Collage of illustrations featured in the 2024 NASA Pi Day Challenge

Learn how pi is used by NASA and how many of its infinite digits have been calculated, then explore the science and engineering behind the 2024 Pi Day Challenge.


Update: March 15, 2024 – The answers to the 2024 NASA Pi Day Challenge are here! Take a peek at the illustrated answer key now available under each problem on the NASA Pi Day Challenge page.


This year marks the 11th 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 on March 14, Pi Day gives us a reason to enjoy our favorite sweet and savory pies and celebrate the mathematical wonder that helps NASA explore the universe. Students can join in the fun once again by using pi to explore Earth and space themselves with the NASA Pi Day Challenge.

Read on to learn more about the science behind this year's challenge and get students solving real problems faced by NASA scientists and engineers exploring Earth, the Moon, asteroids, and beyond!

Infographic of all of the Pi in the Sky 11 graphics and problems

Visit the Pi in the Sky 11 lesson page to explore classroom resources and downloads for the 2024 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

What is Pi

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 map the Moon, measure Earth’s changing surface, receive laser-coded messages from deep space, and calculate asteroid orbits. 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 2024 NASA Pi Day Challenge

This 11th installment of the NASA Pi Day Challenge includes four illustrated math problems designed to get students thinking like scientists and engineers to calculate how to get a laser message to Earth, the change in an asteroid’s orbit, the amount of data that can be collected by an Earth satellite, and how a team of mini rovers will map portions of the Moon’s surface.

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!

Receiver Riddle

In December 2023, NASA tested a new way to communicate with distant spacecraft using technology called Deep Space Optical Communications, or DSOC. From 19,000,000 miles (30,199,000 km) away, the Psyche spacecraft beamed a high-definition video encoded in a near-infrared laser to Earth. The video, showing a cat named Taters chasing a laser, traveled at the speed of light, where it was received at Caltech’s Palomar Observatory. Because of the great distance the laser had to travel, the team needed to aim the transmission at where Earth would be when the signal arrived. In Receiver Riddle, use pi to determine where along Earth's orbit the team needed to aim the laser so that it could be received at the Observatory at the correct moment.

This animation shows how DSOC's laser signals are sent between the Psyche spacecraft and ground stations on Earth - first as a pointing reference to ensure accurate aiming of the narrow laser signal and then as a data transmission to the receiving station. Credit: NASA/JPL-Caltech/ASU| Watch on YouTube

Daring Deflection

In 2022, NASA crashed a spacecraft into the asteroid Dimorphos in an attempt to alter its orbit. The mission, known as the Double Asteroid Redirection Test, or DART, took place at an asteroid that posed no threat to our planet. Rather, it was an ideal target for NASA to test an important element of its planetary defense plan. DART was designed as a kinetic impactor, meaning it transferred its momentum and kinetic energy to Dimorphos upon impact, altering the asteroid's orbit. In Daring Deflection, use pi to determine the shape of Dimorphos’ orbit after DART crashed into it.

An animation shows the surface of an asteroid getting closer and closer. In the last several frames, the animation slows and details of the rocky surface come into view.

This image shows the final minutes of images leading up to the DART spacecraft's intentional collision with asteroid Dimorphos. Credit: NASA/Johns Hopkins APL | › Enlarge image

Orbit Observation

The NISAR mission is an Earth orbiting satellite designed to study our planet's changing ecosystems. It will collect data about Earth's land- and ice-covered surfaces approximately every 6 days, allowing scientists to study changes at the centimeter scale – an unprecedented level of detail. To achieve this feat, NISAR will collect massive amounts of data. In Orbit Observation, students use pi to calculate how much data the NISAR spacecraft captures during each orbit of Earth.

An illustration shows the NISAR spacecraft orbiting above Earth.

The NISAR satellite, shown in this artist’s concept, will use advanced radar imaging to provide an unprecedented view of changes to Earth’s land- and ice-covered surfaces. 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.

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. Credit: NASA/JPL-Caltech | › Full image and caption

Bring the Challenge Into the Classroom

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 the 2024 challenge, you can also dig into the 40 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.

