Learn how pi is used by NASA and how many of its infinite digits have been calculated, then explore the science and engineering that makes the Pi Day Challenge possible.
Update: March 15, 2023 – The answers are here! Visit the NASA Pi Day Challenge page to view the illustrated answer keys for each problem.
This year marks the 10th installment of the NASA Pi Day Challenge. Celebrated on March 14, Pi Day is the annual holiday that pays tribute to the mathematical constant pi – the number that results from dividing any circle's circumference by its diameter.
Every year, Pi Day gives us a reason to celebrate the mathematical wonder that helps NASA explore the universe and enjoy our favorite sweet and savory pies. Students can join in the fun once again by using pi to explore Earth and space themselves in the NASA Pi Day Challenge.
Read on to learn more about the science behind this year's challenge and find out how students can put their math mettle to the test to solve real problems faced by NASA scientists and engineers as we explore Earth, Mars, asteroids, and beyond!
How It Works
Dividing any circle’s circumference by its diameter gives you an answer of pi, which is usually rounded to 3.14. Because pi is an irrational number, its decimal representation goes on forever and never repeats. In 2022, mathematician Simon Plouffe discovered the formula to calculate any single digit of pi. In the same year, teams around the world used cloud computing technology to calculate pi to 100 trillion digits. But you might be surprised to learn that for space exploration, NASA uses far fewer digits of pi.
Here at NASA, we use pi to measure the area of telescope mirrors, determine the composition of asteroids, and calculate the volume of rock samples. But pi isn’t just used for exploring the cosmos. Since pi can be used to find the area or circumference of round objects and the volume or surface area of shapes like cylinders, cones, and spheres, it is useful in all sorts of ways. Transportation teams use pi when determining the size of new subway tunnels. Electricians can use pi when calculating the current or voltage passing through circuits. And you might even use pi to figure out how much fencing is needed around a circular school garden bed.
In the United States, March 14 can be written as 3.14, which is why that date was chosen for celebrating all things pi. 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 that's precisely what the NASA Pi Day Challenge is all about!
The Science Behind the 2023 NASA Pi Day Challenge
This 10th installment of the NASA Pi Day Challenge includes four noodle-nudgers that get students using pi to calculate the amount of rock sampled by the Perseverance Mars rover, the light-collecting power of the James Webb Space Telescope, the composition of asteroid (16) Psyche, and the type of solar eclipse we can expect in October.
Read on to learn more about the science and engineering behind each problem or click the link below to jump right into the challenge.
NASA’s Mars rover, Perseverance, was designed to collect rock samples that will eventually be brought to Earth by a future mission. Sending objects from Mars to Earth is very difficult and something we've never done before. To keep the rock cores pristine on the journey to Earth, the rover hermetically seals them inside a specially designed sample tube. Once the samples are brought to Earth, scientists will be able to study them more closely with equipment that is too large to make the trip to Mars. In Tubular Tally, students use pi to determine the volume of a rock sample collected in a single tube.
When NASA launched the Hubble Space Telescope in 1990, scientists hoped that the telescope, with its large mirror and sensitivity to ultraviolet, visible, and near-infrared light, would unlock secrets of the universe from an orbit high above the atmosphere. Indeed, their hope became reality. Hubble’s discoveries, which are made possible in part by its mirror, rewrote astronomy textbooks. In 2022, the next great observatory, the James Webb Space Telescope, began exploring the infrared universe with an even larger mirror from a location beyond the orbit of the Moon. In Rad Reflection, students use pi to gain a new understanding of our ability to peer deep into the cosmos by comparing the area of Hubble’s primary mirror with the one on Webb.
Orbiting the Sun between Mars and Jupiter, the asteroid (16) Psyche is of particular interest to scientists because its surface may be metallic. Earth and other terrestrial planets have metal cores, but they are buried deep inside the planets, so they are difficult to study. By sending a spacecraft to study Psyche up close, scientists hope to learn more about terrestrial planet cores and our solar system’s history. That's where NASA's Psyche comes in. The mission will use specialized tools to study Psyche's composition from orbit. Determining how much metal exists on the asteroid is one of the key objectives of the mission. In Metal Math, students will do their own investigation of the asteroid's makeup, using pi to calculate the approximate density of Psyche and compare that to the density of known terrestrial materials.
