Constructing the Perfect Piston

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This Demonstration is a top view of a 3D engine piston. It is designed to engage calculus students in learning about the formal definition of a limit. The idea is to determine the range of possible diameters giving a piston with a cross-sectional area within the given tolerance constraints.

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The blue line represents the outer boundary of the piston and the dashed lines represent the range of tolerances for the area. The diameter slider adjusts the size of the blue lines, indicative of the process a machinist goes though when converting a block of steel into a piston. The dashed line indicates the tolerance allowed in the desired area for good combustion. It is possible to overshoot the desired area, in which case the blue line falls outside the maximum possible desired area. On the other hand, if the machinist grinds too long, the piston gets too small and the blue line falls inside of the minimum possible desired area. The box to the right provides a close-up view for smaller tolerances.

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Contributed by: Joshua Fritz, Angela Sharp, and Chad Pierson (March 2011)
Open content licensed under CC BY-NC-SA


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