Forum Question: See Math

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The Greek philosopher Heraclitus stated, Nothing is permanent except change. Evolution is based on the idea that the survival of a species depends on its ability to adapt to changes in the environment. Social change is advocated as a necessary means to creating a better world. It has been suggested that the key to happiness is the recognition and acceptance of the impermanence of life.

Calculus is the mathematics of change. You can train your eyes to look at the world through mathematical lens and see math in everything, everywhere. Our life experiences teach us that change can be sudden and discontinuous, or a seamlessly smooth continuum. The Forum Question this week is to capture change through the lens of calculus and the medium of photography. You are to take a real world photo to illustrate each of the following functions:
- continuous and differentiable.
- continuous, but not differentiable.
- not continuous and not differentiable.
- an invertible function.
- a function that is not one-to-one.

The Forum Question requires setting up a Flickr account. Flickr is an online photo management and sharing application. Flickr enables users to upload photos; organize and sort photos with tags, annotate photos with “hot spot” notes; add comments and captions; and share photos with friends and family. Your five photos are to be uploaded to your Your photostream in Flickr.

With each photo you are to include the following:
1. A title.
2. A description of the photo.
3. A “hot spot” somewhere on the photo, highlighting why you chose it to illustrate the type of function. A “hot spot” is a note that you can place directly onto the photo. Here is an example and  instructions.
4. The following three tags:
(1) Our class tag crmscalc2010.
(2) Your nom de plume.
(3) The tag seemath.

Note: Flickr uses the same tagging system as Delicious in that tags are to be separated by a space. DO NOT USE A COMMA to separate tags. Flickr will look on the comma as part of the tag.

You cannot use screen shots, clip art, or copy pictures off the internet. These must be real world photographs that you have taken. However, you may stage or "set up the shot" in any way you like. Be creative and have fun with this.