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Natalia Nottingham Math Images Project Ideas

Working with: Hana Pearlman and Jane Xu

Ideas: Hana, Jane, and I have decided that we want to work with something related to circles. We discussed many different possible patterns that involve circles, but have not decided which particular one(s) we want to use. One pattern that we were discussing had many circles within each other. The pattern starts with one big circle, then has a smaller circle that is tangent to the original circle. Then there is a smaller circle inside of the second circle that is tangent to the second circle. And the pattern continues with more circles in the same way. The parts of the connected circles form spirals. We were thinking of somehow exploring the relationships between the size and placement of the circles in comparison with the spiral. For example, what would happen if the area/diameter of each circle was equal to the square root of the area/diameter of the next biggest circle? Also, we were thinking of maybe figuring out what size and placement of the circles was needed to form the archimedian spiral. I was also thinking that maybe we could do something similar but with elipses, and study how the circles were similar or how they varied from the elipses (but I'm not sure if we're going to use that idea). We were also thinking of figuring how this could related to real life situations or objects in real life.