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

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

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

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

• 
  Pi Day Challenge Lessons

  Here's everything you need to bring the NASA Pi Day Challenge into the classroom.

  Grades 4-12

  Time Varies

• 
  Slideshow: 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

• 
  Pi Day: What’s Going ’Round

  Tell us what you’re up to this Pi Day and share your stories and photos with NASA.

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

Blogs and Features

• 
  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.

• 
  Slideshow: 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.

Related Lessons for Educators

• 
  Rover Lessons

  Explore a collection of standards-aligned STEM lessons all about rovers.

  Grades K-12

  Time Varies

• 
  Touchdown

  Students design and build a shock-absorbing system that will protect two "astronauts" when they land.

  Grades 3-8

  Time 30 mins - 1 hr

• 
  On Target

  Students modify a paper cup so it can zip down a line and drop a marble onto a target.

  Grades 6-12

  Time 30 mins - 1 hr

• 
  Solar System Scale Models

  Explore a collection of standards-aligned STEM lessons all about the size and scale of our solar system.

  Grades 1-12

  Time Varies

• 
  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 mins - 1 hr

• 
  Math Rocks: A Lesson in Asteroid Dynamics

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

  Grades 8-12

  Time 30 mins - 1 hr

• 
  Asteroid Ace: A 'Pi in the Sky' Math Challenge

  Students use pi to calculate the rotation rate of an asteroid from another solar system in this illustrated math problem.

  Grades 11-12

  Time < 30 mins

• 
  Climate Change Lessons

  Explore a collection of standards-aligned STEM lessons all about Earth's changing climate.

  Grades K-12

  Time Varies

• 
  Using Light to Study Planets

  Students build a spectrometer using basic materials as a model for how NASA uses spectroscopy to determine the nature of elements found on Earth and other planets.

  Grades 6-11

  Time < 2 hrs

NOAA Coral Bleaching activity

• 
  Solar Sleuth: A 'Pi in the Sky' Math Challenge

  In this illustrated math problem, students use pi and data from the Kepler space telescope to find the size of a planet outside our solar system.

  Grades 6-9

  Time < 30 mins

• 
  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.

  Grades 6-12

  Time 30 mins - 1 hr

• 
  Habitable Hunt: A 'Pi in the Sky' Math Challenge

  In this illustrated math problem, students use the mathematical constant pi to find the "habitable zone" around a distant star and determine which of its planets are in that zone.

  Grades 11-12

  Time < 30 mins

Related Activities for Students

• 
  Make a Moon or Mars Rover Game

  Create a Moon or Mars exploration game using Scratch, a visual programming language. Think like NASA space-mission planners to design your game!

  Type Project

  Subject Technology

• 
  Make a Cardboard Rover

  Build a rubber-band-powered rover that can scramble across a room.

  Type Project

  Subject Engineering

• 
  Mars in a Minute: How Do You Choose a Landing Site?

  So, you want to study Mars with a lander or rover – but where exactly do you send it? Learn how scientists and engineers tackle the question of where to land on Mars in this 60-second video.

  Type Video

  Subject Engineering

• 
  Mars in a Minute: How Do You Land on Mars?

  Getting a spacecraft to Mars is one thing. Getting it safely to the ground is a whole other challenge! This 60-second video from NASA's Jet Propulsion Laboratory explains three ways to land on the surface of the Red Planet.

  Type Video

  Subject Engineering

• 
  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

• 
  Mars in a Minute: How Long is a Year on Mars?

  How long is does it take Mars to make one trip around the Sun and why is one Earth year shorter? Find out in one minute!

  Type Video

  Subject Science

• 
  Space Place in a Snap: The Solar System's Formation

  Find out how our solar system formed and how it came to be the busy place it is today.

  Type Video

  Subject Science

• 
  What Is the Kuiper Belt?

  Learn about the Kuiper Belt and some of its famous members, Kuiper Belt Objects.

  Type Article

  Subject Science

• 
  Coral Bleaching Simulator

  Adjust water temperature and pollution levels in this simulator to see what happens to a coral reef depending on the conditions you choose!

  Type Interactive

  Subject Science

• 
  Ocean Worlds

  Where might oceans – and living things – exist beyond Earth? Scientists have their eyes on these places in our own solar system.

  Type Slideshow

  Subject Science

• 
  NASA's Earth Minute: Mission to Earth?

  NASA doesn't just explore outer space! It studies Earth, too, with a fleet of spacecraft and scientists far and wide.

  Type Video

  Subject Science

• 
  NASA's Earth Minute: Earth Has a Fever

  Why is Earth getting hotter and what does that mean for us?

  Type Video

  Subject Science

NOAA Video Series: Coral Comeback

• Article: Giant Exoplanet Hunters: Look for Debris Disks
• Video: The Evolution of a Planet-Forming Disk
• Video: Birth of "Phoenix" Planets?

Multimedia

• 
  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.

• Posters: Exoplanet Travel Bureau

Facts and Figures

• Mars
• Arrokoth (2014 MU69)
• Earth
• Beta Pictoris b
• Beta Pictoris c

Missions and Instruments

• Perseverance Mars rover (Mars 2020)
• Curiosity Mars rover
• New Horizons
• CORAL
• Spitzer

Websites

• NASA Mars Exploration
• NASA Solar System Exploration
• NASA Climate Change
• NASA Exoplanets

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

• 

  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.

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

• 

  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.

TAGS: Pluto, Charon, New Horizons, Images

• 

  ABOUT THE AUTHOR

  NASA/JPL Edu

  NASA/JPL Edu supports science, technology, engineering and mathematics (STEM) education by providing NASA and JPL activities, resources and materials to educators and students in grades K-12 as well as STEM internships and research opportunities to higher education students and faculty.

TAGS: Pluto, New Horizons, Dwarf Planet

• 

  ABOUT THE AUTHOR

  NASA/JPL Edu

  NASA/JPL Edu supports science, technology, engineering and mathematics (STEM) education by providing NASA and JPL activities, resources and materials to educators and students in grades K-12 as well as STEM internships and research opportunities to higher education students and faculty.