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TAGS: Pi Day, Pi, Math, NASA Pi Day Challenge, moon, earth, asteroid, psyche, DART, CADRE, NISAR DSOC

  • Lyle Tavernier
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Collage of illustrations featured in the 2023 NASA Pi Day Challenge

In this cartoonish illustration, various spacecraft are shown with notations such as circles and pi formulas. Text reads, NASA Pi Day Challenge Answers

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!

Infographic of all of the Pi in the Sky 10 graphics and problems

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

The Perseverance rover approaches a lander on the surface of Mars. A small rocket flies toward an orbiter overhead while a Mars helicopter flies in the background. A partially illuminated Earth appears in the distnace.

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

An illustration shows the 18 hexagonal pieces that make up the primary mirror of the James Webb Space Telescope next to the primary mirror of the Hubble Space Telescope. The James Webb Mirror stands taller with a label that reads 6.5 meters in height, while the Hubble mirror is labled with a diameter of 2.4 meters. Two human figures are shown smaller than the Hubble mirror for comparison.

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

An illustration shows the Psyche asteroid in a star field. The asteroid ranges in color from light grey to dark grey to brown and is covered with a rocky, cratered surface.

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

A composite of four images of the sun, each being covered by progressively more of the sun. The final image shows the sun eclipsed by the moon with a ring of light showing behind the moon that is too small to cover the entire disk of the sun.

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

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

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

  • Lyle Tavernier
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Pi to the 15th decimal is shown in a speckled starry band as a silhouetted face looks out over colorful concentric circles and black and white images of an atom, molecules, Earth, and the Voyager spacecraft. The left side of the image fades to black with

While world record holders may have memorized more than 70,000 digits of pi, a JPL engineer explains why you really only need a tiny fraction of that for most calculations – even at NASA.


Update: October 24, 2022 – This article, originally written in 2016, has been updated to reflect the latest values for NASA’s Voyager 1 spacecraft, which continues to venture farther into interstellar space. The author, Marc Rayman, has ventured on too, from the chief engineer for NASA’s Dawn mission, which concluded successfully in 2018, to the chief engineer for mission operations and science at NASA’s Jet Propulsion Laboratory.


The decimals of pi are listed out on an orange background with a large pi symbol in the background.

This graphic shows more than 500 of the infinite number of decimals in pi. Image credit: NASA/JPL-Caltech | + Expand image

We received this question from a fan on Facebook who wondered how many decimals of the never-ending mathematical constant pi (π) NASA-JPL scientists and engineers use when making calculations:

“Does JPL only use 3.14 for its pi calculations? Or do you use more decimals, like say [360 or even more]?”

Here’s JPL’s Chief Engineer for Mission Operations and Science, Marc Rayman, with the answer:

Thank you for your question! This isn't the first time I've heard a question like this. In fact, it was posed many years ago by a sixth-grade science and space enthusiast who was later fortunate enough to earn a doctorate in physics and become involved in space exploration. His name was Marc Rayman.

To start, let me answer your question directly. For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793. Let's look at this a little more closely to understand why we don't use more decimal places. I think we can even see that there are no physically realistic calculations scientists ever perform for which it is necessary to include nearly as many decimal points as you asked about. Consider these examples:

  1. The most distant spacecraft from Earth is Voyager 1. As of this writing, it’s about 14.7 billion miles (23.6 billion kilometers) away. Let’s be generous and call that 15 billion miles (24 billion kilometers). Now say we have a circle with a radius of exactly that size, 30 billion miles (48 billion kilometers) in diameter, and we want to calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 94 billion miles (more than 150 billion kilometers). We don't need to be concerned here with exactly what the value is (you can multiply it out if you like) but rather what the error in the value is by not using more digits of pi. In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 30-billion-mile (48-billion-kilometer) diameter circle would be wrong by less than half an inch (about one centimeter). Think about that. We have a circle more than 94 billion miles (more than 150 billion kilometers) around, and our calculation of that distance would be off by no more than the width of your little finger.
  2. The illustration shows a cartoonish Voyager 1 flying in space with a conical signal eminating from its antenna. An inset shows a more distant view of Voyager with a line extending to Earth and a distance label between the Voyager and Earth marked ~131 AU.

