Update: March 15, 2021 – The answers are here! Visit the NASA Pi Day Challenge slideshow to view the illustrated answer keys (also available as a text-only doc) with each problem.
Learn about pi and the history of Pi Day before exploring some of the ways the number is used at NASA. Then, try the math for yourself in our Pi Day Challenge.
In the News
As March 14 approaches, it’s time to get ready to celebrate Pi Day! It’s the annual holiday that pays tribute to the mathematical constant pi – the number that results from dividing any circle's circumference by its diameter.
Pi Day comes around only once a year, giving us a reason to chow down on our favorite sweet and savory pies while we appreciate the mathematical marvel that helps NASA explore Earth, the solar system, and beyond. There’s no better way to observe this day than by getting students exploring space right along with NASA by doing the math in our Pi Day Challenge. Keep reading to find out how students – and you – can put their math mettle to the test and solve real problems faced by NASA scientists and engineers as they explore the cosmos!
How It Works
Dividing any circle’s circumference by its diameter gives us pi, which is often rounded to 3.14. However, pi is an irrational number, meaning its decimal representation goes on forever and never repeats. Pi has been calculated to 50 trillion digits, but NASA uses far fewer for space exploration.
Some people may think that a circle has no points. In fact, a circle does have points, and knowing what pi is and how to use it is far from pointless. Pi is used for calculating the area and circumference of circular objects and the volume of shapes like spheres and cylinders. So it's useful for everyone from farmers storing crops in silos to manufacturers of water storage tanks to people who want to find the best value when ordering a pizza. At NASA, we use pi to find the best place to touch down on Mars, study the health of Earth's coral reefs, measure the size of a ring of planetary debris light years away, and lots more.
In the United States, one format to write March 14 is 3.14, which is why we celebrate on that date. In 2009, the U.S. House of Representatives passed a resolution officially designating March 14 as Pi Day and encouraging teachers and students to celebrate the day with activities that teach students about pi. And you're in luck, because that's precisely what the NASA Pi Day Challenge is all about.
The Science Behind the 2021 NASA Pi Day Challenge
This year, the NASA Pi Day Challenge offers up four brain-ticklers that will require students to use pi to collect samples from an asteroid, fly a helicopter on Mars for the first time, find efficient ways to talk with distant spacecraft, and study the forces behind Earth's beautiful auroras. Learn more about the science and engineering behind the problems below or click the link below to jump right into the challenge. Be sure to check back on March 15 for the answers to this year’s challenge.
NASA’s OSIRIS-REx mission has flown to an asteroid and collected a sample of surface material to bring back to Earth. (It will arrive back at Earth in 2023.) The mission is designed to help scientists understand how planets form and add to what we know about near-Earth asteroids, like the one visited by OSIRIS-REx, asteroid Bennu. Launched in 2016, OSIRIS-REx began orbiting Bennu in 2018 and successfully performed its maneuver to retrieve a sample on October 20, 2020. In the Sample Science problem, students use pi to determine how much of the spacecraft's sample-collection device needs to make contact with the surface of Bennu to meet mission requirements for success.
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 Twirly Whirly, students use pi to compare the spin rate of Ingenuity’s blades to those of a typical helicopter on Earth.
NASA uses radio signals to communicate with spacecraft across the solar system and in interstellar space. As more and more data flows between Earth and these distant spacecraft, NASA needs new technologies to improve how quickly data can be received. One such technology in development is Deep Space Optical Communications, which will use near-infrared light instead of radio waves to transmit data. Near-infrared light, with its higher frequency than radio waves, allows for more data to be transmitted per second. In Signal Solution, students can compare the efficiency of optical communication with radio communication, using pi to crunch the numbers.
Earth’s magnetic field extends from within the planet to space, and it serves as a protective shield, blocking charged particles from the Sun. Known as the solar wind, these charged particles of helium and hydrogen race from the Sun at hundreds of miles per second. When they reach Earth, they would bombard our planet and orbiting satellites were it not for the magnetic field. Instead, they are deflected, though some particles become trapped by the field and are directed toward the poles, where they interact with the atmosphere, creating auroras. Knowing how Earth’s magnetic field shifts and how particles interact with the field can help keep satellites in safe orbits. In Force Field, students use pi to calculate how much force a hydrogen atom would experience at different points along Earth’s magnetic field.