On Oct. 14, 2023, a solar eclipse will be visible across North and South America, as the Moon passes between Earth and the Sun, blocking the Sun's light from our perspective. Because Earth’s orbit around the Sun and the Moon’s orbit around Earth are not perfect circles, the distances between them change throughout their orbits. Depending on those distances, the Sun's disk area might be fully or only partially blocked during a solar eclipse. In Eclipsing Enigma, students get a sneak peek at what to expect in October by using pi to determine how much of the Sun’s disk will be eclipsed by the Moon and whether to expect a total or annular eclipse.
Celebrate Pi Day by getting students thinking like NASA scientists and engineers to solve real-world problems in the NASA Pi Day Challenge. In addition to solving this year’s challenge, you can also dig into the more than 30 puzzlers from previous challenges available in our Pi Day collection. Completing the problem set and reading about other ways NASA uses pi is a great way for students to see the importance of the M in 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.
National Council of Teachers of Mathematics: Notice and Wonder
Creative brainstorming through noticing and wondering encourages student participation, engagement, and students' understanding of the NASA Pi Day Challenge.
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 create 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
NASA's Mission to Mars Student Challenge
Take part in the exploration of Mars and bring students along for the ride with NASA's Perseverance rover.
Students learn about the phases of the moon by acting them out.
Time 30 min to 1 hour
Modeling the Earth-Moon System
Students learn about scale models and distance by creating a classroom-size Earth-Moon system.
Time 30 min to 1 hour
Math of the Expanding Universe
Students will learn about the expanding universe and the redshift of lightwaves, then perform their own calculations with a distant supernova.
Time 30 min to 1 hour
The Expanded Universe: Playing with Time Activity Guide
In this activity, participants use balloons to model the expansion of the universe and observe how expansion affects wavelengths of light and distance between galaxies
James Webb Space Telescope STEM Toolkit
Find a collection of resources, activities, videos, and more for your students to learn about NASA’s newest space observatory.
Modeling an Asteroid
Lead a discussion about asteroids and their physical properties, then have students mold their own asteroids out of clay.
Time 30 min to 1 hour
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
How to Make a Pinhole Camera
Learn how to make your very own pinhole camera to safely see a solar eclipse in action!
Collection: Exploring Mars
Make a cardboard rover, design a Mars exploration video game and explore more STEM projects, slideshows and videos for students.
What's That Space Rock?
Find out how to tell the difference between asteroids, comets, meteors, meteorites and other bodies in our solar system.
10 Things We Can Learn from Webb's First Images
Take a closer look at how images from NASA's most powerful space telescope yet are helping to answer some of astronomers' most burning questions.
Recursos en español
18 Maneras en Que la NASA Usa Pi
Pi nos lleva lejos en la NASA. Estas son solo algunas de las formas en que pi nos ayuda a explorar el espacio.
Facts and Figures
- Webb Space Telescope
- Mars Exploration
- Perseverance Mars Rover
- Mars Sample Return
- Psyche Mission
- MIRI Instrument
- 2023 Eclipse
UPDATE - May 9, 2016: NASA's Solar Dynamics Observatory, or SDO, spacecraft captured stunning images of the May 9, 2016 transit of Mercury. Visit the mission's Transit of Mercury page to see a collection of videos of the transit compiled using SDO images. And have students play "Can You Spot Mercury?" in our educational slideshow.
In the News
It only happens about 13 times per century and hasn’t happened in nearly a decade, but on Monday, May 9, Mercury will transit the sun. A transit happens when a planet crosses in front of a star. From our perspective on Earth, we only ever see two planets transit the sun: Mercury and Venus. (Transits of Venus are even more rare. The next one won't happen until 2117!) On May 9, as Mercury passes in front of the sun, viewers around Earth (using the proper safety equipment) will be able to see a tiny dark spot moving slowly across the disk of the sun.
CAUTION: Looking directly at the sun can cause permanent vision damage – see below for tips on how to safely view the transit.