    Put your pi math skills to the test with this problem from NASA's Pi Day Challenge. Can you use pi to determine what fraction of a signal from Voyager 1 reaches Earth? Image credit: NASA/JPL-Caltech | + Expand image | › View lesson page

  3. We can bring this closer to home by looking at our planet, Earth. It is more than 7,900 miles (12,700 kilometers) in diameter at the equator. The circumference is roughly 24,900 miles (40,100 kilometers). That's how far you would travel if you circumnavigated the globe – and didn't worry about hills, valleys, and obstacles like buildings, ocean waves, etc. How far off would your odometer be if you used the limited version of pi above? The discrepancy would be the size of a molecule. There are many different kinds of molecules, of course, so they span a wide range of sizes, but I hope this gives you an idea. Another way to view this is that your error by not using more digits of pi would be more than 30,000 times thinner than a hair!
  4. A view of Earth from space showing East Africa, the Middle East, and Asia with swirls and splotches of clouds across the planet.

    Image credit: NASA | + Expand image

  5. Let's go to the largest size there is: the known universe. The radius of the universe is about 46 billion light years. Now let me ask (and answer!) a different question: How many digits of pi would we need to calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom, the simplest atom? It turns out that 37 decimal places (38 digits, including the number 3 to the left of the decimal point) would be quite sufficient. Think about how fantastically vast the universe is. It’s certainly far beyond what you can see with your eyes even on the darkest, most beautiful night of sparkling stars. It’s yet farther beyond the extraordinary vision of the James Webb Space Telescope. And the vastness of the universe is truly far, far, far beyond what we can even conceive. Now think about how incredibly tiny a single atom is. Isn’t it amazing that we wouldn’t need to use many digits of pi at all to cover that entire unbelievable range?
Link to text description available below

If you were to hold a single grain of sand at arm's length, you could cover the entire area of space taken up by this image, which was captured by the James Webb Space Telescope and contains thousands of galaxies. The oldest-known galaxy identified in the image is 13.1 billion years old. Image credit: NASA, ESA, CSA, STScI | + Expand image | › More about the image | Text description (PDF)

Pi is an intriguing number with interesting mathematical properties. It’s fun to think about its truly endless sequence of digits, and it may be surprising how often it appears in the equations scientists and engineers use. But there are no questions – prosaic or esoteric – in humankind’s noble efforts to explore or comprehend the marvels of the cosmos, from the unimaginably smallest scales to the inconceivably largest, that could require very many of those digits.

Hear more from Marc in his inspiring TEDx talk, “If It Isn’t Impossible, It Isn’t Worth Trying” and in his Dawn Journal, where he wrote frequent updates about the Dawn mission’s extraordinary extraterrestrial expedition to the protoplanet Vesta and dwarf planet Ceres.

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TAGS: Pi, Pi Day, Dawn, Voyager, Engineering, Science, Mathematics

  • NASA/JPL Edu
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Collage of spacecraft featured in the 2022 NASA Pi Day Challenge

Graphic showing the various spacecraft featured in the 2022 NASA Pi Day Challenge overlaid with text that reads NASA Pi Day Challenge Answers

Learn about pi and some of the ways the number is used at NASA. Then, dig into the science behind the Pi Day Challenge.


Update: March 15, 2022 – The answers are here! Visit the NASA Pi Day Challenge slideshow to view the illustrated answer keys for each of the problems in the 2022 challenge.

In the News

No matter what Punxsutawney Phil saw on Groundhog Day, a sure sign that spring approaches is Pi Day. Celebrated on March 14, 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.

Every year, Pi Day gives us a reason to not only celebrate the mathematical wonder that helps NASA explore the universe, but also to enjoy our favorite sweet and savory pies. Students can join in the fun by using pi to explore Earth and space themselves in our ninth annual 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, the Moon, Mars, and beyond!
Infographic of all of the Pi in the Sky 9 graphics and problems

Visit the Pi in the Sky 9 lesson page to explore classroom resources and downloads for the 2022 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

An spacecraft orbiting the Moon shines a laser into a dark crater.

