Dilations in Math, Art, and Science
Historically, dilations have been fundamentally indispensable in the development of cultures around the world. The Greeks for example, without dilations would have merely been a bunch of homeless philosophers instead of the brilliant architects they were. In this paper I’ll discuss the uses and the history of dilations.
Dilations have long been used in the world, both past and present. Early examples include Greek, Roman, and other ancient cultures using dilations to accomplish various complex engineering feats. Overseers would commonly sit a set distance from a construction site, and a pole of some sort with a fixed length was placed in front of them. Because of this layout, the engineers were allowed to see both length and height (if desired) of the specified building or construction.
Artists also commonly utilized the use of simple dilations to make scaled and accurate artwork in the 1400 and 1500’s. Even today, you see dilations in use. For instance, a picture of the globe, or a map of a particular area can be magnified many times, creating dilation (see the example on the visual board.) On a golf course, you might look at the flagpole at the end of the course to get a fairly accurate sense of the distance from you to the green. Common sense dictates that the smaller the 4′ flag is in your perspective, the farther the golf hole is from you, and vice versa.
Dilation Instructions: To perform a simple dilation, follow these instructions. Place one point, the size of a pencil tip, at any place on a piece of paper (preferably the near the middle to keep this simple.) Now, measure a compass width to approximately ? inch. Make a light circle surrounding your dilation origin (pencil dot; dilation center.) Place a dot at any place on that circle, and then exactly ? inch away from the dot you just made, draw another dot on the circle. After this, measure your compass width to approximately 1-inch wide. Draw another circle about your origin (original dot; pencil dot; dilation center.) Make a line that goes through both your origin, and one of your dots that are on the first inner circle. Do the same with the origin and the other dot on the first inner circle. Now, find the place where each line intersects the second circle and place a dot on those two places. Erase the inner and outer circles and the two lines and you have a dilation!
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