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Dilation Essay, Research Paper

Dilation

Dilation has been used for millions of years. Even in the ancient times and still

we use it until this day. An example of dilation used in ancient times is when ancient

Egyptians built the pyramids. The pyramids were built in different sizes, but

proportional. Now in this day and time we use dilation in many aspects. Dilation is used

in both science and math. In science the microscope shows dilation, without

microscopes many of the scientific discoveries wouldn’t be possible! In math dilation

mainly is used in Geometry to draw figure of different sizes in proportional sizes. In

art dilation is used widely for, example architecture, paintings, and statues. In our

everyday life we have many examples of dilation like, binoculars, toy cars, little

ornaments that represent larger ones in a smaller version.

This involves the use of dilations, that is, transformations of the plane that

are either contractions or expansions about a point (the center of the dilation), by a

constant (positive) ratio. A dilation can either be an expansion (if the ratio is larger

than one) or a contraction (if it is smaller than one).

Look at the figure below.Construct a point C in the plane, and mark it as the center of

dilation. Now draw any polygonal figure, and dilate it about the center C by a fixed

ratio (1/2, or 3, or whatever). Drag around this polygon, and observe how the image

changes. In particular look at the vertices, their images and the center. Can you see

any relation among them? To find the scale factor we have to add one side of both

corresponding sides and divide them by the corresponding side of the preimage. For

example, side A for the preimage is equal to 5 and side A for the image is equal to 10.

Thus, 5+10/5 so the scale factor will equal 3!!!!

Preimage Image

When I first learned about dilation, I thought that is wasn’t important and that

there was no use for it at all, but doin this project made my perspective of dilation and

Geomety change. Dilation is important. I have learned that dilation isn’t used in just

Geometry, it is used in science, math, art, and our everyday life. Dilation is used

everywhere, without you even realizing it, but hopefully after reading this you have

realized that we need dilation.


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