Do you like geometry? We do! We wanted to do a Wonder of the Day about a special shape, but couldn’t decide which shape to feature. The more we thought about it, though, the more we kept circling back around to the same shape. What was it? The circle, of course!

What do you like best about circles? We like their perfectly round shapes. They don’t have those pointy ends you’ll find on squares and triangles.

Some of our favorite things are shaped like circles. For example, our favorite dessert — pie — is shaped like a circle. And so is our favorite toy: the hula hoop. What other circle-shaped things do you see or use every day?

Geometry teachers define a circle as the set of points on a plane that are all the exact same distance from a central point. This means that circles are flat. When you study circles, you learn that every circle has a radius, a diameter, a circumference and an area.

A circle’s radius is the distance from its center to its edge. A circle’s diameter is the distance across the circle at its widest point. The diameter of a circle is always exactly twice its radius.

A circle’s perimeter — the distance all the way around its edge — is called its circumference. To calculate the circumference of a circle, you need to know its radius.

The formula for the circumference of a circle is 2πr, where r is the radius of the circle and π is the value pi (approximately 3.141592). Since the diameter of a circle is twice the radius, you can also think of the formula for the circumference of a circle as πd, where d is the diameter of the circle.

The area of the circle is the measurement of the number of square units inside of a circle. Once again, you need to know the radius. The formula for the area of a circle is πr2. The 2 in the formula is an exponent, which means you multiply the radius by itself. So, the formula for the area of a circle could actually be written πrr instead.

One neat thing about circles that all geometry teachers know is that if you know one of these facts — either radius, diameter, circumference or area — you can figure out all the other values! For example, if you know the radius of a circle, you can then figure out its diameter, circumference and area.

One other interesting aspect of circles is that every circle can be divided into 360 units called degrees. So, if you turn around in a full circle, you turn 360 degrees. If you simply turn halfway around — a half-circle — you turn 180 degrees.

So why 360 degrees instead of something simpler, like 100 degrees? Mathematicians believe the ancient Babylonians are to blame. In about 2400 B.C., they noticed the circular motion of the Earth around the Sun. They also calculated that it took about 360 days for this circular orbit to be completed.

Therefore, they decided to divide the circular path into 360 degrees. That way they could easily track each day’s passage on a circular calendar. So if you get confused in geometry by the number of degrees in a circle, blame the Babylonians!

65 Join the Discussion

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  1. So I LOVE Wonderopolis!!! It makes reading fun for children like me!!

    First of all I hate geometry. It’s really hard. BUT THIS MIGHT HAVE HELPED ME WITH THIS KIND OF GEOMETRY.

    So when I go to school today I’m going to tell my teacher (Mrs. Geise) and my friends about what I learned and about wonderopolis!!

    So thank you so much for teaching me about circular geometry!!!!!!

    • Thank you for WONDERing with us, Cate! We know that geometry can be tough sometimes, but we’re proud of you for trying your very best. We sure hope that our circle Wonder helped you see geometry in a new light and it will help you in the future! Thanks for sharing the Wonder with Mrs. Geise, your classmates and friends! HOORAY for great Wonder Friends like you! :)

    • Well we are so glad to hear that you’ve learned something new about that perfectly round shape, Delaney W! Thanks for WONDERing with us today! We hope you have a marvelous Monday! :)

  2. This is our first wonder and we liked it! We wonder how long it took the artist to make those circles in the snow. We’re curious about tomorrow’s wonder… We can’t wait to see what happens next!

    • Welcome to Wonderopolis! We’re so glad that our Friends in Mrs. Hess’ class are here today– HOORAY! Thanks for sharing your thoughts about our Wonder video, and using your imaginations to guess tomorrow’s Wonder, too! Keep up the great work! :)

    • Hi there, Bobby! We know that geometry can be tough to understand from time to time, but we hope you will watch the Wonder video and read the Wonder itself. We hope you enjoy WONDERing about circles even more! :)

    • What a great guess, Wonder Friends in Ms. Bayko’s class! We can’t wait to find out what tomorrow’s Wonder shall describe! :)

  3. We made some connections with today’s Wonder because our Math Teacher read Sir Cumference and the Great Knight of Angleland to us last week. We are learning about geometry concepts in her class right now. Whooohooo for making connections!

    Mrs. Ski had multiple exclamation points there but the students pointed out her punctuation infraction and it has been revised accordingly. :)

    We think that tomorrow’s Wonder of the Day will be about kings, medieval times, THOR!, pirates, funny voices, Harry Potter, Vikings, why people from different times and places talk differently, French, Ireland, or other dialects. Mrs. Ski is hoping beyond hope that it is related to Thor. :)

    • HOORAY, so many fun connections to the Wonder today! Hello, Mrs. Ski’s AM Class! Sir Cumference and the Great Knight of Angleland sounds like a SUPER book- we’ll have to check it out!

