Teachable Moments  March 5, 2021
Take Math to Mars and Beyond With NASA's Pi Day Challenge
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 textonly 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.
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 brainticklers 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 OSIRISREx 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 nearEarth asteroids, like the one visited by OSIRISREx, asteroid Bennu. Launched in 2016, OSIRISREx 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 samplecollection 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 nearinfrared light instead of radio waves to transmit data. Nearinfrared 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

Pi in the Sky Lessons
Here's everything you need to bring the NASA Pi Day Challenge into the classroom.
Grades 412
Time Varies

NASA Pi Day Challenge
The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.
Grades 412
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.

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 use 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 K8
Time 30 min to 1 hour

Whip Up a MoonLike Crater
Whip up a moonlike crater with baking ingredients as a demonstration for students.
Grades 16
Time 30 min to 1 hour

Make a Paper Mars Helicopter
In this lesson, students build a paper helicopter, then improve the design and compare and measure performance.
Grades 28
Time 30 min to 1 hour

Speaking in Phases
Students learn how waves are used in communication between faraway spacecraft and the Deep Space Network on Earth.
Grades 38
Time 30 min to 1 hour

Catching a Whisper from Space
Students kinesthetically model the mathematics of how NASA communicates with spacecraft.
Grades 412
Time 12 hours

Collecting Light: Inverse Square Law Demo
In this activity, students learn how light and energy are spread throughout space. The rate of change can be expressed mathematically, demonstrating why spacecraft like NASA’s Juno need so many solar panels.
Grades 68
Time under 30 min

Build a Relay Inspired by Space Communications
In this intermediatelevel programming challenge, students use microdevices along with light and mirrors to build a relay that can send information to a distant detector.
Grades 812
Time 12 hours

Math Rocks: A Lesson in Asteroid Dynamics
Students use math to investigate a reallife asteroid impact.
Grades 812
Time 30 min to 1 hour
Related Activities for Students

Code a Mars Helicopter Video Game
Create a video game that lets players explore the Red Planet with a helicopter like the one going to Mars with NASA's Perseverance rover!
Type Project
Subject Technology

Make a Paper Mars Helicopter
Build a paper helicopter, then see if you can improve the design like NASA engineers did when making the first helicopter for Mars.
Type Project
Subject Engineering

How Does NASA Spot a NearEarth Asteroid?
Watch this oneminute video to find out how NASA spots and tracks asteroids that fly close to Earth.
Type Video
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
Explore More
Infographic
Facts and Figures
Missions and Instruments
Websites
TAGS: Pi, Pi Day, NASA Pi Day Challenge, Math, Mars, Perseverance, Ingenuity, Mars Helicopter, OSIRISREx, Bennu, Asteroid, Auroras, Earth, Magnetic Field, DSOC, Light Waves, DSN, Deep Space Network, Space Communications
Teachable Moments  March 6, 2020
We've Got the Formula for a Stellar Pi Day
Update: March 16, 2020 – The answers to the 2020 NASA Pi Day Challenge are here! View the illustrated answer key (also available as a textonly 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.
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 realworld 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 soupmakers 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 doughnutshaped 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 412
Time Varies

Slideshow: NASA Pi Day Challenge
The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.
Grades 412
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 standardsaligned STEM lessons all about rovers.
Grades K12
Time Varies

Touchdown
Students design and build a shockabsorbing system that will protect two "astronauts" when they land.
Grades 38
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 612
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Grades 112
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Modeling an Asteroid
Lead a discussion about asteroids and their physical properties, then have students mold their own asteroids out of clay.
Grades 35
Time 30 mins  1 hr

Math Rocks: A Lesson in Asteroid Dynamics
Students use math to investigate a reallife asteroid impact.
Grades 812
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 1112
Time < 30 mins

Climate Change Lessons
Explore a collection of standardsaligned STEM lessons all about Earth's changing climate.
Grades K12
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 611
Time < 2 hrs

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 69
Time < 30 mins

Exploring Exoplanets with Kepler
Students use math concepts related to transits to discover realworld data about Mercury, Venus and planets outside our solar system.
Grades 612
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 1112
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 spacemission planners to design your game!
Type Project
Subject Technology

Make a Cardboard Rover
Build a rubberbandpowered 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 60second 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 60second 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
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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
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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.
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Subject Science

