Hello, everyone! Now it's time to think about Seokguram Grotto which is on the hillside of Tohamsan Mountain. This mountain is about 740 meters high. But this grotto, this particular structure I'm going to introduce is on the hillside, not on the foot. It's about halfway up the hill which is slightly below 400 meters above sea level. So, what you see here is the front structure. And you enter this, and then this mound is the top of the grotto. Grotto means a man-made cave. A cave is a natural formation, but then, an artificial cave is called grotto, G-R-O-T-T-O. So when you enter, then you get to see the cave, the grotto. And you get to meet this white Buddha statue. And this Buddha statue is deep inside the grotto. How does the grotto look? So we'll come back to appreciate more about this grotto and the Buddha statue itself, and then, also the mathematics behind it and the engineering and technology behind it. We will try to understand more about this fantastic structure built around 715 AD. So it's not a new thing. It's a very old one. Then the statue itself looks like this. And when one approaches it for the first time, several of my Western friends thought that this was carved recently because this is so white and looks so new. So it looks very new. But this is original, and this was carved and built in 751. Long time ago. And the material of the cave as well as the statue and everything is firestone, firestone discovered in the same mountain. The structure... A projection from the side looks like this. And so as you can see, there's a podium. The podium is here. And then there's a Buddha statue up here. And then the hall is dome structure. How big is the dome structure? You might ask. And the dome structure is very big actually. The diameter here is more than 6 meters. And so the radius is more than 3 meters. It's quite big. And as you can see, this is a spherical dome, and so the radius of that, you can actually imagine, is the same as the radius of the room. So it's a large structure. And then there's a frontal structure. And the frontal structure here, there is this roof, tiled roof. And so actually you see the statue from here. So the visitor is here. And from the visitor to the Buddha statue is quite far actually. You can imagine how far it is. From this point to the back, it's almost 10 meters. More than 33 feet. So it's quite a distance. I'll come back to that. Then you project from the top. Then the visitor comes here and looks at the statue. And maybe we can approach this far. About this far probably. But there's a glass wall, so we cannot go very close. And we have to see it from this side. And to the back, it's 10 meters. It's quite far. And this round thing is the podium where the Buddha statue stands over there. Okay. So then when you look at this, then naturally several questions arise. Let's ask some of them. The first one is about the dome. This was built in 751. And this dome is quite difficult to build usually. So how was it constructed? It's a good question. The second thing is that the grotto determines the location and the viewpoint of the visitors. Therefore, the visitor's eyes are about here, the average height. And then when you see the Buddha statue from your point of view, because of the distance, the view might change the actual scale. That's again projective geometry. But that must have been understood in constructing this grotto. And therefore, we have to understand from a mathematical understanding to fathom, to actually understand how builders had to come up with some techniques. And we will try to understand some of them. Because it's a grotto, a grotto is always a very difficult structure to maintain because of temperature control and moisture control. And those things should be asked. And then there should be many other questions. But I'm not going to continue asking questions, so let's proceed. Now we look at inside the dome part. The dome part is large, as large as the diameter of approximately 20 feet. 6 meters and more actually. So one of the questions is that... Even though this is a dome structure, the weight is amazing. If you look at this centerpiece, according to some physicist's measurement, the centerpiece is approximately 2 metric tons in weight. It's very very heavy. And so, how did they construct this thing without having it fall in? That's the danger over here. Not just this piece, but all these pieces are large and heavy. And so these tiles could fall in. And how was the construction actually done in 751 so that this dome structure does not fall in? So that's an interesting thing. Actually in Samguk Yusa, which is one of the old history books or parahistory books written by a Buddhist priest named Ilyeon in Goryeo time which was about 800 years ago. At that time, this structure actually suffered a falling-in accident. And that's what this crack is about. And the centerpiece was cracked. But then according to the Buddhist record, the story says that the builder was very angry and he was sleeping at night. In his dream, heavenly god came in and said, "Don't worry. I'll fix it." And then in the morning, according to the Buddhist record, the story by Ilyeon priest, it was indeed fixed. So he was very happy. But in all honesty, I think the builders knew how to fix it. They were inspired by the heavenly god maybe and then knew how to do this thing. And then we will try to find out how this construction actually went. And then some of the secrets are hidden in the halo disk in the back and also the statue itself. And so we are going to understand one by one. And while we are up to it, there are more questions you might want to ask about artistry, architecture, viewpoint, impressions, lighting, illumination, and all the other features. But it's interesting to discover what the Silla people knew in 750 AD. So we will continue.