      We are proud of all of you for helping Mrs. Ski edit her comment… sometimes emotion gets the best of us all! :)

      You have suggested such great ideas for tomorrow’s Wonder that we can barely contain our excitement! YIPPEE! :)

    • Great guess, Jusin! We Wonder if you can determine how many degrees are in a circle from the passage below:

      “One other interesting aspect of circles is that every circle can be divided into 360 units called degrees. So, if you turn around in a full circle, you turn 360 degrees. If you simply turn halfway around — a half-circle — you turn 180 degrees.

      So why 360 degrees instead of something simpler, like 100 degrees? Mathematicians believe the ancient Babylonians are to blame. In about 2400 B.C., they noticed the circular motion of the Earth around the Sun. They also calculated that it took about 360 days for this circular orbit to be completed.

      Therefore, they decided to divide the circular path into 360 degrees. That way they could easily track each day’s passage on a circular calendar. So if you get confused in geometry by the number of degrees in a circle, blame the Babylonians!” :)

  4. Today’s circle study was fun!! Thank you Babylonians!! We think tomorrow’s Wonder is about Pirates: how they navigated their ships or how they found their treasure!

    • WOOHOO, we’re glad that our Wonder Friends, Gwen and Angus, are back today! Thanks for sharing your comment– we LOVE your enthusiasm! We cannot wait for tomorrow’s Wonder… what a SUPER guess! Ahoy! :)

  5. We thought the video for today’s Wonder has 360 degrees of awesome! Room for 360 thumbs up! It really turned our heads around. Lots of us are interested in how the people didn’t mess up while walking. Did they use GPS or have a map or was it freeform?

    We think tomorrow’s Wonder will be about THOR!, kings, vikings, yodeling, pirates, medieval times, people who talk differently, British people, and old times in Europe or even leprechauns.

    • WOHOO, we’re so glad that Mrs. Ski’s PM class is sending us (many) virtual thumbs up! :)

      We think that the participants in today’s Wonder video are very skilled, as well as the team who filmed the video! It must have taken a lot of coordination and practice to get it just right! :)

      Thanks for sharing ALL your WONDERful guesses for tomorrow’s Wonder; we look forward to chatting again soon! :)

  6. We are having fun guessing tomorrow’s wonder… is it about Scotland? The British… The Vikings? Or (as we have noticed in a novel we are reading) the way they talk in the 13 Colonies?

    • So many stellar guesses from Mrs. Bolin’s Class! YIPPEE! We are glad to hear that you’ve been using your imaginations and ideas from the novel you are reading! Great work! :)

    • Great question, Morgan! Degrees is a unit of measurement; in this case, degrees is used to measure a circle. Degrees can also measure the temperature. We Wonder what the temperature in your city is right now? :)

    • We’re so glad to hear that you enjoyed this Wonder video, Ririco! Thanks for sharing your comment! Have a SUPER day! :)

    • We wanted to Wonder about circles today, Zachary, and we hope you enjoyed it! We look forward to WONDERing about other cool shapes, soon! :)

  7. How come the circle can be any other shape like square, triangle, or rectangle? That’s what I want to know. -Marilyn was here xD ♥

    • We are glad you’re WONDERing about shapes on your own, Marilyn! You can fit a square, a triangle, and other shapes inside a circle, because a circle is perfectly round! We are proud of you for WONDERing about shapes, Marilyn. Sometimes geometry can be a bit tricky to understand! :)

    • HOORAY, we’re so glad to hear it, Grace W! Circles are very fun to Wonder about! What a great guess for tomorrow’s Wonder, we can’t wait to find out what it will be! :)

    • Hi there, lili13! We Wonder if you can find out the answer to our Wonder in the excerpt below:

      “One other interesting aspect of circles is that every circle can be divided into 360 units called degrees. So, if you turn around in a full circle, you turn 360 degrees. If you simply turn halfway around — a half-circle — you turn 180 degrees.

      So why 360 degrees instead of something simpler, like 100 degrees? Mathematicians believe the ancient Babylonians are to blame. In about 2400 B.C., they noticed the circular motion of the Earth around the Sun. They also calculated that it took about 360 days for this circular orbit to be completed.” :)

    • HOORAY, we’re glad to hear it, Vince! Today’s Wonder video was really spectacular! Thanks for sharing your comment! :)

    • We Wonder if you can read the excerpt below, Clara, to find the answer to today’s Wonder:

      “One other interesting aspect of circles is that every circle can be divided into 360 units called degrees. So, if you turn around in a full circle, you turn 360 degrees. If you simply turn halfway around — a half-circle — you turn 180 degrees.

      So why 360 degrees instead of something simpler, like 100 degrees? Mathematicians believe the ancient Babylonians are to blame. In about 2400 B.C., they noticed the circular motion of the Earth around the Sun. They also calculated that it took about 360 days for this circular orbit to be completed.