This artist's concept shows the Lunar Flashlight spacecraft, a six-unit CubeSat designed to search for ice on the Moon's surface using special lasers. Image credit: NASA/JPL-Caltech | › Full image details

Dome-covered seismometer sits on the surface of Mars while clouds pass overhead.

Clouds drift over the dome-covered seismometer, known as SEIS, belonging to NASA's InSight lander, on Mars. Credit: NASA/JPL-Caltech. | › Full image and caption

The SWOT spacecraft passes over Florida, sending signals and collecting data.

This animation shows the collection of data over the state of Florida, which is rich with rivers, lakes and wetlands. Credits: NASA/JPL-Caltech | + Expand image

A spacecraft points to a star that has three planets orbiting it.

Illustration of NASA’s Transiting Exoplanet Survey Satellite (TESS). Credits: NASA | + 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 2021, a supercomputer calculated pi to more than 62 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 understand how much signal we can receive from a distant spacecraft, to calculate the rotation speed of a Mars helicopter blade, and to collect asteroid 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. Architects use pi when designing bridges or buildings with arches; electricians use pi when calculating the conductance of wire; and you might even want to use pi to figure out how much frozen goodness you are getting in your ice cream cone.

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 2022 NASA Pi Day Challenge

This ninth installment of the NASA Pi Day Challenge includes four brain-busters that get students using pi to measure frost deep within craters on the Moon, estimate the density of Mars’ core, calculate the water output from a dam to assess its potential environmental impact, and find how far a planet-hunting satellite needs to travel to send data back to Earth.

Read on to learn more about the science and engineering behind the problems or click the link below to jump right into the challenge.

› Take the NASA Pi Day Challenge

› Educators, get the lesson here!

Lunar Logic

NASA’s Lunar Flashlight mission is a small satellite that will seek out signs of frost in deep, permanently shadowed craters around the Moon’s south pole. By sending infrared laser pulses to the surface and measuring how much light is reflected back, scientists can determine which areas of the lunar surface contain frost and which are dry. Knowing the locations of water-ice on the Moon could be key for future crewed missions to the Moon, when water will be a precious resource. In Lunar Logic, students use pi to find out how much surface area Lunar Flashlight will measure with a single pulse from its laser.

Core Conundrum

Since 2018, the InSight lander has studied the interior of Mars by measuring vibrations from marsquakes and the “wobble” of the planet as it rotates on its axis. Through careful analysis of the data returned from InSight, scientists were able to measure the size of Mars’ liquid core for the first time and estimate its density. In Core Conundrum, students use pi to do some of the same calculations, determining the volume and density of the Red Planet’s core and comparing it to that of Earth’s core.

Dam Deduction

The Surface Water and Ocean Topography, or SWOT mission will conduct NASA's first global survey of Earth's surface water. SWOT’s state-of-the-art radar will measure the elevation of water in major lakes, rivers, wetlands, and reservoirs while revealing unprecedented detail on the ocean surface. This data will help scientists track how these bodies of water are changing over time and improve weather and climate models. In Dam Deduction, students learn how data from SWOT can be used to assess the environmental impact of dams. Students then use pi to do their own analysis, finding the powered output of a dam based on the water height of its reservoir and inferring potential impacts of this quick-flowing water.

Telescope Tango

The Transiting Exoplanet Survey Satellite, or TESS, is designed to survey the sky in search of planets orbiting bright, nearby stars. TESS does this while circling Earth in a unique, never-before-used orbit that brings the spacecraft close to Earth about once every two weeks to transmit its data. This special orbit keeps TESS stable while giving it an unobstructed view of space. In its first two years, TESS identified more than 2,600 possible exoplanets in our galaxy with thousands more discovered during its extended mission. In Telescope Tango, students will use pi to calculate the distance traveled by TESS each time it sends data back to Earth.

