• Visit
    • Calendar
    • After Dark Thursdays
    • Buy Tickets
    • Exhibits
    • Museum Galleries
    • Artworks on View
    • Hours
    • Getting Here
    • Visitor FAQ
    • Event Rentals
    • Field Trips
  • Education
    • Professional Development Programs
    • Free Educator Workshops
    • Tools for Teaching and Learning
    • Learning About Learning
    • Community Programs
    • Educator Newsletter
  • Explore
    • Browse by Subject
    • Activities
    • Video
    • Exhibits
    • Apps
    • Blogs
    • Websites
  • About Us
    • Our Story
    • Partnerships
    • Global Collaborations
    • Explore Our Reach
    • Arts at the Exploratorium
    • Contact Us
  • Join + Support
    • Donate Today!
    • Membership
    • Join Our Donor Community
    • Engage Your Business
    • Attend a Fundraiser
    • Explore Our Reach
    • Thank You to Our Supporters
    • Donor & Corporate Member FAQ
    • Host Your Event
    • Volunteer
  • Store
  • Visit
    • Frequently Asked Questions
    • Calendar
      • Today
      • This Week
      • Online
      • After Dark Thursday Nights
      • Arts
      • Conferences
      • Cinema Arts
      • Free + Community Events
      • Fundraising Events
      • Kids + Families
      • Members
      • Special Hours
      • Private Event Closures
    • Prices
    • Hours
    • Getting Here
    • Museum Map
    • Free Admission and Reduced Admission
    • Accessibility
    • Tips for Visiting with Kids
    • How to Exploratorium
    • Exhibits
    • Tactile Dome
    • Artworks on View
    • Cinema Arts
    • Kanbar Forum
    • Black Box
    • Museum Galleries
      • Bernard and Barbro Osher Gallery 1: Human Phenomena
        • Tactile Dome
          • 1971 Press Release
        • Black Box
        • Curator Statement
      • Gallery 2: Tinkering
        • Curator Statement
      • Bechtel Gallery 3: Seeing & Reflections
        • Curator Statement
      • Gordon and Betty Moore Gallery 4: Living Systems
        • Curator Statement
      • Gallery 5: Outdoor Exhibits
        • Curator Statement
      • Fisher Bay Observatory Gallery 6: Observing Landscapes
        • Wired Pier Environmental Field Station
        • Curator Statement
    • Restaurant & Café
    • School Field Trips
      • Getting Here
        • Bus Routes for Field Trips and Other Groups
      • Admission and Tickets
      • Planning Guide
      • Reservations
        • Field Trip Request Form
      • Resources
    • Event Rentals
      • Full Facility & Gallery Bundles
      • Fisher Bay Observatory Gallery & Terrace
      • Moore East Gallery
      • Bechtel Central Gallery & Outdoor Gallery
      • Osher West Gallery
      • Kanbar Forum

      • Weddings
      • Proms and School Events
      • Daytime Meetings, Events, & Filmings
      • Happy Hour on the Water

