Problem Set
Rad Reflection: A ‘Pi in the Sky’ Math Challenge
Overview
The "Pi in the Sky" math 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. In this problem from the 10th set, students use pi to compare the area of the Hubble Space Telescope and Webb Telescope’s primary mirror.
Materials
Background
Rad Reflection
When NASA launched the Hubble Space Telescope in 1990, scientists hoped that the telescope, with its large mirror and sensitivity to ultraviolet, visible, and nearinfrared light, would unlock secrets of the universe from an orbit high above the atmosphere. Indeed, their hope became reality. Hubble’s discoveries, which are made possible in part by its mirror, rewrote astronomy textbooks. In 2022, the next great observatory, the James Webb Space Telescope, began exploring the infrared universe with an even larger mirror from a location beyond the orbit of the Moon. In Rad Reflection, students use pi to gain a new understanding of our ability to peer deep into the cosmos by comparing the area of Hubble’s primary mirror with the one on Webb.
Procedures
Rad Reflection
The James Webb Space Telescope was designed to look back at some of the earliest galaxies in the universe. To capture light from these distant and faint objects, the telescope must be very sensitive. Webb uses 18 hexagonal mirrors that combine to form a massive primary mirror with a surface area of 26.4 m^{2}. This large mirror allows the telescope to collect incredibly faint infrared light and reflect it onto four onboard science instruments, like the MidInfrared Instrument, or MIRI. This science instrument can reveal stars hidden within gas and dust clouds and tell scientists about the materials that make up distant galaxies.
Launched in 1990, the Hubble Space Telescope changed our understanding of the universe when it began operations using a primary mirror that had a diameter of just 2.4 meters.
How much bigger is the area of Webb’s primary mirror than Hubble’s?
› Learn more about the James Webb Space Telescope
NASA's Universe of Learning materials are based upon work supported by NASA under award number NNX16AC65A to the Space Telescope Science Institute, working in partnership with Caltech/IPAC, Center for Astrophysics  Harvard & Smithsonian, and the Jet Propulsion Laboratory.
Assessment
Extensions
Participate
Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge

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
In this challenge, students can use pi to solve some of the same problems faced by NASA scientists and engineers.
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.

National Council of Teachers of Mathematics: Notice and Wonder
Creative brainstorming through noticing and wondering encourages student participation, engagement, and students' understanding of the NASA Pi Day Challenge.
Subject Mathematics
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 Expanded Universe: Playing with Time Activity Guide
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James Webb Space Telescope STEM Toolkit
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Multimedia

Downloads
Can't get enough pi? Download this year's NASA Pi Day Challenge graphics, including mobile phone and desktop backgrounds:

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.
Recursos en español
Facts and Figures
Websites
NASA's Universe of Learning materials are based upon work supported by NASA under award number NNX16AC65A to the Space Telescope Science Institute, working in partnership with Caltech/IPAC, Center for Astrophysics  Harvard & Smithsonian, and the Jet Propulsion Laboratory.