Teach It

Celebrate Pi Day by getting students thinking like NASA scientists and engineers to solve real-world problems in NASA Pi Day Challenge. 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

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

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TAGS: Pi Day, Pi, Math, NASA Pi Day Challenge, Moon, Lunar Flashlight, Mars, InSight, Earth, Climate, SWOT, Exoplanets, Universe, TESS, Teachers, Educators, Parents, Students, Lessons, Activities, Resources, K-12

  • Lyle Tavernier
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Illustration of spacecraft on a light blue background that reads "NASA Pi Day Challenge"

Cartoonish illustration of spacecraft on a dark purple background with various pi formulas

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.

Infographic of all of the Pi in the Sky 7 graphics and problems

Visit the Pi in the Sky 8 lesson page to explore classroom resources and downloads for the 2021 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

In this black and white animated image, a circular device stretched out from a robotic arm descends quickly toward a rocky surface, touches it, and then ascends as debris flies all around.

Captured on Oct. 20, 2020, during the OSIRIS-REx mission’s Touch-And-Go (TAG) sample collection event, this series of images shows the SamCam imager’s field of view as the NASA spacecraft approached and touched asteroid Bennu’s surface. Image credit: NASA/Goddard/University of Arizona | › Full image and caption

The Ingenuity Mars helicopter has a small box-like body topped by two sets of oblong blades. Four stick-like legs extend from the body of the helicopter.

In this illustration, NASA's Ingenuity Mars Helicopter stands on the Red Planet's surface as NASA's Perseverance rover (partially visible on the left) rolls away. Image credit: NASA/JPL-Caltech | › Full image and caption

A giant dish with a honeycomb-patterned device at its center is shown in a desert landscape.

This artist's concept shows what Deep Space Station-23, a new antenna dish capable of supporting both radio wave and laser communications, will look like when completed at the Deep Space Network's Goldstone, California, complex. Image credit: NASA/JPL-Caltech | + Expand image

A swirling fabric of glowing neon green, orange, and pink extends above Earth's limb. A partial silhouette of the ISS frames the right corner of the image.

Expedition 52 Flight Engineer Jack Fischer of NASA shared photos and time-lapse video of a glowing green aurora seen from his vantage point 250 miles up, aboard the International Space Station. This aurora photo was taken on June 26, 2017. Image credit: NASA | › Full image and caption

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.

› Take the NASA Pi Day Challenge

› Educators, get the lesson here!

Sample Science

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.

Whirling Wonder

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.

Signal Solution

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.

Force Field

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.

Teach It

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

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

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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

  • Lyle Tavernier
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Illustration of spacecraft on a light purple background that reads "NASA Pi Day Challenge"

Update: March 16, 2020 – The answers to the 2020 NASA Pi Day Challenge are here! View the illustrated answer key (also available as a text-only doc).


In the News

Our annual opportunity to indulge in a shared love of space exploration, mathematics and sweet treats has come around again! Pi Day is the March 14 holiday that celebrates the mathematical constant pi – the number that results from dividing any circle's circumference by its diameter.

Infographic of all of the Pi in the Sky 7 graphics and problems

Visit the Pi in the Sky 7 lesson page to explore classroom resources and downloads for the 2019 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

Overhead view of Mars with a comparison of the smaller landing ellipse made possible by Range Trigger technology

A new Mars landing technique called Range Trigger is reducing the size of the ellipse where spacecraft touch down. Image credit: NASA/JPL-Caltech | › Full image and caption

Composite image of the Kuiper Belt object Arrokoth from NASA's New Horizons spacecraft. Image credit: NASA/Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute/Roman Tkachenko | › Full image and caption

Diagram of an airplane flying over a section of ocean with an example of the spectral data that CORAL collects

The CORAL mission records the spectra of light reflected from the ocean to study the composition and health of Earth's coral reefs. Image credit: NASA | + Expand image

Rays of bright orange and red shoot out diagonally from a blue circle surrounding the star Beta Pictoris

The star Beta Pictoris and its surrounding debris disk in near-infrared light. Image credit: ESO/A.-M. Lagrange et al. | › Full image and caption

Besides providing an excuse to eat all varieties of pie, Pi Day gives us a chance to appreciate some of the ways NASA uses pi to explore the solar system and beyond. You can do the math for yourself – or get students doing it – by taking part in the NASA Pi Day Challenge. Find out below how to test your pi skills with real-world problems faced by NASA space explorers, plus get lessons and resources for educators.

How It Works

The ratio of any circle's circumference to its diameter is equal to pi, which is often rounded to 3.14. But pi is what is known as an irrational number, so its decimal representation never ends, and it never repeats. Though it has been calculated to trillions of digits, we use far fewer at NASA.

Pi is useful for all sorts of things, like calculating the circumference and area of circular objects and the volume of cylinders. That's helpful information for everyone from farmers irrigating crops to tire manufacturers to soup-makers filling their cans. At NASA, we use pi to calculate the densities of planets, point space telescopes at distant stars and galaxies, steer rovers on the Red Planet, put spacecraft into orbit and so much more! With so many practical applications, it's no wonder so many people love pi!

In the U.S., 3.14 is also how we refer to March 14, which is why we celebrate the mathematical marvel that is pi on that date each year. 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.

The NASA Pi Day Challenge

This year's NASA Pi Day Challenge poses four puzzlers that require pi to compare the sizes of Mars landing areas, calculate the length of a year for one of the most distant objects in the solar system, measure the depth of the ocean from an airplane, and determine the diameter of a distant debris disk. Learn more about the science and engineering behind the problems below or click the link to jump right into the challenge.

› Take the NASA Pi Day Challenge
› Educators, get the lesson here!

Mars Maneuver

Long before a Mars rover touches down on the Red Planet, scientists and engineers must determine where to land. Rather than choosing a specific landing spot, NASA selects an area known as a landing ellipse. A Mars rover could land anywhere within this ellipse. Choosing where the landing ellipse is located requires compromising between getting as close as possible to interesting science targets and avoiding hazards like steep slopes and large boulders, which could quickly bring a mission to its end. In the Mars Maneuver problem, students use pi to see how new technologies have reduced the size of landing ellipses from one Mars rover mission to the next.

Cold Case

In January 2019, NASA's New Horizons spacecraft sped past Arrokoth, a frigid, primitive object that orbits within the Kuiper Belt, a doughnut-shaped ring of icy bodies beyond the orbit of Neptune. Arrokoth is the most distant Kuiper Belt object to be visited by a spacecraft and only the second object in the region to have been explored up close. To get New Horizons to Arrokoth, mission navigators needed to know the orbital properties of the object, such as its speed, distance from the Sun, and the tilt and shape of its orbit. This information is also important for scientists studying the object. In the Cold Case problem, students can use pi to determine how long it takes the distant object to make one trip around the Sun.

Coral Calculus

Coral reefs provide food and shelter to many ocean species and protect coastal communities against extreme weather events. Ocean warming, invasive species, pollutants, and acidification caused by climate change can harm the tiny living coral organisms responsible for building coral reefs. To better understand the health of Earth's coral reefs, NASA's COral Reef Airborne Laboratory, or CORAL, mission maps them from the air using spectroscopy, studying how light interacts with the reefs. To make accurate maps, CORAL must be able to differentiate among coral, algae and sand on the ocean floor from an airplane. And to do that, it needs to calculate the depth of the ocean at every point it maps by measuring how much sunlight passes through the ocean and is reflected upward from the ocean floor. In Coral Calculus, students use pi to measure the water depth of an area mapped by the CORAL mission and help scientists better understand the status of Earth's coral reefs.

Planet Pinpointer

Our galaxy contains billions of stars, many of which are likely home to exoplanets – planets outside our solar system. So how do scientists decide where to look for these worlds? Using data gathered by NASA's Spitzer Space Telescope, researchers found that they're more likely to find giant exoplanets around young stars surrounded by debris disks, which are made up of material similar to what's found in the asteroid belt and Kuiper Belt in our solar system. Sure enough, after discovering a debris disk around the star Beta Pictoris, researchers later confirmed that it is home to at least two giant exoplanets. Learning more about Beta Pictoris' debris disk could give scientists insight into the formation of these giant worlds. In Planet Pinpointer, put yourself in the role of a NASA scientist to learn more about Beta Pictoris' debris disk, using pi to calculate the distance across it.

Participate

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

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TAGS: K-12 Education, Math, Pi Day, Pi, NASA Pi Day Challenge, Events, Space, Educators, Teachers, Parents, Students, STEM, Lessons, Problem Set, Mars 2020, Perseverance, Curiosity, Mars rovers, Mars landing, MU69, Arrokoth, New Horizons, Earth science, Climate change, CORAL, NASA Expeditions, coral reefs, oceans, Spitzer, exoplanets, Beta Pictoris, stars, universe, space telescope, Climate TM

  • Lyle Tavernier
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Illustration of spacecraft against a starry background

Update: March 15, 2019 – The answers to the 2019 NASA Pi Day Challenge are here! View the illustrated answer key


In the News

The excitement of Pi Day – and our annual excuse to chow down on pie – is upon us! The holiday celebrating the mathematical constant pi arrives on March 14, and with it comes the sixth installment of the NASA Pi Day Challenge from the Jet Propulsion Laboratory’s Education Office. This challenge gives students in grades 6-12 a chance to solve four real-world problems faced by NASA scientists and engineers. (Even if you’re done with school, they’re worth a try for the bragging rights.)

https://www.jpl.nasa.gov/edu/teach/activity/pi-in-the-sky-6/

Visit the "Pi in the Sky 6" lesson page to explore classroom resources and downloads for the 2019 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech/Kim Orr | + Expand image

Why March 14?

Pi, the ratio of a circle’s circumference to its diameter, is what is known as an irrational number. As an irrational number, its decimal representation never ends, and it never repeats. Though it has been calculated to trillions of digits, we use far fewer at NASA. In fact, 3.14 is a good approximation, which is why March 14 (or 3/14 in U.S. month/day format) came to be the date that we celebrate this mathematical marvel.

The first-known Pi Day celebration occurred in 1988. 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.

The 2019 Challenge

This year’s NASA Pi Day Challenge features four planetary puzzlers that show students how pi is used at the agency. The challenges involve weathering a Mars dust storm, sizing up a shrinking storm on Jupiter, estimating the water content of a rain cloud on Earth and blasting ice samples with lasers!

›Take on the 2019 NASA Pi Day Challenge!

The Science Behind the Challenge

In late spring of 2018, a dust storm began stretching across Mars and eventually nearly blanketed the entire planet in thick dust. Darkness fell across Mars’ surface, blocking the vital sunlight that the solar-powered Opportunity rover needed to survive. It was the beginning of the end for the rover’s 15-year mission on Mars. At its height, the storm covered all but the peak of Olympus Mons, the largest known volcano in the solar system. In the Deadly Dust challenge, students must use pi to calculate what percentage of the Red Planet was covered by the dust storm.

The Terra satellite, orbiting Earth since 1999, uses the nine cameras on its Multi-Angle Imaging SpectroRadiometer, or MISR, instrument to provide scientists with unique views of Earth, returning data about atmospheric particles, land-surface features and clouds. Estimating the amount of water in a cloud, and the potential for rainfall, is serious business. Knowing how much rain may fall in a given area can help residents and first responders prepare for emergencies like flooding and mudslides. In Cloud Computing, students can use their knowledge of pi and geometric shapes to estimate the amount of water contained in a cloud.

Jupiter’s Great Red Spot, a giant storm that has been fascinating observers since the early 19th century, is shrinking. The storm has been continuously observed since the 1830s, but measurements from spacecraft like Voyager, the Hubble Space Telescope and Juno indicate the storm is getting smaller. How much smaller? In Storm Spotter, students can determine the answer to that very question faced by scientists.

Scientists studying ices found in space, such as comets, want to understand what they’re made of and how they interact and react with the environment around them. To see what molecules may form in space when a comet comes into contact with solar wind or sunlight, scientists place an ice sample in a vacuum and then expose it to electrons or ultraviolet photons. Scientists have analyzed samples in the lab and detected molecules that were later observed in space on comet 67P/Churyumov-Gerasimenko. To analyze the lab samples, an infrared laser is aimed at the ice, causing it to explode. But the ice will explode only if the laser is powerful enough. Scientist use pi to figure out how strong the laser needs to be to explode the sample – and students can do the same when they solve the Icy Intel challenge.

