 Okay, I'm back. Now, I've had a request to do some down-and-dirty math, specifically geometry. Seems like some people are gonna be writing a test this week, and they need to know what's what. Unfortunately, this is Vancouver. Well, fortunately, this is Vancouver, but unfortunately, this is the fall in Vancouver. So it rains a lot here. I haven't had a chance to go outside and find any fresh walls to do some math on. So we're gonna use a back of a ping-pong table as a chalkboard to lay out all the work and just talk about it real quick, okay? One thing to keep in mind is mathematics is a language, but it's broken up into different segments, okay? You have algebra, you have calculus, you have statistics, and it just goes on from there. But one of the most important aspects of mathematics and one of the first areas that we started talking about was geometry. Since we live in the world, it's a three-dimensional world. One of the first things that we wanted to do was to understand how things were laid out, how to make things, and all of that goes into geometry. So a long time ago, you know, before calculus began, before God, differential equations began, before a lot of different branches of mathematics started out, mathematicians were specifically talking about geometry. Astronomy was a huge part of how geometry was developed because we're trying to understand our place in the universe, how things have, you know, rotated. At night time, people would look up in the sky and they would track stars going across, they would see the sun going across the horizon and the moon coming around. So they tried to understand how everything was laid out. And the only way they could have done that is to, you know, draw the things, draw the patterns, draw the orbit of the sun, the moon, the stars, how they rotated, and try to grasp how everything worked, okay? So geometry was one of the first branches of mathematics that we got into, to understand our place in the universe and for us to be able to make things, homes, shelters, just anything, the wheel, you know, they had to come up with the concept of wheel and actually make it round. So keep that in mind when we're going through this stuff. What we're going to start doing is start with the basics, which is basically trigonometry. Now trigonometry is a branch of geometry, but it specifically deals with objects that have three sides and basically that's triangles, trigonometry triangles. So whenever you hear the word trigonometry or triangles, keep in mind that you're thinking about or you're dealing with things that have three sides to them, okay? So what I'm going to do is I'm going to lay out right angle triangle and put in some of the functions associated with the right angle triangle and we'll talk about a little bit further. Now, we're specifically going to talk about a right angle triangle, but there are different types of triangles. There's a scaling triangle. There's a equilateral triangle and isosceles triangle. Now, scaling triangles are triangles that don't have any equal sides. Isosceles triangles are triangles that have two equal sides. Equilateral triangles are triangles that have all the sides equal, but right angle triangles is the one that we're really concerned about because right angle triangles branches off to different segments of mathematics as well, and it's the most powerful stuff. It's the one that contains everything and a lot of functions that we can deal with, okay? So I'm going to lay this stuff out and we'll talk about it as soon as it's done. Okay? We'll see where it goes.