| 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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