Pi Day is a fun and engaging way to get students thinking like NASA scientists and engineers. By solving the NASA Pi Day Challenge problems below, reading about other ways NASA uses pi, and doing the related activities, students can see first hand how math is an important part of STEM.
Pi Day Resources
Pi in the Sky Lessons
Here's everything you need to bring the NASA Pi Day Challenge into the classroom.
NASA Pi Day Challenge
The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.
How Many Decimals of Pi Do We Really Need?
While you may have memorized more than 70,000 digits of pi, world record holders, a JPL engineer explains why you really only need a tiny fraction of that for most calculations.
18 Ways NASA Uses Pi
Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.
10 Ways to Celebrate Pi Day With NASA on March 14
Find out what makes pi so special, how it’s used to explore space, and how you can join the celebration with resources from NASA.
Infographic: Planet Pi
This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.
Pi Day: What's Going 'Round
Tell us what you're up to this Pi Day and share your stories and photos on our showcase page.
Related Lessons for Educators
Robotic Arm Challenge
In this challenge, students will use a model robotic arm to move items from one location to another. They will engage in the engineering design process to design, build and operate the arm.
Time 30 min to 1 hour
Whip Up a Moon-Like Crater
Whip up a moon-like crater with baking ingredients as a demonstration for students.
Time 30 min to 1 hour
Make a Paper Mars Helicopter
In this lesson, students build a paper helicopter, then improve the design and compare and measure performance.
Time 30 min to 1 hour
Speaking in Phases
Students learn how waves are used in communication between far-away spacecraft and the Deep Space Network on Earth.
Time 30 min to 1 hour
Catching a Whisper from Space
Students kinesthetically model the mathematics of how NASA communicates with spacecraft.
Time 1-2 hours
Collecting Light: Inverse Square Law Demo
In this activity, students learn how light and energy are spread throughout space. The rate of change can be expressed mathematically, demonstrating why spacecraft like NASA’s Juno need so many solar panels.
Time under 30 min
Build a Relay Inspired by Space Communications
In this intermediate-level programming challenge, students use microdevices along with light and mirrors to build a relay that can send information to a distant detector.
Time 1-2 hours
Math Rocks: A Lesson in Asteroid Dynamics
Students use math to investigate a real-life asteroid impact.
Time 30 min to 1 hour
Related Activities for Students
Code a Mars Helicopter Video Game
Create a video game that lets players explore the Red Planet with a helicopter like the one going to Mars with NASA's Perseverance rover!
Make a Paper Mars Helicopter
Build a paper helicopter, then see if you can improve the design like NASA engineers did when making the first helicopter for Mars.
How Does NASA Spot a Near-Earth Asteroid?
Watch this one-minute video to find out how NASA spots and tracks asteroids that fly close to Earth.
What's That Space Rock?
Find out how to tell the difference between asteroids, comets, meteors, meteorites and other bodies in our solar system.
Facts and Figures
Missions and Instruments
TAGS: Pi, Pi Day, NASA Pi Day Challenge, Math, Mars, Perseverance, Ingenuity, Mars Helicopter, OSIRIS-REx, Bennu, Asteroid, Auroras, Earth, Magnetic Field, DSOC, Light Waves, DSN, Deep Space Network, Space Communications
Update: March 15, 2018 – The answers to the 2018 NASA Pi Day Challenge are here! View the illustrated answer key
In the News
The 2018 NASA Pi Day Challenge
Can you solve these stellar mysteries with pi? Click to get started.
Pi Day, the annual celebration of one of mathematics’ most popular numbers, is back! Representing the ratio of a circle’s circumference to its diameter, pi has many practical applications, including the development and operation of space missions at NASA’s Jet Propulsion Laboratory.
The March 14 holiday is celebrated around the world by math enthusiasts and casual fans alike – from memorizing digits of pi (the current Pi World Ranking record is 70,030 digits) to baking and eating pies.
JPL is inviting people to participate in its 2018 NASA Pi Day Challenge – four illustrated math puzzlers involving pi and real problems scientists and engineers solve to explore space, also available as a free poster! Answers will be released on March 15.
Why March 14?
Pi is what’s known as an irrational number, meaning its decimal representation never ends and it never repeats. It has been calculated to more than one trillion digits, but NASA scientists and engineers actually use far fewer digits in their calculations (see “How Many Decimals of Pi Do We Really Need?”). The approximation 3.14 is often precise enough, hence the celebration occurring on March 14, or 3/14 (when written in U.S. month/day format). The first known celebration occurred in 1988, and in 2009, the U.S. House of Representatives passed a resolution designating March 14 as Pi Day and encouraging teachers and students to celebrate the day with activities that teach students about pi.
