Area of a Sphere
Area of a Sphere was used to calculate the square footage of the Exosphere, which features 580,000 sq feet of LEDs — a creative canvas so bold and bright you can see it from space!
Volume of a Sphere
Did you know you can fit the entire Statue of Liberty inside of Sphere? Volume of a Sphere was used to calculate the interior square footage of the venue and maximize the size of its immersive technologies – from our 160,000 sq ft LED media plane (that’s 4x football fields!) to the 17,385 seats inside the Bowl.
Finite Element Method
Did you know many parts of Sphere were built first in virtual reality? Our engineers and architects used the Finite Element Method to transform equations like this into computer models of key structures across the venue – testing their strength and functionality before they even existed IRL.
What goes into constructing the world’s largest Spherical building? A lot of triangles. If you look closely at Sphere’s exoskeleton, you’ll see the laws of Geodesic Math in action – where hundreds of interlocking triangles create the 360° shape and structure for this world-first immersive venue.
Law of Sines
Like any global entertainment icon, Sphere would be nowhere without knowing our angles. The Law of Sines was used to calculate architectural angles across the building, from the pitch of the Atrium escalators to the curve of the archways in front of you.
At Sphere, almost every equation you’ll see circles back to Pi. Defined as the ratio of the circumference of any circle to its diameter, it’s how we can calculate everything from the size of our pizzas to the exact location of the best seat in the house.
Stereographic Projection helps explain how immersive imagery works at Sphere. Our custom cameras take cues from this formula to capture ultra-wide imagery that fits seamlessly onto Sphere’s curved LED canvas – while mirroring the science of how the human eye sees the real world around it.
Ever met anyone with perfect 20/20 vision? The equation for Visual Acuity calculates the smallest dot the eye can see at a particular distance. Your eye doctor uses it to figure out your prescription. We used it at Sphere to calculate how many pixels it would take to display images in ultra-high resolution.
Snell’s Law informs how light travels through the lenses of Sphere’s immersive cameras. If you’ve ever twisted a lens or moved your camera to focus better on an image, that’s this equation in action – it’s what allows us to display crystal clear images in 16K, perfectly in focus.
Lens Projection Formulas
At Sphere, our giant LED screen wraps over and behind the audience, delivering a totally immersive visual environment. We use Lens Projection Formulas and the math of spherical trigonometry inform how we map the images we capture onto this gigantic curved display.
Sit down, grab a drink, and get comfy. Fanger’s Equation predicts how temperature changes are “felt” by Sphere’s audience. We used it to calculate everything from the ideal setting of our AC system, to the degree drop it takes to make you feel immersed in a 4D blizzard.
Linear Stress Constitutive Equation
How can Sphere’s 4D effects units simulate the force of an explosion without exploding themselves? The Linear Stress Constitutive Equation dictates how much air can be pushed through a material without breaking or warping – in our case, 1.499 million cubic feet per minute!
The Venturi Effect is an equation that’s all about going with the flow – specifically the air flow that powers our 4D wind effects. Though we prefer a slight breeze, Sphere’s effects units can technically achieve blasts of up to 140 mph. That’s enough to blow the roof off a building!
At Sphere, you may occasionally find yourself in a fog. The Navier-Stokes Equations are a set of formulas used to calculate the flow and thrust of our 4D effects, enabling us to create otherworldly atmospherics inside the theatre.
There’s nothing worse than lag when you’re playing a video game. Using the hidden math of the Shannon Hartley Theorem, Sphere was able to create an ultra-fast wireless environment so that 10,000 people can interact with our screen simultaneously from any seat in the house.
Wave-field synthesis is the magical math behind the best quality sound in the business. The Huygens-Fresnel Principle describes how sound waves propagate and combine into new wave forms. This allows Sphere to optimize for your ears, maintain amplitude over distance, and deliver immersive soundscapes with lifelike precision.
The Helmholtz Equation is used to calculate how 3D sound travels through Sphere. Behind our LED media plane, there are 168,000 speakers that use this math to create realistic, 360 audio environments leveraging a new sonic technology known as “wave field synthesis.”
The Kirchhoff-Helmholtz Integral is the equation behind Sphere’s crystal clear audio. In most venues, sound scattering is a major problem, with some seats getting a much better sonic experience than others. In Sphere, the power of math helps us ensure optimal audio for every seat in the house.
Kirchhoff Integral Theorem
The Kirchhoff Integral Theorem is the hidden equation behind Sphere’s ability to direct sound like laser beams. With it, we can deliver unique audio experiences to different listening locations all across the venue. Keep an ear out for them as you explore.
Woah, did you feel that? Infrasound is audio that you can feel but not hear. The Wave Equation is used to program and control Sphere’s infrasound seating and audio systems – enabling us to simulate a range of amazing, ultra-sensory effects, from the swell of the tide to a total shift in gravity.
At Sphere, we’re not just sending out light and music into space – we’re also receiving it. The equations of Hartley’s Law inform how data can be transmitted across vast distances. So the next time you see a live feed of earth or stars, or space sounds on the Exosphere, that’s this equation in action!
Take out your phone and take a selfie. Notice how your camera immediately figured out where your face was? The Laplacian Operator is an equation that informs the how cameras and computers can understand what they’re looking at. We use AI tools like this at Sphere to help capture and process our own imagery in ultra-high resolution.
Cauchy Momentum Equation
Hey! What’s that smell? The Cauchy Momentum Equation was used to the pipe and hose sizes for carrying the super-heated steam and compressed air used to power Sphere’s atmospheric effects.
When visiting Sphere, you’ll likely be transported to some pretty amazing places, from the far reaches of space, to the bottom of the ocean. The Sellmeier Equation helps us understand how light filters through different environments so we can capture them as close to life as possible.