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This manuscript presents a linear algebra-based technique that only requires two unique photographs from a digital camera to mathematically construct a 3D surface representation which can then be 3D printed. Basic computer vision theory and manufacturing principles are also briefly discussed.

Albertson and Berman [1] conjectured that every planar graph has an induced forest on half of its vertices; the current best result, due to Borodin [3], is an induced forest on two fifths of the vertices. We show that the Albertson-Berman conjecture holds, and is tight, for planar graphs of treewidth 3 (and, in fact, for any graph of treewidth at most 3).… (More)

Over the past few years, the 3D printing industry has experienced remarkable innovation, making it possible for anyone with access to a computer, design software, and a good idea to become a manufacturer. Recently, relatively inexpensive 3D printers have come on the market and are being purchased by colleges, universities, and libraries. In this primer, we… (More)

Albertson and Berman conjectured that every planar graph has an induced forest on half of its vertices. The best known lower bound, due to Borodin, is that every planar graph has an induced forest on two fifths of its vertices. In a related result, Chartran and Kronk, proved that the vertices of every planar graph can be partitioned into three sets, each of… (More)

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