NASA's Earth Minute: Earth Has a Fever
Why is Earth getting hotter and what does that mean for us?
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Subject Science
NOAA Video Series: Coral Comeback
 Article: Giant Exoplanet Hunters: Look for Debris Disks
 Video: The Evolution of a PlanetForming 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
Missions and Instruments
Websites
TAGS: K12 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
Teachable Moments  March 8, 2019
NASA Rocket Science? It's Easy As Pi
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 612 a chance to solve four realworld problems faced by NASA scientists and engineers. (Even if you’re done with school, they’re worth a try for the bragging rights.)
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 firstknown 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 solarpowered Opportunity rover needed to survive. It was the beginning of the end for the rover’s 15year 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 MultiAngle Imaging SpectroRadiometer, or MISR, instrument to provide scientists with unique views of Earth, returning data about atmospheric particles, landsurface 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/ChuryumovGerasimenko. 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.
Explore More
Participate

Pi Day Challenge Lessons
Here's everything you need to bring the NASA Pi Day Challenge into the classroom.
Grades 412
Time Varies

Slideshow: NASA Pi Day Challenge
The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.
Grades 412
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.
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The Sky and Dichotomous Key
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Grades K3
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Precipitation Towers: Modeling Weather Data
This lesson uses stacking cubes as a way to graph precipitation data, comparing the precipitation averages and seasonal patterns for several locations.
Grades K5
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Create a Comet with Dry Ice
Build an icy model of a comet out of dry ice  complete with shooting jets!  as a demonstration for students.
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Comet on a Stick
Students build their own comet models using craft materials.
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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.

