Physics Photo of the Week

March
14, 2008

Two Pi's from one Pie

Today is Pi Day! What a fitting way to celebrate Pi Day with a Pie! Especially a cream pie. In a complete circle of a pie, there are 2 Pi radians. Radians are a "natural" way to measure angles - much more natural than measuring in degrees. A radian is defined as the angle produced by an arc segment of a circle in which the curved length of the arc segment is exactly one radius. The drawing at left is a segment circle that is exactly one radian. The radius of the segment is 8 units. The curve on the outside of the segment is also 8 units. The arc in the wedge is then exactly one radian - the natural unit for angles. In the more familiar units of degrees, one radian is equivalent to the rather "unnatural" 57.2958... degrees.

Back to the complete circle: Since the circumference of a circle is exactly 2 Pi times the radius, the angle of a complete circle is the whole circumference divided by the radius. That leaves 2 Pi radians.

In dividing a pie among a family of six, each share is 1/6 of 2 Pi, or Pi/3. If Mom asks you how much pie you would like, merely say, "I would like Pi/3 radians please". The chocolate cream pie featured above is marked for easy cutting into pi/3 radian sectors to serve a family of six.

Many thanks to Vicki for making the pie!

There will be no Physics Photo of the Week next week, March 21, due to spring break at Warren Wilson College. The next Physics Photo of the Week will be published on March 27, 2008 when we will celebrate the Equinox.

Two Pi's from one Pie

Today is Pi Day! What a fitting way to celebrate Pi Day with a Pie! Especially a cream pie. In a complete circle of a pie, there are 2 Pi radians. Radians are a "natural" way to measure angles - much more natural than measuring in degrees. A radian is defined as the angle produced by an arc segment of a circle in which the curved length of the arc segment is exactly one radius. The drawing at left is a segment circle that is exactly one radian. The radius of the segment is 8 units. The curve on the outside of the segment is also 8 units. The arc in the wedge is then exactly one radian - the natural unit for angles. In the more familiar units of degrees, one radian is equivalent to the rather "unnatural" 57.2958... degrees.

Back to the complete circle: Since the circumference of a circle is exactly 2 Pi times the radius, the angle of a complete circle is the whole circumference divided by the radius. That leaves 2 Pi radians.

In dividing a pie among a family of six, each share is 1/6 of 2 Pi, or Pi/3. If Mom asks you how much pie you would like, merely say, "I would like Pi/3 radians please". The chocolate cream pie featured above is marked for easy cutting into pi/3 radian sectors to serve a family of six.

Many thanks to Vicki for making the pie!

There will be no Physics Photo of the Week next week, March 21, due to spring break at Warren Wilson College. The next Physics Photo of the Week will be published on March 27, 2008 when we will celebrate the Equinox.

Physics
Photo of the
Week is
published weekly during the academic year on Fridays by the Warren
Wilson College Physics
Department. These photos feature an interesting phenomena in
the world around us. Students, faculty, and others are invited to
submit digital (or film) photographs for publication and
explanation. Atmospheric phenomena are especially welcome.
Please send any photos to dcollins@warren-wilson.edu.

Click here to see the Physics Photo of the Week Archive.

Click here to see the Physics Photo of the Week Archive.

Observers are invited to submit
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