Illustration (split-screen) of helicopter on Earth flying compared with Ingenuity flying on Mars.


The "Pi in the Sky" math challenge gives students a chance to take part in recent discoveries and upcoming celestial events, all while using math and pi just like NASA scientists and engineers. In this problem from the eighth set, students use the mathematical constant pi to determine how quickly the Ingenuity helicopter's blades must rotate in order for it to fly.



On the right hand side of the image, the Perseverance Mars rover looks forward toward the camera. In the lower left, the Ingenuity helicopter sits on the surface of Mars.

NASA’s Perseverance Mars rover took a selfie with the Ingenuity helicopter, seen here about 13 feet (3.9 meters) from the rover on April 6, 2021. Image credit: NASA/JPL-Caltech/MSSS | + Expand image

Joining the Perseverance rover on Mars is the first helicopter designed to fly on another planet. Named Ingenuity, the helicopter is a technology demonstration, meaning it's a test to see if a similar device could be used for a future Mars mission. To achieve the first powered flight on another planet, Ingenuity must spin its blades at a rapid rate to generate lift in Mars’ thin atmosphere. In Whirling Wonder, students use pi to compare the spin rate of Ingenuity’s blades to those of a typical helicopter on Earth.


Joining the Perseverance rover on Mars is a small helicopter named Ingenuity. With twin counter-rotating blades spanning 1.2 meters, Ingenuity is a test of new technology and is designed to achieve the first powered flight on another world.

Despite Mars having less gravity than Earth, the atmosphere on the Red Planet is much thinner than it is here on our home planet. This makes it challenging to lift off the ground on Mars. To generate enough lift for Ingenuity, engineers determined that the helicopter's blades need to rotate at approximately 250 radians per second on Mars.

How fast – in rotations per minute – do Ingenuity’s blades spin?

How does that compare to a typical helicopter on Earth with blades that spin at 500 rotations per minute?

› Learn more about the Ingenuity helicopter

Illustration (split-screen) of helicopter on Earth flying compared with Ingenuity flying on Mars.

Image credit: NASA/JPL-Caltech | › Download PDF


Illustrated answer key for the Sample Science problem

Image credit: NASA/JPL-Caltech | + Expand image

Download text-only answer key (doc)


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