Game: Comet Quest  NASA SpacePlace
Control a spacecraft and use it to explore an icy comet!
Facts and Figures
 Mars
 Jupiter
 Earth
 Comets
 Comet 67P/ ChuryumovGerasimenko
 What is a Laser? – NASA SpacePlace
 What Is the Water Cycle? – Climate Kids
Missions and Instruments
 Hubble Space Telescope
 Voyager
 Juno
 Opportunity Rover
 Rosetta
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Websites
TAGS: Pi Day, K12, STEM, Science, Engineering, Technology, Math, Pi, Educators, Teachers, Informal Education, Museums, Earth Science, Earth, Climate Change
Teachable Moments  March 9, 2018
Pi Goes the Distance at NASA
Update: March 15, 2018 – The answers to the 2018 NASA Pi Day Challenge are here! View the illustrated answer key
In the News
The 2018 NASA Pi Day Challenge
Can you solve these stellar mysteries with pi? Click to get started.
Pi Day, the annual celebration of one of mathematics’ most popular numbers, is back! Representing the ratio of a circle’s circumference to its diameter, pi has many practical applications, including the development and operation of space missions at NASA’s Jet Propulsion Laboratory.
The March 14 holiday is celebrated around the world by math enthusiasts and casual fans alike – from memorizing digits of pi (the current Pi World Ranking record is 70,030 digits) to baking and eating pies.
JPL is inviting people to participate in its 2018 NASA Pi Day Challenge – four illustrated math puzzlers involving pi and real problems scientists and engineers solve to explore space, also available as a free poster! Answers will be released on March 15.
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 NASA scientists and engineers actually use far fewer digits in their calculations (see “How Many Decimals of Pi Do We Really Need?”). The approximation 3.14 is often precise enough, hence the celebration occurring on March 14, or 3/14 (when written in U.S. month/day format). The first known celebration occurred in 1988, and 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.
NASA’s Pi Day Challenge
Lessons: Pi in the Sky
Explore the entire NASA Pi Day Challenge lesson collection, including free posters and handouts!
To show students how pi is used at NASA and give them a chance to do the very same math, the JPL Education Office has once again put together a Pi Day challenge featuring realworld math problems used for space exploration. This year’s challenge includes exploring the interior of Mars, finding missing helium in the clouds of Jupiter, searching for Earthsize exoplanets and uncovering the mysteries of an asteroid from outside our solar system.
Here’s some of the science behind this year’s challenge:
Scheduled to launch May 5, 2018, the InSight Mars lander will be equipped with several scientific instruments, including a heat flow probe and a seismometer. Together, these instruments will help scientists understand the interior structure of the Red Planet. It’s the first time we’ll get an indepth look at what’s happening inside Mars. On Earth, seismometers are used to measure the strength and location of earthquakes. Similarly, the seismometer on Insight will allow us to measure marsquakes! The way seismic waves travel through the interior of Mars can tell us a lot about what lies beneath the surface. This year’s Quake Quandary problem challenges students to determine the distance from InSight to a hypothetical marsquake using pi!
Also launching in spring is NASA’s Transiting Exoplanet Survey Satellite, or TESS, mission. TESS is designed to build upon the discoveries made by NASA’s Kepler Space Telescope by searching for exoplanets – planets that orbit stars other than our Sun. Like Kepler, TESS will monitor hundreds of thousands of stars across the sky, looking for the temporary dips in brightness that occur when an exoplanet passes in front of its star from the perspective of TESS. The amount that the star dims helps scientists determine the radius of the exoplanet. Like those exoplanethunting scientists, students will have to use pi along with data from Kepler to find the size of an exoplanet in the Solar Sleuth challenge.
Jupiter is our solar system’s largest planet. Shrouded in clouds, the planet’s interior holds clues to the formation of our solar system. In 1995, NASA’s Galileo spacecraft dropped a probe into Jupiter’s atmosphere. The probe detected unusually low levels of helium in the upper atmosphere. It has been hypothesized that the helium was depleted out of the upper atmosphere and transported deeper inside the planet. The extreme pressure inside Jupiter condenses helium into droplets that form inside a liquid metallic hydrogen layer below. Because the helium is denser than the surrounding hydrogen, the helium droplets fall like rain through the liquid metallic hydrogen. In 2016, the Juno spacecraft, which is designed to study Jupiter’s interior, entered orbit around the planet. Juno’s initial gravity measurements have helped scientists better understand the inner layers of Jupiter and how they interact, giving them a clearer window into what goes on inside the planet. In the Helium Heist problem, students can use pi to find out just how much helium has been depleted from Jupiter’s upper atmosphere over the planet’s lifetime.
In October 2017, astronomers spotted a uniquelyshaped object traveling in our solar system. Its path and high velocity led scientists to believe ‘Oumuamua, as it has been dubbed, is actually an object from outside of our solar system – the first ever interstellar visitor to be detected – that made its way to our neighborhood thanks to the Sun’s gravity. In addition to its high speed, ‘Oumuamua is reflecting the Sun’s light with great variation as the asteroid rotates on its axis, causing scientists to conclude it has an elongated shape. In the Asteroid Ace problem, students can use pi to find the rate of rotation for ‘Oumuamua and compare it with Earth’s rotation rate.
Explore More
Join the Conversation
 Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge
 Pi Day: What’s Going ‘Round – Tell us what you’re up to this Pi Day and share your stories and photos with NASA.
StandardsAligned Lessons
 Pi in the Sky 5
 Pi in the Sky 4
 Pi in the Sky 3
 Pi in the Sky 2
 Pi in the Sky
 Pi in the Sky Challenge (slideshow for students)
Multimedia
 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.
 Kepler186f Travel Poster
 Video: First Interstellar Asteroid Wows Scientists
 Planet Pi
Facts and Figures
Missions
Websites
TAGS: Pi Day, Math, Science, Engineering, NASA Pi Day Challenge, K12, Lesson, Activity, Slideshow, Mars, Jupiter, Exoplanets, Kepler, Kepler186f, Juno, InSight, TESS, ‘Oumuamua, asteroid, asteroids, NEO, Nearth Earth Object
Teachable Moments  March 10, 2017