NASA’s Pi Day Challenge
Lessons: Pi in the Sky
Explore the entire NASA Pi Day Challenge lesson collection, including free posters and handouts!
To show students how pi is used at NASA and give them a chance to do the very same math, the JPL Education Office has once again put together a Pi Day challenge featuring real-world math problems used for space exploration. This year’s challenge includes exploring the interior of Mars, finding missing helium in the clouds of Jupiter, searching for Earth-size exoplanets and uncovering the mysteries of an asteroid from outside our solar system.
Here’s some of the science behind this year’s challenge:
Scheduled to launch May 5, 2018, the InSight Mars lander will be equipped with several scientific instruments, including a heat flow probe and a seismometer. Together, these instruments will help scientists understand the interior structure of the Red Planet. It’s the first time we’ll get an in-depth look at what’s happening inside Mars. On Earth, seismometers are used to measure the strength and location of earthquakes. Similarly, the seismometer on Insight will allow us to measure marsquakes! The way seismic waves travel through the interior of Mars can tell us a lot about what lies beneath the surface. This year’s Quake Quandary problem challenges students to determine the distance from InSight to a hypothetical marsquake using pi!
Also launching in spring is NASA’s Transiting Exoplanet Survey Satellite, or TESS, mission. TESS is designed to build upon the discoveries made by NASA’s Kepler Space Telescope by searching for exoplanets – planets that orbit stars other than our Sun. Like Kepler, TESS will monitor hundreds of thousands of stars across the sky, looking for the temporary dips in brightness that occur when an exoplanet passes in front of its star from the perspective of TESS. The amount that the star dims helps scientists determine the radius of the exoplanet. Like those exoplanet-hunting scientists, students will have to use pi along with data from Kepler to find the size of an exoplanet in the Solar Sleuth challenge.
Jupiter is our solar system’s largest planet. Shrouded in clouds, the planet’s interior holds clues to the formation of our solar system. In 1995, NASA’s Galileo spacecraft dropped a probe into Jupiter’s atmosphere. The probe detected unusually low levels of helium in the upper atmosphere. It has been hypothesized that the helium was depleted out of the upper atmosphere and transported deeper inside the planet. The extreme pressure inside Jupiter condenses helium into droplets that form inside a liquid metallic hydrogen layer below. Because the helium is denser than the surrounding hydrogen, the helium droplets fall like rain through the liquid metallic hydrogen. In 2016, the Juno spacecraft, which is designed to study Jupiter’s interior, entered orbit around the planet. Juno’s initial gravity measurements have helped scientists better understand the inner layers of Jupiter and how they interact, giving them a clearer window into what goes on inside the planet. In the Helium Heist problem, students can use pi to find out just how much helium has been depleted from Jupiter’s upper atmosphere over the planet’s lifetime.
In October 2017, astronomers spotted a uniquely-shaped object traveling in our solar system. Its path and high velocity led scientists to believe ‘Oumuamua, as it has been dubbed, is actually an object from outside of our solar system – the first ever interstellar visitor to be detected – that made its way to our neighborhood thanks to the Sun’s gravity. In addition to its high speed, ‘Oumuamua is reflecting the Sun’s light with great variation as the asteroid rotates on its axis, causing scientists to conclude it has an elongated shape. In the Asteroid Ace problem, students can use pi to find the rate of rotation for ‘Oumuamua and compare it with Earth’s rotation rate.
Join the Conversation
- Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge
- Pi Day: What’s Going ‘Round – Tell us what you’re up to this Pi Day and share your stories and photos with NASA.
- Pi in the Sky 5
- Pi in the Sky 4
- Pi in the Sky 3
- Pi in the Sky 2
- Pi in the Sky
- Pi in the Sky Challenge (slideshow for students)
- 18 Ways NASA Uses Pi – Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.
- Kepler-186f Travel Poster
- Video: First Interstellar Asteroid Wows Scientists
- Planet Pi
Facts and Figures
TAGS: Pi Day, Math, Science, Engineering, NASA Pi Day Challenge, K-12, Lesson, Activity, Slideshow, Mars, Jupiter, Exoplanets, Kepler, Kepler-186f, Juno, InSight, TESS, ‘Oumuamua, asteroid, asteroids, NEO, Nearth Earth Object