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!

Visit the Pi in the Sky 10 lesson page to explore classroom resources and downloads for the 2023 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

This illustration shows a concept for multiple robots that would team up to ferry to Earth samples of rocks and soil being collected from the Martian surface by NASA's Mars Perseverance rover. Image credit: NASA/JPL-Caltech | › Full image and caption

Image from animation comparing the relative sizes of James Webb's primary mirror to Hubble's primary mirror. Credit: NASA/Goddard Space Flight Center . | › Full animation

This illustration depicts the metal-rich asteroid Psyche, which is located in the main asteroid belt between Mars and Jupiter. Credits: NASA/JPL-Caltech/ASU | + Full image and caption

This image sequence shows an annular solar eclipse from May 2012. The bottom right frame illustrates the distinctive ring, or "annulus," of such eclipses. A similar eclipse will be visible from the South Pacific on May 10, 2013. Credits: Brocken Inaglory, CC BY-SA 3.0, via Wikimedia Commons | + Expand image

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.

› Take the NASA Pi Day Challenge

› Educators, get the lesson here!

Tubular Tally

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.

Rad Reflection

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.

Metal Math

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.

Eclipsing Enigma

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.

Teach It

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.

  Grades 4-12

  Time Varies

• 
  NASA Pi Day Challenge

  The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.

  Grades 4-12

  Time Varies

• 
  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.

• 

  Downloads

  Can't get enough pi? Download this year's NASA Pi Day Challenge graphics, including mobile phone and desktop backgrounds:

  • Pi in the Sky 10 Poster (PDF, 11.3 MB)
  • Perseverance Mars Rover Background: Phone | Desktop
  • James Webb Space Telescope Background: Phone | Desktop
  • Psyche Mission Background: Phone | Desktop
  • 2023 Eclipse Background: Phone | Desktop
• 
  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.

  Subject Mathematics

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  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.

Plus, join the conversation using the hashtag #NASAPiDayChallenge on Facebook, Twitter, and Instagram.

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.

  Grades K-8

  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.

  Grades K-12

  Time Varies

• 
  Moon Phases

  Students learn about the phases of the moon by acting them out.

  Grades 1-6

  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.

  Grades 6-8

  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.

  Grades 9-12

  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.

  Grades 3-5

  Time 30 min to 1 hour

• 
  Math Rocks: A Lesson in Asteroid Dynamics

  Students use math to investigate a real-life asteroid impact.

  Grades 8-12

  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!

  Type Project

  Subject Engineering

• 
  Collection: Exploring Mars

  Make a cardboard rover, design a Mars exploration video game and explore more STEM projects, slideshows and videos for students.

  Type Project

  Subject Science

• 
  What's That Space Rock?

  Find out how to tell the difference between asteroids, comets, meteors, meteorites and other bodies in our solar system.

  Type Slideshow

  Subject Science

• 
  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.

  Type Slideshow

  Subject Science

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

• Asteroids Overview
• Eclipse Facts & Safety
• Mars Sample Handling
• Webb Telescope Key Facts

Websites

• Webb Space Telescope
• Mars Exploration
• Perseverance Mars Rover
• Mars Sample Return
• Psyche Mission
• MIRI Instrument
• 2023 Eclipse

Articles

• NASA’s Perseverance Rover Completes Mars Sample Depot

Videos

• Bringing Mars Rock Samples Back to Earth

Interactives

• Eyes on Asteroids

TAGS: Pi Day, Pi, Math, NASA Pi Day Challenge, sun, moon, earth, eclipse, asteroid, psyche, sample return, mars, perseverance, jwst, webb, hubble, telescope, miri

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  ABOUT THE AUTHOR

  Lyle Tavernier, Educational Technology Specialist, NASA-JPL Education Office

  Lyle Tavernier is an educational technology specialist at NASA's Jet Propulsion Laboratory. When he’s not busy working in the areas of distance learning and instructional technology, you might find him running with his dog, cooking or planning his next trip.