### Overview

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.

### Background

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.

### Procedures

#### 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?

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

### Assessment

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

### Extensions

#### Participate

Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge