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

  • Lyle Tavernier
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In the News

We visited Pluto!

On July 14, 2015 at 4:49 a.m. PDT, NASA's New Horizons spacecraft sped past Pluto -- a destination that took nearly nine and a half years to reach -- and collected scientific data along with images of the dwarf planet.

Pluto, famous for once being the ninth planet, was reclassified as a dwarf planet in 2006 after new information emerged about the outer reaches of our solar system. Worlds similar to Pluto were discovered in the region of our solar system known as the Kuiper Belt. The Kuiper Belt --named for astronomer Gerard Kuiper --is a doughnut-shaped area beyond the orbit of Neptune that is home to Pluto, other dwarf planets such as Eris, Makemake, and Haumaea, as well as hundreds of thousands of other large icy bodies, and perhaps trillions of comets orbiting our sun. Over the next several years, the New Horizons spacecraft is expected to visit one to two more Kuiper Belt objects.

Even though it will take 16 months for New Horizons to return all the Pluto science data to Earth, we have already made some interesting and important discoveries about Pluto.

Why It's Important

Through careful measurements of new images, scientists have determined that Pluto is actually larger than previously thought: 2,370 kilometers in diameter.  This is important information for scientists because it helps them understand the composition of Pluto. Because of the orbital interactions between Pluto and its moon Charon, Pluto’s mass is well known and understood. Having a more precise diameter gives scientists the ability to more accurately calculate the average density. A greater diameter means Pluto’s density is less than we thought. If you do the math, you’ll see that Pluto’s calculated density dropped from 2,051 kg/m3 to 1,879 kg/m3 with this new finding. Most rock has a density between 2000-3000 kg/m3 and ice at very cold temperatures has a density of 927 kg/m3, so we can conclude that Pluto is a bit more icy than previously believed. In addition to helping scientists calculate the density of Pluto, this measurement confirms Pluto as the largest known object in the Kuiper Belt!

Teach It

We’ve provided some math problems (and answers) for you to use in the classroom. They’re a great way to provide students with real-world examples of how the math they’re learning in class is used by scientists. There are also some additional resources below that you can use to integrate the Pluto flyby into your lessons, or use the flyby as a lesson opener!

Pluto Math Problems

  1. Find the radius(r) of Pluto.
    2,370 kilometers ÷ 2 = 1,185 km

  2. Find the circumference of Pluto.
    C = 2 π r = 7,446 km

  3. Find the surface area of Pluto.
    SA = 4 π r2 = 17,646,012 km2

  4. Find the volume of Pluto.
    4/3 π r3  = 6,970,174,651 km3

  5. Find the density of Pluto in kg/m3.
    mass/volume
    Pluto mass = 1.31 × 1022kg
    Convert volume in km3 to m3: 6,970,174,651 × 1,000,000,000 = 6.970174651 × 1018m3
    1.31 × 1022kg / 6.970174651 × 1018m3 = 1,879 kg/m3

  6. How does this new density calculation compare to the previous calculation (2051 kg/m3) when Pluto’s diameter was thought to be 2,302 km?

Explore More

Take a look at some of the lessons, videos, activities and interactives related to Pluto. They’re a great way to engage students in STEM and learning more about their solar system!

  • Video: What is a Dwarf Planet? (K-12)
    Dwarf planets are a lot like regular planets. What’s the big difference? Find out in 60 seconds.

  • Activity: Solar System Bead Activity (4-8)
    The solar system is big, and Pluto is way out there! Students calculate scale distances to create a model of objects in our solar system.
    Next Generation Science Standards: MS-ESS1-3
    Common Core Math: 4.MD.A.2, 5.NBT.B.7

  • Activity: How Far? How Faint? (9-12)
    Calculate how much light Pluto receives from the sun, compared to Earth.
    Common Core Math: HSF.IF.C.7.E

  • Resource: Pluto Facts and Figures
    Get lots of facts and figures about this dwarf planet in the Kuiper belt!

  • Interactive: Eyes on Pluto
    Ride along with New Horizons in this simulation of its closest approach to Pluto!

  • Participate: Pluto Time
    Though Pluto is a distant world with very different characteristics from Earth, for just a moment near dawn and dusk each day, you can experience “Pluto Time.” This is when the amount of light reaching Earth matches that of noon on Pluto. Find out exactly when Pluto Time happens in your area and share your photos online!

  • News and Images: NASA New Horizons Website
    Get the latest news and images from NASA's New Horizons mission.


TAGS: Pluto, New Horizons, Math, Teachable Moment

  • Lyle Tavernier
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The first set of close-up images returned from NASA's New Horizons mission reveal surprises and new insights about Pluto and its moons. 

See the latest images on NASA's New Horizons website

New Horizons became the first mission to explore Pluto on July 14, 2015 when it flew within 7,800 miles (12,500 kilometers) of the dwarf planet.

Stay tuned for related educational resources and activities.

TAGS: Pluto, Charon, New Horizons, Images

  • NASA/JPL Edu
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After a 3-billion-mile journey and a decade of space flight, NASA's New Horizons mission became the first to explore the dwarf planet Pluto on Tuesday, passing within 7,800 miles (12,500 kilometers) of the distant and mysterious world. 

Scientists are awaiting a series of status updates from the spacecraft that indicate it survived the flyby and is in good health -- scheduled for about 6 p.m. PDT -- as well as data and images collected during the closest approach.

Read more about the encounter and see the latest images

TAGS: Pluto, New Horizons, Dwarf Planet

  • NASA/JPL Edu
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