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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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