Celebrate Pi Day Like a NASA Rocket Scientist
UPDATE: March 16, 2017 – An illustrated answer key for the 2017 NASA Pi Day Challenge is now available here.
Were you able to solve these stellar mysteries using pi? Check your answers on our illustrated answer key and download the free "Pi in the Sky^{4}" poster set.
NASA is giving space fans a reason to celebrate Pi Day, the March 14 holiday created in honor of the mathematical constant pi. For the fourth year in a row, the agency’s Jet Propulsion Laboratory has created an illustrated Pi Day Challenge featuring four math problems NASA scientists and engineers must solve to explore space. The challenge is designed to get students excited about pi and its applications beyond the classroom. This year’s problem set, designed for students in grade six through high school – but fun for all – features Mars craters, a total solar eclipse, a close encounter with Saturn, and the search for habitable worlds.
› Take the NASA Pi Day Challenge!
› Educators, get the standardsaligned Pi Day Challenge lesson and download the free poster and handouts. The answers to all four problems will be released in a companion infographic on March 16.
Read on for more about Pi Day, the science behind the 2017 problem set and to learn how NASA scientists and engineers use pi.
Take the NASA Pi Day Challenge
Solve a Martian crater mystery, measure the size of the moon’s shadow during a total solar eclipse, get into a daring orbit around Saturn, and discover potentially habitable worlds beyond our solar system. You don’t have to be a NASA rocket scientist to do stellar math with pi.
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 NASA scientists and engineers actually use far fewer digits in their calculations (see “How Many Decimals of Pi Do We Really Need?”). The approximation 3.14 is often precise enough, 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
While many of us celebrate by eating pithemed pie and trying to memorize as many digits of pi as possible (the record is 70,030 digits), scientists and engineers at NASA take pi even further, using it in their daytoday work exploring space!
“Finding the volume of a sphere, area of a circle (and thus volume of a cylinder) are well known applications of pi,” said Charles Dandino, a JPL engineer who designs robots for extreme environments. “But those relationships also form the basis for how stiff a structure is, how it will vibrate, and understanding how a design might fail.”
Rachel Weinberg works on the Orbiting Carbon Observatory 3, or OCO3, instrument, which will track the distribution of carbon dioxide across Earth. She says pi came in handy during her studies at MIT and still does today for her work at JPL. “Just the other day during a meeting, the team went to the whiteboard and used pi to discuss the angles and dimensions of optical components on OCO3,” she said.
Pi allows us to calculate the size and area of two and threedimensional shapes, says Anita Sengupta, a JPL engineer, who has worked on a variety of planetary missions. “In my career, pi has allowed me to calculate the size of a shield needed to enter the atmosphere of Venus and the size of a parachute that could safely land the Curiosity rover on the surface of Mars. Most recently we used pi in our calculations of the expanding atom cloud we will create for an experiment called the Cold Atom Laboratory, which will fly aboard the International Space Station.”
The Science Behind the Challenge
The Pi Day Challenge gives students a chance to take part in recent discoveries and upcoming celestial events, all while using math and pi just like NASA scientists and engineers.
“Students always want to know how math is used in the real world,” said Ota Lutz, a senior education specialist at JPL who helped create the Pi Day Challenge. “This problem set demonstrates the interconnectedness of science, math and engineering, providing teachers with excellent examples of crosscutting concepts in action and students with the opportunity to solve realworld problems.”
NASA's Pi Day Challenge in the Classroom!
The NASA Pi Day Challenge is available as a standardsaligned lesson for grades 612. In the illustrated math problem set, students use pi to solve realworld science and engineering problems related to craters on Mars, a total solar eclipse, a daring orbit about Saturn, and the search for habitable worlds.
Here’s some of the science behind this year’s problem set.
The craters that cover Mars can tell us a lot about the Red Planet. Studying ejecta – the material blasted out during an impact – can tell us even more. Information about ejecta patterns even came up during a recent workshop to discuss and select the final candidates for the Mars 2020 rover landing site. For the first problem in our Pi Day Challenge, students use pi and the area and perimeter of two craters to identify which was made by an impactor that struck Mars at a low angle. Researchers found that lowangle impactors create an unusual ejecta pattern around craters on Mars. As part of the research, scientists are currently working to identify and catalog these craters.
The year 2017 brings a unique astronomical event to the United States for the first time in nearly 40 years! On August 21, 2017, a total solar eclipse will cross the continental United States. Starting in Oregon, the shadow of the moon will cross the country at more than 1,000 miles per hour, making its way to the Atlantic Ocean off the coast of South Carolina. Everyone inside the moon’s shadow will witness one of the most impressive sights nature has to offer. So how big is the shadow? In the second part of NASA’s Pi Day Challenge, students will use pi to calculate the area of the moon’s shadow on Earth during the total solar eclipse.
This year also marks the final chapter in the exciting story of NASA’s Cassini mission at Saturn. Since 2004, Cassini has been orbiting the ringed giant, vastly improving our understanding of the second largest planet in the solar system. After more than 12 years around Saturn, Cassini’s fuel is running low, so mission operators have devised a grand finale that will take the spacecraft closer to Saturn than ever before – inside the gap between the planet and its rings – and finally into Saturn’s cloud tops, where it will burn up. The finale is designed to prevent the spacecraft from crashing into and possibly contaminating any of Saturn’s scientifically intriguing moons. In the Pi Day Challenge, students will use pi to safely navigate the spacecraft on its final orbits and dive into Saturn.