      • Rentals FAQ
      • Event Planning Resources
      • Rental Request Form
      • Download Brochure (pdf)
    • Groups / Tour Operators
      • Group Visit Request Form
    • Exploratorium Store
    • Contact Us
  • Education
    • Black Teachers and Students Matter
    • Professional Development Programs
      • Free Educator Workshops
      • Professional Learning Partnerships
      • Teacher Institute
        • About the Teacher Institute
        • Summer Institute for Teachers
        • Teacher Induction Program
        • Leadership Program
        • Teacher Institute Research
        • CA NGSS STEM Conferences
          • NGSS STEM Conference 2020
        • Science Snacks
          • Browse by Subject
          • Special Collections
          • Science Snacks A-Z
          • NGSS Planning Tools
          • Frequently Asked Questions
        • Digital Teaching Boxes
        • Meet the Teacher Institute Staff
        • Resources for Supporting Science Teachers
      • Institute for Inquiry
        • What Is Inquiry?
        • Watch and Do Science
        • Inquiry-based Science and English Language Development
          • Educators Guide
            • Conceptual Overview
              • Science Talk
              • Science Writing
            • Classroom Video Gallery
              • Magnet Investigation
              • Snail Investigation
            • Teacher Professional Development
            • Project Studies
            • Acknowledgments
          • Conference: Exploring Science and English Language Development
            • Interviews with Participants
            • Plenary Sessions
            • Synthesis, Documentation, and Resources
        • Workshops
          • Participant Portal
          • Fundamentals of Inquiry
            • Summary Schedule
          • BaySci Science Champions Academy
          • Facilitators Guides
          • Commissioned Workshops
        • Resource Library
        • Meet the IFI Staff
      • Resources for California Educators
      • K-12 Science Leader Network
      • Resources for Supporting Science Teachers
      • Field Trip Explainer Program
      • Cambio
    • Tools for Teaching and Learning
      • Learning Toolbox
      • Science Snacks
      • Digital Teaching Boxes
      • Science Activities
      • Tinkering Projects
      • Recursos gratuitos para aprender ciencias
      • Videos
      • Exhibits
      • Publications
      • Apps
      • Educator Newsletter
      • Exploratorium Websites
    • Educator Newsletter
    • Advancing Ideas about Learning
      • Visitor Research and Evaluation
        • What we do
        • Reports & Publications
        • Projects
        • Who we are
      • Center for Informal Learning in Schools
    • Community Programs
      • High School Explainer Program
      • Xtech
      • Community Educational Engagement
      • California Tinkering Afterschool Network
        • About
        • Partners
        • Resources
        • News & Updates
        • Further Reading
  • Explore
    • Browse by Subject
      • Arts
      • Astronomy & Space Sciences
        • Planetary Science
        • Space Exploration
      • Biology
        • Anatomy & Physiology
        • Ecology
        • Evolution
        • Genetics
        • Molecular & Cellular Biology
        • Neuroscience
      • Chemistry
        • Combining Matter
        • Food & Cooking
        • Materials & Matter
        • States of Matter
      • Data
        • Data Collection & Analysis
        • Modeling & Simulations
        • Visualization
      • Earth Science
        • Atmosphere
        • Geology
        • Oceans & Water
      • Engineering & Technology
        • Design & Tinkering
        • Real-World Problems & Solutions
      • Environmental Science
        • Global Systems & Cycles
        • Human Impacts
      • History
      • Mathematics
      • Nature of Science
        • Measurement
        • Science as a Process
        • Size & Scale
        • Time
      • Perception
        • Light, Color & Seeing
        • Listening & Hearing
        • Optical Illusions
        • Scent, Smell & Taste
        • Tactile & Touch
      • Physics
        • Electricity & Magnetism
        • Energy
        • Heat & Temperature
        • Light
        • Mechanics
        • Quantum
        • Sound
        • Waves
      • Social Science
        • Culture
        • Language
        • Psychology
        • Sociology
    • Browse by Content Type
      • Activities
      • Blogs
        • Spectrum
          • Arts
          • Behind the Scenes
          • News
          • Education
          • Community & Collaborations
          • Science
        • Eclipse
        • Studio for Public Spaces
        • Tangents
        • Resonance See & Hear Blog
        • Fabricated Realities
        • Tinkering Studio: Sketchpad
        • Exploratorium on Tumblr
      • Exhibits
      • Video
      • Websites
      • Apps
        • Total Solar Eclipse
  • About Us
    • Our Story
    • Land Acknowledgment
    • Explore Our Reach
    • Impact Report
    • Awards
    • Our History
      • 50 Years 1969–2019

    • Leadership Cabinet
    • Board of Trustees
    • Board of Trustees Alumni
    • Staff Scientists
    • Staff Artists

