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 11th set, students use pi to determine how far a team of rovers drive on the Moon.



A small rover is attached to an elevated rack while two engineers hold their hands out toward the underside of the rover.

Engineers test the system that will lower three small rovers onto the lunar surface as part of the CADRE project. Image credit: NASA/JPL-Caltech | > Full image and caption

Moon Mappers

The CADRE project aims to land a team of mini rovers on the Moon in 2025 as a test of new exploration technology. Three suitcase-size rovers, each working mostly autonomously, will communicate with each other and a base station on their lunar lander to simultaneously measure data from different locations. If successful, the project could open the door for future multi-robot exploration missions. In Moon Mappers, students explore the Moon with pi by determining how far a CADRE rover drives on the Moon’s surface.


Moon Mappers

NASA’s CADRE project is made up of a network of three small rovers. The rovers are designed to work together to create a 3D map of a scientifically intriguing area of the Moon's surface known as Reiner Gamma. Communicating with each other and a base station aboard a lunar lander, the rovers will be largely autonomous, making decisions and acting without the need for constant human intervention.

Each suitcase-size rover has a field of view that is about π/2 radians wide, and its sensors can accurately map as far as 2 meters ahead. Assuming the rovers drive in a “lawnmower” pattern, how far does each rover have to drive to survey its portion of a 20 m x 20 m square of the Moon’s surface?

› Learn more about the CADRE project

A sensor beam in the shape of a sector of a circle extends from the eye-like cameras of a small lunar rover. The angle measure of the sector is π/2 and the length of the segment radius is 2 meters. An inset depicts three rovers inside a square area driving in a lawnmower pattern – going horizontally, turning vertically, then driving horizontally in the other direction.

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


Illustrated answer key for the Moon Mapper problem.

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

Download text-only answer key (Google Docs)



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