 Okay, we're going to do a little preliminary review of where we've been and why these angles are important to the measurement or the plotting of sun charts. So we know that we have a set of several earth-sun angles, right? So earth-sun angles, use my wonderful writing, and we're going to break those down into the latitude, phi, the longitude, right? So we've got latitude and longitude, and we're also going to need the declination, the declination which is going to be a function of the day number n, right? And the hour angle, and the hour angle again is omega, and that's going to be just converting time into an angular value, which we do for the location at hand. So along with those earth-sun angles, we have our sun observer angles, and the sun observer angles is going to be broken down into three simple angles, which is going to be the solar altitude, altitude angle alpha with the subscript s relating it to the behavior of the sun, gamma s is going to be the azimuth angle of the sun, right? And the third angle is going to be theta z, which is the zenith angle for the sun. Now I'm going to use the information from latitude, longitude, declination, and hour angle to ultimately calculate the sun observer angles over here. The important angles for our future shading plots and for our sun path diagrams are going to boil down to plotting altitude and azimuth, right? So we're going to use these earth-sun angles to calculate sun observer angles, right here, and if we plot those angles over the course of the day, over the number of hours in the day, we're going to ultimately plot the altitude and azimuth angles according to their hour angle, and the complement, of course, of the altitude angle is the zenith angle. I forgot to mention that. But we're going to be able to make these plots that are going to look like this. They're going to be a square plot where on the x-axis we're going to have a plot of azimuths, and on the y-axis we're going to have a plot of altitude angles, right? And so the altitude angle will go from zero to 90 degrees, and depending on the system that we're using, negative values might be to the west and positive values are negative to the east and positive to the west. We could also plot here the complement from zero down to 90 would be theta z, just so we know. And again, if I plotted the solar altitude and solar azimuth angles, what I'm going to get is a plot of an arc over the hour angles, and this lower plot will be for winter, right? And when the sun is low in the sky, low in the sky means a low altitude angle. When the summer comes the sun is high in the sky, and so we have a higher angle in the summer. And basically this boundary, this boundary from here to here is going to be the winter solstice and the summer solstice. These plots are basically plotting a series of altitude and azimuth angles for our sun charts. And we will next be plotting a series of angles for shading that we will use. So that's our basic overview. Let's go on to the next stage.