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Type of math needed to solve a 2nd problem

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jasonbe

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What type of math would I need if I wanted to represent the curves drawn as a result of single stack of overlapping uncapped pens being slid down a chute? The pens would be pointed in the same direction in the stack. The stack of overlapping pens would have a length many times larger than any one pen being slid down the chute. The chute would be elevated from a piece of paper. The pens would have a near vertical orientation in relation to the paper before they struck the paper, created curves, bounced, and created more curves.
 
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