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# An Analysis of the Principles of Dilation Throughout the History of Architecture

Dilation 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 wouldnt 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 belowConstruct 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 12 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 5105 so the scale factor will equal 3 Preimage Image When I first learned about dilation I thought

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