Step 1:  Create a 200px by 200px blank document and fill the background layer with white. Create a blank transparent layer on top and select it. Then, using the Elliptical Marquee Tool, create an oval shape and Edit > Fill it with Black. Do NOT lose your selection.

Step 2: Using the cursor keys, move the selection around 45px to the right (or whatever distance looks right to you).

Step 3:  Now press DEL on the keyboard and lose your selection.  There you have it - a crescent shape ready for further manipulation.  You can add a little individuality to your work by clicking on Edit > Transform > Perspective. Drag the corners around until you have achieved the effect you desire, and press ENTER to finalize the change.

Variations: Layer effects (especially gradients) are great when used on crescent shapes, as the example to the left shows.  Just have a play around and see what you can come up with - the example logo below took a mere 5 minutes to create from start to finish, and would look good on a corporate interface.

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