Ask Dr. Math

Middle School Archive

Browse Middle School Conic Sections/Circles
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Circle formulas - area, circumference.
    Is a circle a polygon?
    Why is a circle 360 degrees?

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Explorations of the Circle [02/09/1999]

What is the definition of a circle? How does it relate to pi? What are the important parts of a circle?

Finding a Circle's Area Without Pi [02/24/2001]

How can I find the area of a circle without using pi?

Finding Miles Per Hour [03/06/2002]

If a wheel is making 64.2 revolutions per minute, how many miles per hour is it going?

Finding the Area of a Circle [3/25/1996]

Is there an easy way to do find the area of a circle?

Finding the Circumference [11/27/1997]

Would you be able to tell me how to work out the circumference of a circle?

Finding the Table's Diameter [05/05/2001]

A circular table is pushed into the corner of a room so that it touches both walls. On the edge of the table is a scratch 8" from one wall and 9" from the other wall. What is the diameter of the table?

Folding a Circle to Get an Ellipse [01/08/2001]

How can I prove that taking a point on a circle, folding it to an interior point, and repeating this process creates an envelope of folds that forms an ellipse?

Formula for the Area of a Circle [12/17/1998]

The formula, and how it works.

From Degrees to Radians [09/22/1998]

What are radians? How do you convert degrees to radians?

History of Circle Area Formula [03/19/2007]

Do we know who figured out that pi*r^2 gives the area of a circle?

How Did Eratosthenes Measure the Circumference of the Earth? [6/26/1996]

Didn't Eratosthenes measure the lengths of shadows of sticks at different locations on the same day and time of the year, so he had two right triangles...?

Inscribing a Regular Pentagon within a Circle [04/15/1999]

What are the reasons for the steps in inscribing a regular pentagon within a circle with only the help of a compass and a straightedge?

Intersection of Circles [10/08/1998]

I do not understand the term intersection in geometry.

An Introduction to Pi and Its Use in Circle Problems [04/28/2004]

The doctor helps a confused student with circle parts, their relation to each other, and pi.

Is a Circle a Polygon? [03/07/1999]

A circle is not a polygon.

Lateral Surface of a Cone [02/10/1999]

How do you find the formula for the lateral surface of a right cone?

Measuring the Circumference of the Earth [08/16/1999]

How did Eratosthenes use a mathematical formula to prove the earth is round?

Origin of the 360-Degree Circle [11/10/1999]

Did the Babylonians discover the 360-degree circle?

Perimeter of an Oval [04/08/1999]

What is the perimeter of an oval called?

Pi and the Area of Circles [05/11/1997]

If pi truly goes on and on forever without repeating, is it impossible to find the exact area of a circle?

Placing Coins That Touch [8/7/1996]

How many 20-cent coins can you put around a 20-cent coin so that all of them touch?

Polygons and Circles [4/3/1996]

Is a circle a polygon? Why or why not?

Polygons, Infinite Sides, and Circles [04/03/1997]

Can a regular polygon with an infinite number of sides be a circle?

Radians and Degrees [11/21/1994]

Why are radians preferable to degree measures?

Radius of a Pizza [8/27/1996]

If a pizza has an area of 30 inches, what is its radius?

Regions, Chords, and Circles [02/05/1998]

A given circle has n chords. Each chord crosses every other chord but no three meet at the same point. How many individual regions are in the circle?

The Relation of Perimeter to Area [10/2/1995]

I'm puzzled by the ability of two fences with the same perimeter to have very different areas inside them. I realize by LxW an 8' x 10' fence will have more area than a 6' x 12' fence, but WHY? Both fences have 18' surrounding them but different areas. Also does a circle or a square conserve more area with identical perimeters?

Rhumb Lines and Great Circle Routes [09/24/1998]

Can you explain great circles and rhumb lines and how they relate to shortest distances in geometry?

Rounding Pi [06/01/1999]

Can you prove that the value of Pi cannot be rounded down to 3.0? Is there an error in the Bible?

Simple Closed Curve [05/22/2001]

Why is a simple closed curve called just that?

Square Inscribed in a Circle [09/28/1997]

What percent of the circle is contained within the square?

Subtend [07/23/1997]

Please give me the definition of the word "Subtends."

Symmetry Lines [03/30/2000]

How many symmetry lines are in a circle?

Three Cuts and Seven Pieces [01/18/1999]

Is there any way that you can cut a pie into seven pieces with just three straight cuts?

Traceable Mathematical Curves [10/27/1997]

Is there any way to tell just by looking if a curve is traceable or not? Is there some property of a curve that will tell you this? Do curves have formulas?

Tracing an Ellipse [08/17/1997]

How do you form an ellipse using 3 points?

Uses of Ellipses [04/02/2003]

Where are ellipses found in real life?

Walking Around the World [08/18/1999]

How much farther does a man's head go than his feet when he walks around the world? Is this a trick question?

Ways to Remember the Meaning of Circumference, Radius, Diameter, and Chord [03/18/2004]

If the minute hand touched the edge of the clock, would it be most like a diameter, radius, circumference, or chord of a circle? I have a hard time remembering what each of those means.

What is Circumference? [06/25/2001]

My friend told me it's somewhat like the measurement of the outside of a circle, but I don't understand that.

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