing Stan Lee's family for contract control of Marvel characters. I hope they fail and burn to death, as she says, and Joe. The area of a circle was one of the first derivations I saw in math. It blew me away. You basically split the circle into an infinite amount of triangles and then rearrange those into a rectangle. Then you simply use the area of the rectangle. Really? Very cool. Very cool. Here, deep flake. Check this out. Here's Pai. Here's a circle. Right? Here's the center of the circle. The most important thing about a circle or the only thing that defines a circle is the radius. Here's a radius. Okay. Now, the radius is the most important thing about a circle because everything's based on the radius. If I give you the radius of a circle, you can make the exact same circle as I did here or there, wherever you are. Keep that in mind. Now, for you, if you're standing here, let's say you're standing on a big circle, right? If you're going to move this way, right? Then I could tell you in one way that you know that almost everyone knows where I want you to go. I can put a grid on this circle. Here's an X. Here's a Y, right? Because we make the center of the circle 0, 0. This is 0.00. What I can do is say, okay, from angle theta, go to 120 degrees on the circle and you would go here. From there, you would go here. Thank you very much. From here to here, that would be 120 degrees, right? That's one way I can tell you where I want you to go from a circle, right? Over here, maybe it was 30 degrees. I would tell you go to 30 degrees on the circle and you know where you are, right? Now, there's another way I could tell you where to go on a circle. I could tell you where to go on a circle using geometry, using coordinate system, X and Y coordinates, because if we draw a triangle here, right angle triangle, right? Then this point here is your X and Y, where this is your X, right? Or X1 and Y1, Y1, and this here would be your Y1. So instead of telling you, I want you to go 30 degrees along the circle, I could just say go to coordinate X1, Y1 and you end up there. Or go to coordinate X2 and Y2. I could tell you to go here, right? Here's X2, here's Y2 and you end up there, right? That's one way of doing it, right? So I can give you an angle and I tell you what the radius is and you're there, right? So there's two variables that you got taken care of. Or I could also put a coordinate system on there and give you two variables and you end up at the same place. So I could tell you where to go on a circle on the surface of a circle or in the circumference of a circle by giving you either the angle, theta, okay? Or the radius, R. Or I could give you a coordinate system, right? Now, one thing that's a fact, universal fact, universal fact, mathematicians are the laziest human beings on this planet, right? Tap it, fast. Thank you very much for the follow. Seriously, mathematicians are the laziest human beings on this planet. And what they did, they went two variables. I don't want two variables. I want to deal with one variable. I don't want two variables. I want to cut down my variables because when you cut down your variables, the problem becomes simpler, right? You got one less variable to deal with. Awesome, right? As long as you can do the same thing. So what mathematicians did, they said, okay, what is the most important thing about a circle? For you to draw the same circle that I draw, what do you need? You just need the radius. The radius is really the only thing that defines a circle, right? So mathematicians said this, you know what? This is what we're going to do. We're not going to measure the angle in degrees, right? Because degrees is a new variable, right? Theta in degrees and radius in distance measurements, feet, centimeters, whatever you want, right? Length. So forget about the degrees here, okay? Angle in degrees, okay? What we're going to do is define this, okay? We're going to come up with a new measurement of an angle and we're going to call it radians. Radians, radians. And what is radians? We're going to define radians or one radian. So one radian to be the equivalent distance you would travel along a circle, okay, that was equivalent to the distance of the radius, right? So if this is R, right? If this is R and this is your radius, then we're going to say that one radian, one radian is you taking this distance and putting it along the circle. So if we take this, one radian would be this, basically. Take a look. To there. This distance here would be the equivalent of R, right? So if this was 10 meters, then this would be 10 meters. You follow? Right? I hope that makes sense. Pretty straightforward. And what we're going to do, we're going to call this one radian. So what I'm going to do is I'm going to erase this. I'm going to do this. So if the radius of a circle is 10, right? And if you travel along the arc of a circle, 10 units, then we're going to call this one radian. One rad. And rad is just short for like degrees is degrees and one radian is right, right? This is the angle. So when I say I've traveled one radian along the circle, that means I've traveled the equivalent of the radius. So if I draw your circle here, right? And I put you here, right? And here's the radius R. And I say travel five radians along the circle, right? Then what you would do, you would go, here's a radius. So five of these. So here's one, let's say, here's two, here's three, here's four, here's five. So you would go, this is where you end up, right? I didn't have to give you degrees. I didn't have to give you degrees. I got a rate of theta in degrees. I created a new variable, which is radians, which is dependent on the radius. So it's really the radius, right? Cool, cool. What's pi? Pi is universal for every circle, no matter what size it is. Because if you travel from one end of a circle, if you go exactly half the circle to that side, you have traveled pi radians. Because from there to here would have been five radians. And from there to there is pi radians, and pi is 3.1415, I believe, if I'm not mistaken. So if you're standing here, I tell you to travel pi radians along the circle, you would go, oh, I know where that is. That's where I'm going to go. That's where you are. So pi is on a unit circle, a unit circle would be 1 if we're going to call it, but that's what it is. Pi radians, pi radius is half a circle. That's why the circumference of a circle, circumference of a circle is 2 pi r. r is your radius, how long your radius is, and 2 pi is you traveling 2 pi radians. So if I tell you you're standing here to go 2 pi radians along the arc length of a circle, you would go, and if I ask you how long, what's the distance there, you would go, oh, the distance is 2 pi because that's how many radians have traveled, the angle of travel in the circle, times the radius 2 pi r. If I tell you to travel 5 radians, oh, sorry, not 5, 5 pi radians, it means you're going to go 1 pi, 2 pi, 3 pi, 4 pi, 5 pi radians. You just traveled 5 pi radians. Right? That means you traveled 5 pi times 10. That's the distance you traveled. That's what pi is. That's what pi is. I hope that made sense.