Finally, students will investigate a relatively new and very exciting realm in astronomy, the search for habitable worlds. The discovery of exoplanets – worlds orbiting stars outside of our solar system – has changed our understanding of the universe. Until 1995, exoplanets hadn’t even been detected. Now, using the transit method – where planets are detected by measuring the light they block as they pass in front of a star – more than 2,300 exoplanets have been discovered. Recently, astronomers discovered a record seven Earthsize planets orbiting a single star called Trappist1. Students will use pi to identify which of Trappist1’s planets orbit in the star’s habitable zone – the area where liquid water could exist.
Explore More
Join the Conversation
 Join the conversation and share your Pi Day Challenge answers with @NASA/JPL_Edu on social media using the hashtag #NASAPiDayChallenge
 Pi Day: What’s Going ‘Round – Tell us what you’re up to this Pi Day and share your stories and photos with NASA.
StandardsAligned Lessons
Multimedia
Facts and Figures
Missions
Websites
TAGS: Pi Day, Math, Science, Engineering, NASA Pi Day Challenge, K12, Lesson, Activity, Slideshow
Edu News  March 16, 2016
How Many Decimals of Pi Do We Really Need?
Earlier this week, we received this question from a fan on Facebook who wondered how many decimals of the mathematical constant pi (π) NASAJPL 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: 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360
We posed this question to the director and chief engineer for NASA's Dawn mission, Marc Rayman. Here's what he said:
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 sixthgrade 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 present. Consider these examples:
 The most distant spacecraft from Earth is Voyager 1. It is about 12.5 billion miles away. Let's say we have a circle with a radius of exactly that size (or 25 billion miles 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 78 billion miles. 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 25 billion mile diameter circle would be wrong by 1.5 inches. Think about that. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps less than the length of your little finger.
 We can bring this down to home with our planet Earth. It is 7,926 miles in diameter at the equator. The circumference then is 24,900 miles. That's how far you would travel if you circumnavigated the globe (and didn't worry about hills, valleys, obstacles like buildings, rest stops, waves on the ocean, etc.). How far off would your odometer be if you used the limited version of pi above? It would be off by 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 10,000 times thinner than a hair!
 Let's go to the largest size there is: the visible universe. The radius of the universe is about 46 billion light years. Now let me ask 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)? The answer is that you would need 39 or 40 decimal places. If you think about how fantastically vast the universe is — truly far beyond what we can conceive, and certainly far, far, far beyond what you can see with your eyes even on the darkest, most beautiful, starfilled night — and think about how incredibly tiny a single atom is, you can see that we would not need to use many digits of pi to cover the entire range.
Read more from Marc Rayman on the Dawn Journal, where he writes monthly updates about the Dawn spacecraft currently exploring the dwarf planet Ceres to provide scientists with a window into the dawn of the solar system.
Can you use pi like a NASA scientist?› Take the Pi in the Sky Challenge!
TAGS: Pi, Pi Day, Dawn, Voyager, Engineering, Science, Mathematics
Teachable Moments  March 16, 2016
Pi Day the NASA Way
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.
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 pithemed pies or reciting from memory as many of the neverending 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!
› 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 storiesTo 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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Pi Day Challenges
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TAGS: pi, pi day, math, mathematics
Edu News  March 9, 2015
Take the 2015 Pi Day Challenge!
UPDATE  March 16, 2015: The pi challenge answer key is now available for download.
In honor of the "Pi Day of the Century" (3/14/15), the Education Office at NASA's Jet Propulsion Laboratory has crafted another stellar math challenge to show students of all ages how NASA scientists and engineers use the mathematical constant pi.
The 2015 problem set  available as a web infographic and printable handouts  features four realworld, NASA math problems for students in grades 4 through 11, including: calculating the dizzying number of times a Mars rover's wheels have rotated in 11 years; finding the number of images it will take the Dawn spacecraft to map the entire surface of the dwarf planet Ceres (the first dwarf planet to be explored); learning the potential volume of water on Jupiter's moon Europa; and discovering what fraction of a radio beam from our most distant spacecraft reaches Earth.
The word problems, which were crafted by NASA/JPL education specialists with the help of scientists and engineers, give students insight into the real calculations space explorers use every day and a chance to see some of the realworld applications of the math they're learning in school.
"Pi in the Sky 2" Downloads:
 Poster  Download PDF (8 MB)
 Handouts  Download PDF (7 MB)
 Answers  Download PDF (8 MB)
Edu News  March 11, 2014
Take the 2014 Pi Day Challenge!
UPDATE  March 17, 2014: The pi challenge answer key is now available for download.
In honor of everyone's favorite mathematical holiday, Pi Day, which celebrates the mathematical constant 3.14 on March 14, NASA/JPL Edu has crafted a set of stellar middle and highschool math problems to show students that pi is more than just a fancy number.
Pi is all over our skies! It helps power our spacecraft, keeps our Mars rovers' wheels spinning, lets us peer beneath the clouds on Jupiter and gives us new perspectives on Earth. Take part in the fun and see if your classroom can solve some of the same problems that real NASA scientists and engineers do.
Each pifilled word problem gets a graphic treatment in this printable infographic (available in both postersize and 8.5by11 handouts) that helps students visualize the steps they need to get to a solution. A companion answer key is also available below and walks students through each step of the solutions. It can be printed on the back of the problemset infographic for an educational classroom poster.
"Pi in the Sky" Downloads:
 Poster  Download PDF (5 MB)
 Handouts  Download PDF (11 MB)
 Answers  Download PDF (9 MB)