MAA Found Math: Anne Burns (Long Island University) received Third Place for "Circles on Orthogonal Circles"Â in the 2011 Mathematical Art Exhibition Awards at the 2011 Joint Mathematics Meetings in New Orleans.
"A loxodromic MÃ¶bius transformation has two fixed points, one attracting and the other repelling," said Burns. "Starting with a small circle around the repelling fixed point and repeatedly applying the MÃ¶bius transformation results in a family of circles that grow at first, each containing the previous one. Successive images eventually pass over the perpendicular bisector of the line connecting the fixed points and shrink down as they are attracted to the other fixed point. Each circle in a second family of circles passes through the fixed points and is mapped to another circle in that family. Each circle in the second family is orthogonal to every circle in the first family."
The 2011 Joint Mathematics Meetings were held January 6 - 9 in New Orleans
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