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- TL;DR Summary
- Very large sphere structure covered with LED lights

My wife was in Las Vegas over the weekend to visit her sons and grandson, and saw this new structure there, the MSG sphere.

In this image the sphere appears to be a very large basketball. Other images I've seen are of a huge eye, animated fireworks displays, an image of the earth, along with lots of others.

She mentioned that it's covered in 580,000 sq. ft. of LEDs, so did a quick calculation to get its approximate size. Assuming it's a perfect sphere (it's not, the sphere sits on a base circle rather than a single point), I solved the equation ##580,000 (\text{ sq. ft. }) = 4\pi r^2## to get ##r \approx 430 (\text{ ft})##.

I've seen a couple of figures for the cost, one of which is $2.3 Billion, and another that is lower. The MSG apparently stands for Madison Square Garden, as in the western branch of this venue.

It struck me that there has to be a ton of mathematics involved to display animated images on a near-spherical surface, let alone just static images. This web page lists some of the equations used for the images and animations shown on the outer surface, as well as those displayed on the massive screens inside -- https://www.thespherevegas.com/science. These range from the fairly simple equation for the surface area of a sphere (which I used) to the Kirkhoff Equation, Kirkhoff-Helmholtz Integral, Huygens-Fresnel Principle, and quite a few others.If you do a web search, you can find many more images of this sphere.

In this image the sphere appears to be a very large basketball. Other images I've seen are of a huge eye, animated fireworks displays, an image of the earth, along with lots of others.

She mentioned that it's covered in 580,000 sq. ft. of LEDs, so did a quick calculation to get its approximate size. Assuming it's a perfect sphere (it's not, the sphere sits on a base circle rather than a single point), I solved the equation ##580,000 (\text{ sq. ft. }) = 4\pi r^2## to get ##r \approx 430 (\text{ ft})##.

I've seen a couple of figures for the cost, one of which is $2.3 Billion, and another that is lower. The MSG apparently stands for Madison Square Garden, as in the western branch of this venue.

It struck me that there has to be a ton of mathematics involved to display animated images on a near-spherical surface, let alone just static images. This web page lists some of the equations used for the images and animations shown on the outer surface, as well as those displayed on the massive screens inside -- https://www.thespherevegas.com/science. These range from the fairly simple equation for the surface area of a sphere (which I used) to the Kirkhoff Equation, Kirkhoff-Helmholtz Integral, Huygens-Fresnel Principle, and quite a few others.If you do a web search, you can find many more images of this sphere.