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Samuel Zbarsky, 17, of Rockville, submitted a mathematics project to the Intel Science Talent Search that has implications for the study of geometry and has potential applications in the construction of efficient computer networks. Sam addressed the following conjecture: Suppose we want to connect points in Euclidean high-dimensional space so that each point is connected to no more than three other points. The claim is that the ratio of the total path length to the sum of distances from the starting point is at most 1.5. A 1994 proof had shown that this ratio could be no more than 1.666, and another mathematician had subsequently reduced this to 1.63. Sam’s results improved on this even further, proving that it was between 1.447 and 1.561. At Montgomery Blair High School in Silver Spring, Sam is captain of the math team and participates in computer club, science bowl and the It’s Academic team. He is fluent in Russian and has won honors at numerous competitions including the International Linguistics Olympiad, USA Math Olympiad, USA Physics Olympiad and the Harvard- MIT math tournament. Sam is the son of Alexander and Margaret Zbarsky, and he credits his father as being the most influential person in the development of his scientific career.
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