ShmoopTube

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What is Dilation? a la Shmoop.

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Dr. Derango has been hard at [Dr Derango in a lab]

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work in his secret laboratory for the past several months, and he’s finally ready to

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unveil his latest dastardly device.

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It’s a ray gun that can both shrink and enlarge objects… [Dr Derango using a raygun to enlarge a puppy]

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…unfortunately, there’s a slight glitch.

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Rather than affecting the actual object it’s pointed at, it creates a second, similar object [An apple and a second apple appears]

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that is either bigger or smaller than the first.

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It kind of defeats the purpose, but Dr. Derango doesn’t want to have to admit to the people

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who gave him the grant that he fouled up, so…he’s putting on a brave face and just [Dr Derango hiding in a bush]

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going with it. The good doctor tests out his device first

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on a wedge of cheese.

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He loves cheese…who doesn’t?...so why not create more of it? [Dr Derango uses raygun on a wedge of cheese]

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He turns one dial to “enlarge”, sets the scale factor to “4” and points it at the cheese.

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Within moments, a second, much larger wedge appears behind the first. [Larger wedge of cheese appears beside a normal wedge of cheese]

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The doctor is glad that all of his extensive dilation knowledge he picked up in high school

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hasn’t gone to waste.

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He knows that this is a perfect example of the phenomenon. In this instance, his ray

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gun acts as the center of dilation…

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…the original wedge of cheese represents the preimage… [Original wedge of cheese and second wedge of cheese appears]

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…and the secondary wedge represents the image.

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Because there is a scale factor of 4, the dimensions of the new wedge are all exactly

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4 times greater than that of the original hunk o’ cheese.

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Encouraged by the success of this first trial, Dr. Derango decides to switch the dial to

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“reduce”. He turns the scale factor to point-three. [Dr Derango turns the scale factor to reduce on the raygun]

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He then steps inside the tent in the backyard that his wife has been making him sleep in

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ever since he began his experiments.

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He points his gun at the tent, which has always been too large for his taste. [Dr Derango holding a raygun in a tent]

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He likes things snug and cozy.

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And…boom. Suddenly, a second tent appears, with every measurement exactly three-tenths

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as large as the original. The trial is a success…although Dr. Derango

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really wishes he would have thought things through a little more carefully. [Dr Derango eneveloped in a small tent]

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He is not looking forward to the look his wife is sure to give him when he has to explain

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himself this time… [Dr Derango wifes slams the door]

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