      Therefore, they decided to divide the circular path into 360 degrees. That way they could easily track each day’s passage on a circular calendar. So if you get confused in geometry by the number of degrees in a circle, blame the Babylonians!” :)

  8. I never knew why circles had 360 degrees. Thanks for helping this big kid learn something new today. See, even adults WONDER about lots of stuff! :)

    • HOORAY, we’re glad you’re WONDERing with us today, Bethany Rose! We love to Wonder with friends of all ages! We’re glad you learned something new today– thank you for sharing your comment! :)

  9. I loved today’s wonder, and it was really helpful because our class is starting circles in geometry. But I’m really curious: what would the formulas be if instead of the circle it would be a sphere?

    • What a great connection to your lesson, Colin! HOORAY! We are glad to know that you liked our Wonder about circles– they are really fun to think about! :)

      We bet you can do some WONDERing of your own about spheres, or perhaps your teacher can help you Wonder about that 3D shape, too! :)

    • We’re glad to hear that our geometry Wonder helped you today, Mikaela! We’re proud of you for WONDERing with us– thanks for being a great Wonder Friend! :)

  10. Dear WONDEROPOLIS I am in Las Vegas yah I am having fun I miss you guys I want you to come back this is a letter from Nicole Davis this teaches me this is the last letter I am going to ever make I am banned from the computer forever well goodbye WONDEROPOLIS I will miss you remember this letter from a long time.

  11. Dear Wonderopolis,

    Finding the area of a circle seems complicated, and with all the signs for the radius, circumference and the diameter it is even more complicated. I think it would be fun to find the area of a circle.

    From, Alex

    • Dear Wonder Friend Alex,
      Thanks for sharing your comment! We know that sometimes math can seem complicated in the beginning, but we believe in you! One of the cool things about math is that there is always a connection; the radius, diameter and circumference are all related! We hope you have a super day filled with Wonder! :)

  12. My favorite part of circles is it is smooth and round. Could you maybe do one on sphere? I thought circles were 360 degrees now I know for sure.

    • We’re glad you’re WONDERing about WONDERing, Michael! We have lots of Wonder Friends who help research all our Wonders. We go to the library, use credible sources from the Internet, and even talk to experts to get our Wonders just right! We also love to hear from Wonder Friends like you; you can nominate a Wonder of your very own: http://wonderopolis.org/nominate-wonder/ :)

  13. Dear wonderopolis,

    How did the Babylonian people get 360 days for the earth to go around the sun? And here is another object that is a circle: the frisbee.

    • Great question, Kenneth! We provided an excerpt from our circular Wonder… the answer is included below:

      “One other interesting aspect of circles is that every circle can be divided into 360 units called degrees. So, if you turn around in a full circle, you turn 360 degrees. If you simply turn halfway around — a half-circle — you turn 180 degrees.

      So why 360 degrees instead of something simpler, like 100 degrees? Mathematicians believe the ancient Babylonians are to blame. In about 2400 B.C., they noticed the circular motion of the Earth around the Sun. They also calculated that it took about 360 days for this circular orbit to be completed.

      Therefore, they decided to divide the circular path into 360 degrees. That way they could easily track each day’s passage on a circular calendar. So if you get confused in geometry by the number of degrees in a circle, blame the Babylonians!”

      Thanks for sharing your comment, and thinking of another circular object! :)

  14. Dear Wonderopolis,

    I did not know that in about 2400 BC they noticed the circular motion of the earth around the sun. They also calculated that it took 360 days for this circular orbit to be completed. What other shape has the same area as the circle? Maybe a frisbee.

    • Hey there, Lexi, we’re glad to learn that you understand why there are 365 days in the calendar year! We think you hit the nail right on the head– other circular objects include a frisbee, a hula hoop, and a basketball (which is a 3D object– a sphere!) :)

    • Dear Imogene, Reyna and Katie Beth, we’re so very sorry to hear that your friend William is fighting cancer. We are keeping him in our thoughts and we wish him health! We understand how tough it might be to have a friend dealing with cancer, so we want to make sure you take a look at this Wonder. It’s all about cancer, what it means, and how many survivors there are. We are sending hope and love your way! http://wonderopolis.org/wonder/what-is-cancer/ :)

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Have you ever wondered…

  • How many degrees are in a circle?
  • What is the relationship between the radius and diameter of a circle?
  • What do you call the distance around the edge of a circle?

Wonder Gallery

CircleVimeo Video

Try It Out

Ready to get some hands-on experience with circles? Geometry can be tough at first, so we’ve found a few helpful online activities that will help you understand what you’ve learned about circles.

If you want to learn more about degrees and angles, check out this fun online Angles activity. Can you correctly guess all the angles you need to squirt the various objects with the water hose?

Here are some more fun interactive circle activities to expand your circular knowledge:

Still Wondering

Illuminations’ Circle Tool interactive allows children to compare the relationships between radius, diameter, circumference and area by manipulating a circle.

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