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.

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.

#### 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

#### Related Activities for Students

NOAA Video Series: Coral Comeback

#### Websites

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

You may have noticed that there's an extra day on your calendar this year. That's not a typo; it's leap day! Leap day is another name for Feb. 29, a date that typically comes around every four years, during a leap year. Why doesn't Feb. 29 appear on the calendar every year? Read on to find out how the imperfect match between the length of a calendar year and Earth's orbit results in the need to make small adjustments to our calendar on a regular basis. Explore leap day resources for students, too.

The length of a year is based on how long it takes a planet to revolve around the Sun. Earth takes about 365.2422 days to make one revolution around the Sun. That's about six hours longer than the 365 days that we typically include in a calendar year. As a result, every four years we have about 24 extra hours that we add to the calendar at the end of February in the form of leap day. Without leap day, the dates of annual events, such as equinoxes and solstices, would slowly shift to later in the year, changing the dates of each season. After only a century without leap day, summer wouldn’t start until mid-July!

But the peculiar adjustments don't end there. If Earth revolved around the Sun in exactly 365 days and six hours, this system of adding a leap day every four years would need no exceptions. However, Earth takes a little less time than that to orbit the Sun. Rounding up and inserting a 24-hour leap day every four years adds about 45 extra minutes to every four-year leap cycle. That adds up to about three days every 400 years. To correct for that, years that are divisible by 100 don't have leap days unless they’re also divisible by 400. If you do the math, you'll see that the year 2000 was a leap year, but 2100, 2200 and 2300 will not be.

After learning more about leap years with this article from NASA's Space Place, students can do the math for themselves with this leap day problem set. Follow that up with writing a letter or poem to be opened on the next leap day. And since we've got an extra 24 hours this year, don't forget to take a little time to relax!

### Explore More

Check out these related resources for kids from NASA Space Place:

TAGS: K-12 Education, Math, Leap Day, Leap Year, Events, Space, Educators, Teachers, Parents, Students, STEM, Lessons