In this video, I'm going to attempt to square the circle. And I say attempt, because this is literally impossible. It was proven in the 19th century that you can't exactly square the circle. What does it mean to square the circle or circle the square, it means to bring the Circle in the Square into a kind of equality so that they have the same circumference and perimeter. And this is impossible because of the transcendental nature of pi. You see pi can never really be rationalized and brought down to earth.

The circle represents heaven or the infinite. It's the most perfect of forms the most symmetrical. The square is the most terrestrial, the most mundane of forms. It's how we divide land. It's how we make grids and create buildings. It's the most.

It's the closest to humankind, shall I say. And so squaring the circle is really an activity that brings the mundane together. With the transcendent, and as such, it's part of the human spirit to attempt to square the circle. And I'd like to show you an approximation that is 99.9% accurate. Let's begin by drawing a line horizontally, and then draw a circle on that line. I'll label the center of the circle point A.

And then I'll go ahead and draw another circle, and another one. And I'll label these points B, and C. Now I'll draw a fourth circle from B up to the edge of the construction. And I'll label these points D and E. I'd also like to put in a perpendicular bisector of the segment d e. And I'll do that using the perpendicular tool here. And I'll drop that in at point B. I'll label the top and bottom crossings as F and G. And now, I'll make a circle from G on the bottom. And I'll have that go up here so that it's perpendicular to the edge there that makes a tangent point right there, which I'll label as point H. And there's a symmetrical tangent point on the other side, which is point i. This large circle also crosses the original horizontal at j, and k. This is really all we need to square the circle at this point.

I'm going to draw a large circle from B out to J. This is the circle that we've been looking for. I'm going to colorize that as a thick line, red circle and now For the square, the square actually fits right around the smaller circle. So to construct that, I'm going to draw a parallel line from the horizontal up here and drop it at F and another one at G. And then going the other way, I'll draw drag a parallel out from the central line and drop that at D and E. This forms the square that we need. I'll go to the artists palette here and select a different color, maybe blue. And then I'll go ahead and draw in the square.

And there you have it, we've squared the circle with 99.9% accuracy that's so accurate, that the margin of error is within the line thickness.