    • Arts at the Exploratorium
      • Artworks on View
      • Artist-in-Residence Program
      • Cinema Arts
        • History and Collection
        • Cinema Artists-in-Residence
        • Resources and Collaborating Organizations
        • Kanbar Forum
      • Center for Art & Inquiry
        • Begin Here
          • Lessons
            • Bob Miller/Light Walk
            • Ruth Asawa/Milk Carton Sculpture
          • Workshops
      • Resonance
        • About the Series
        • See & Hear
        • Past Seasons
      • Over the Water
      • Black Box
      • Upcoming Events
      • Temporary Exhibitions
      • Arts Program Staff
    • Teacher Institute
    • Institute for Inquiry
    • Explainer Programs
    • Studio for Public Spaces
    • Exhibit Making
    • Partnerships
      • Building Global Connections
        • Global Collaborations
          • Projects
          • Approach
          • People
          • Impact
      • Partnering with Science Agencies
        • NASA
        • NOAA
      • Partnering with Educational Institutions
      • Osher Fellows

    • Job Opportunities
    • Become a Volunteer

    • Contact Info
    • Newsletter
    • Educator Newsletter
    • Blogs
    • Follow & Share
    • Press Office

    • FY21 Audit Report
    • 990 FY20 Tax Return
    • Use Policy
      • Privacy Policy
      • Intellectual Property Policy
  • Join + Support
    • Donate Today!
    • Membership
      • Membership FAQ
      • Member Benefits
      • After Dark Membership
      • Member Events
      • May Is for Members
    • Join Our Donor Community
    • Engage Your Business
      • Corporate Membership
      • Luminary Partnerships
    • Attend a Fundraiser
      • Wonder Funday
      • Science of Cocktails
      • Party at the Piers
        • Event Leadership and Host Committee
    • Explore Our Reach
    • Thank You to Our Supporters
    • Donor & Corporate Member FAQ
    • Volunteer
      • How to Apply
      • Application for Internships
      • Our Contract
      • Application for Individuals
  • Press Office
    • Press Releases
    • News Coverage
    • Events Calendar
    • Photographs
    • Press Video
    • Press Kits
    • Press Visits
    • Exploratorium Logos
    • Recent Awards
    • Praise for the Exploratorium
    • Join Our Press List
  • Store

Masks and vaccinations are recommended. Plan your visit  

Visitor FAQ Buy Tickets Donate Today
Exploratorium
Exploratorium
  • Visit
    • Calendar
    • After Dark Thursdays
    • Buy Tickets
    • Exhibits
    • Museum Galleries
    • Artworks on View
    • Hours
    • Getting Here
    • Visitor FAQ
    • Event Rentals
    • Field Trips
  • Education
    • Professional Development Programs
    • Free Educator Workshops
    • Tools for Teaching and Learning
    • Learning About Learning
    • Community Programs
    • Educator Newsletter
  • Explore
    • Browse by Subject
    • Activities
    • Video
    • Exhibits
    • Apps
    • Blogs
    • Websites
  • About Us
    • Our Story
    • Partnerships
    • Global Collaborations
    • Explore Our Reach
    • Arts at the Exploratorium
    • Contact Us
  • Join + Support
    • Donate Today!
    • Membership
    • Join Our Donor Community
    • Engage Your Business
    • Attend a Fundraiser
    • Explore Our Reach
    • Thank You to Our Supporters
    • Donor & Corporate Member FAQ
    • Host Your Event
    • Volunteer
  • Store
Science Snacks
Science activity using straight lines to learn about circles
Science activity using straight lines to learn about circles
  • Science activity using straight lines to learn about circles
  • Science activity using straight lines to learn about circles

Pi Graph

Use straight lines to learn about circles.

Graphing data can help you discover patterns in nature. This Snack reveals an important ratio found in circles.