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

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TAGS: Pi Day, K-12, STEM, Science, Engineering, Technology, Math, Pi, Educators, Teachers, Informal Education, Museums, Earth Science, Earth, Climate Change

  • Lyle Tavernier
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Cartoon animation of NASA-JPL spacecraft

UPDATE: March 16, 2016 – The answers the the NASA Pi Day Challenge are now available as an illustrated answer key. Download a poster version of the answer key on the "Pi in the Sky 3" activity page.

NASA Pi Day Challenge Answer Key

› Check your answers!


This post was originally published on March 9, 2016

In the News

Pi Day, the informal holiday beloved by math enthusiasts – and even by the math averse – is almost here! March 14 marks the yearly celebration of the mathematical constant (pi), which represents the ratio of a circle’s circumference to its diameter. More than just a number for mathematicians, pi has all sorts of applications in the real world, including on missions developed by NASA’s Jet Propulsion Laboratory. And as a holiday that encourages more than a little creativity – whether it’s making pi-themed pies or reciting from memory as many of the never-ending decimals of pi as possible (the record is 70,030 digits) – it’s a great way to have fun and celebrate the M in STEM.

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 3.14 is often a precise enough approximation, hence the celebration occurring on March 14, or 3/14 (when written in US month/day format). The first known celebration occurred in 1988, and in 2009, the US 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.

Why It’s Important

Pi Day is lots of fun, but its importance lies in the role that pi plays in the everyday work of scientists and engineers at JPL.

Fred Calef, a geospatial information scientist at JPL, uses pi to make measurements – like perimeter, area and volume – of features on Mars. “I use pi to measure the circularity of features, or how round or compact they are," said Calef. "Craters become more elliptical if the projectile hits the surface at a lower angle, so I use pi to measure how round a crater is to see if it impacted at a low angle.”

"We use pi every day commanding rovers on Mars," said Hallie Gengl, a rover planner for the Mars Exploration Rover Opportunity, "Everything from taking images, turning the wheels, driving around, operating the robotic arm, and even talking to Earth.”

Bryana Henderson, who specializes in planetary ices, uses lasers to explode ice samples and study their composition. "I use pi to calculate the width of my laser beam, which in turn can be used to calculate the amount of energy, or fluence, that hits my ice sample," said Henderson. "A larger fluence equals a bigger explosion in the ice, so this is a very important parameter for us."

The Pi Day Challenge

JPL has released the third installment of its popular Pi Day challenge, which gives students and the public a chance to put their pi skills to the test to solve some of the same problems NASA scientists and engineers do. The set of four illustrated math problems are compiled into a graphic (as well as classroom handouts) designed for students in grade 4 through high school – but fun for all!

Pi in the Sky 3 activity

› Check out this year's Pi Day challenge!

This year’s problem set shows how pi can be used to map the surface of Saturn’s hazy moon Titan, track the Mars Reconnaissance Orbiter as it explores the Red Planet, keep Earth’s satellites powered as Mercury transits the sun, and put the Juno spacecraft into orbit around Jupiter.

“For Pi Day, we like to give students and the public a glimpse into how math is used at JPL through questions that feature current events involving our space missions,” said Ota Lutz, an education specialist at JPL who helped create the problem set. “For instance, to put the Juno spacecraft into orbit around Jupiter on July 4, engineers will have to slow the spacecraft just the right amount. In the Pi Day challenge, students use pi to calculate that change in velocity.”

In the challenge, students will also use pi to calculate how much sunlight is blocked by our solar system’s innermost planet as it passes between Earth and the sun. This year, Pi Day comes just a few months before the May 9 transit of Mercury, making this a timely problem.

On March 16, the answers to all four problems and the steps needed to find those answers will be released in a companion infographic on the Pi Day challenge activity page.

In addition to the Pi Day challenge, JPL is inviting the public to share their Pi Day pictures and stories online. On March 14, JPL will join in on the fun with Pi Day photos and stories from the lab.

› Share Your Pi Day photos and stories

To see a compilation of all 12 Pi Day challenge questions optimized for mobile devices and screen readers, visit: http://www.jpl.nasa.gov/edu/nasapidaychallenge

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