Why It's Important
Then and Now
In the early 1600s, Johannes Kepler discovered that both Mercury and Venus would transit the sun in 1631. It was fortunate timing: The telescope had been invented just 23 years earlier and the transits wouldn’t happen in the same year again until 13425. Kepler didn’t survive to see the transits, but French astronomer Pierre Gassendi became the first person to see the transit of Mercury (the transit of Venus wasn’t visible from Europe). It was soon understood that transits could be used as an opportunity to measure the apparent diameter – how large a planet appears from Earth – with great accuracy.
In 1677, Edmond Halley observed the transit of Mercury and realized that the parallax shift of the planet – the variation in Mercury’s apparent position against the disk of the sun as seen by observers at distant points on Earth – could be used to accurately measure the distance between the sun and Earth, which wasn’t known at the time.
Today, radar is used to measure the distance between Earth and the sun with greater precision than can be found using transit observations, but the transit of Mercury still provides scientists with opportunities for scientific investigation in two important areas: exospheres and exoplanets.
Some objects, like the moon and Mercury, were originally thought to have no atmosphere. But scientists have discovered that these bodies are actually surrounded in an ultra-thin atmosphere of gases called an exosphere. Scientists want to better understand the composition and density of the gases that make up Mercury’s exosphere and transits make that possible.
“When Mercury is in front of the sun, we can study the exosphere close to the planet,” said NASA scientist Rosemary Killen. “Sodium in the exosphere absorbs and re-emits a yellow-orange color from sunlight, and by measuring that absorption, we can learn about the density of gas there.”
When Mercury transits the sun, it causes a slight dip in the sun’s brightness as it blocks a tiny portion of the sun's light. Scientists discovered they could use that phenomenon to search for planets orbiting distant stars, called exoplanets, that are otherwise obscured from view by the light of the star. When measuring the brightness of far-off stars, a slight recurring dip in the light curve (a graph of light intensity) could indicate an exoplanet orbiting and transiting its star. NASA’s Kepler mission has found more than 1,000 exoplanets by looking for this telltale drop in brightness.
Additionally, scientists have begun exploring the exospheres of exoplanets. By observing the spectra of the light that passes through an exosphere – similar to how we study Mercury’s exosphere – scientists are beginning to understand the evolution of exoplanet atmospheres as well as the influence of stellar wind and magnetic fields.
Mercury will appear as a tiny dot on the sun’s surface and will require a telescope or binoculars with a special solar filter to see. Looking at the sun directly or through a telescope without proper protection can lead to serious and permanent vision damage. Do not look directly at the sun without a solar filter.
The transit of Mercury will begin at 4:12 a.m. PDT, meaning by the time the sun rises on the West Coast, Mercury will have been transiting the sun for nearly two hours. Fortunately, it will take seven and a half hours for Mercury to completely cross the sun’s face, so there will be plenty of time for West Coast viewers to witness this event. See the transit map to learn when and where the transit will be visible.
Don’t have access to a telescope, binoculars or a solar filter? Visit the Night Sky Network website for the location of events near you where amateur astronomers will have viewing opportunities available.
NASA also will stream a live program on NASA TV and the agency’s Facebook page from 7:30 to 8:30 a.m. PDT (10:30 to 11:30 a.m. EDT) -- an informal roundtable during which experts representing planetary, heliophysics and astrophysics will discuss the science behind the Mercury transit. Viewers can ask questions via Facebook and Twitter using #AskNASA.
Here are two ways to turn the transit of Mercury into a lesson for students.
- Exploring Exoplanets with Kepler - Students use math concepts related to transits to discover real-world data about Mercury, Venus and planets outside our solar system.
- Pi in the Sky 3 - Try the "Sun Screen" problem on this illustrated math problem set that has students calculate the percentage drop in sunlight reaching Earth when Mercury transits.
- NASA TV (live transit coverage)
- NASA Transit Website (near real-time images of the transit)
- Night Sky Network Events
- Video: What’s Up – May 2016
- Transit Map
- Solar System Transits
- NASA Museum Alliance Resources
- Kepler Mission Website
- Exoplanet Exploration Website
- Eyes on Exoplanets Interactive
- Exoplanet Travel Bureau Posters
- Video: What’s in an Exoplanet Name?
- Video: The Search for Another Earth
- Kepler Education Activities