Grade Bands: 
6-8
9-12
Subject: 
Data
Mathematics
Nature of Science
Measurement
Keywords: 
pi
patterns
constant
graph
NGSS and EP&Cs: 
CCCs
Patterns
Scale, Proportion, and Quantity

  • Facebook logo
  • Reddit logo
  • Twitter logo


Tools and Materials

  • Cylindrical or circular objects of different sizes, such as plates, poster tubes, rolls of tape, or bottle caps
  • String
  • Metric ruler
  • Paper and pencil (not shown)
  • Graph paper
  • Optional: several partners and a large piece of graph paper to collect group data

Assembly

None needed.


To Do and Notice

On a piece of paper, create a chart like the one below. Measure the diameter of each object and record it on the chart. Then—using a piece of string wrapped around the object—measure the circumference, and record it on the chart.

           Object                      Diameter (cm)       Circumference (cm)
     
     
     
     
     
     
     
     

 

On your graph paper, plot the points that represent each object, where the x coordinate is the diameter and the y coordinate is the circumference. (If you’re doing this with other people, you might want to combine all your data points on a large piece of graph paper.)

Draw a best-fit straight line that goes through the points. Not all points will touch, but you can estimate the line in space that the points seem to best cluster around.

Calculate the slope of the line by choosing a point on the line and dividing the y coordinate by the x coordinate.


What's Going On?

In this Snack, the points you plot for different circles or cylinders should form a straight line, which indicates that there’s something constant in the linear relationship between any circle’s diameter and circumference.

This constant of proportionality is called the slope of the line. When you divided the y coordinate (circumference) by the x coordinate (diameter), you should have found something close to the value of pi, one of the most important mathematical constants.

Pi, which is defined by the ratio of a circle’s circumference to its diameter and expressed with the Greek symbol π, is approximately 3.14. This relationship is often represented as the formula for a circle’s circumference: c = π*d.


Going Further

This Science Snack is part of a collection that showcases female mathematicians and math educators whose work aids or expands our understanding of the phenomena explored in each Snack.

Highlighted Scientist: Dr. Emma Haruka Iwao

Source: Wikimedia Commons

Emma Haruka Iwao (pictured above) is a mathematician and computer scientist who broke the Guinness world record for calculating the most digits of pi in 2019, and held that record until 2020. Fascinated with pi since childhood, she calculated pi on her computer when she was 12 years old! Inspired by her own fascination with pi, Iwao and a Google team computed pi to 31.4 trillion decimal places (3.14 x 1,013), far more digits than the previous record. Explore the mathematical constant pi with our Pi Graph Science Snack.



Related Snacks

Science activity to demonstrate pi using circumference and string
Cutting Pi

String and scissors are all you need to find pi all around you.

Science activity to estimate pi with the random tossing of toothpicks
Pi Toss

Randomly toss some toothpicks, with pi as your reward.

Science activity that explores how graphing can reveal patterns in data
Plot the Dot

Graphing can be a slippery slope to understanding.



Creative Commons License



This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Attribution: Exploratorium Teacher Institute

  • Education
    • Teacher Institute
    • Tools for Teaching and Learning
      • Science Snacks
        • Browse by Subject
        • Special Collections
        • Science Snacks A-Z
        • NGSS Planning Tools
        • Frequently Asked Questions



Connect with us!



  •   Sign up for our educator newsletter

  •   Follow #ExploEDU

  •   Teacher Institute YouTube

  •   Teacher Institute Facebook

  •  teacherinstitute @exploratorium.edu

Exploratorium
Visit
Join
Give

Pier 15
(Embarcadero at Green Street)
San Francisco, CA 94111
415.528.4444

Contact Us

  • Plan Your Visit
  • Calendar
  • Buy Tickets
  • Getting Here
  • Store
  • Event Rentals
  • About Us
  • Become a Member
  • Donate
  • Jobs
  • Volunteer
  • Press Office
  • Land Acknowledgment

Get at-home activities and learning tools delivered straight to your inbox

The Exploratorium is a 501(c)(3) nonprofit organization. Our tax ID #: 94-1696494
© 2023 Exploratorium | Terms of Service | Privacy Policy | Your California Privacy Rights |