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A hinged dissection of a set of polygons S is a collection of polygonal pieces hinged together at vertices that can be rotated into any member of S. We present a hinged dissection of all edge-to-edge gluings of n congruent copies of a polygon P that join corresponding edges of P. This construction uses kn pieces, where k is the number of vertices of P. When… (More)

- Erich Friedman
- 2000

Let s(n) be the side of the smallest square into which we can pack n unit squares. We improve the best known upper bounds for s(n) when We present relatively simple proofs for the values of s(n) when n = 2, 3, 5, 8, 15, 24, and 35, and more complicated proofs for n=7 and 14. We also prove many other lower bounds for various s(n). We also give the best known… (More)

- Erich Friedman
- 2002

- Erich Friedman
- 2002

- Erich Friedman
- 2002

- Erich Friedman
- 2004

In [2], the authors consider the problem of finding the maximum number of points colored with 2 colors that contain no empty monochromatic convex fourgons, and gave the lower bound of 18. In [1], the author increased this lower bound by giving such a configuration of 20 points. We exhibit below 30 two-colored points, no three points colinear, with no empty… (More)

This paper shows how to hinge together a collection of polygons at vertices in such a way that a single object can be reshaped into any n-omino, for a given value of n. An n-omino is deened generally as a connected union of n unit squares on the integer grid. Our best dissection uses 2n , 1 polygons. We generalize this result to the connected unions of… (More)

- Erich Friedman
- 2002

While Ludwig Boltzmann's contributions to theoretical science are many, the Boltzmann distribution formula is arguably his most important contribution to the field of chemistry. The formula predicts the energy distribution of molecules in an equilibrium system at a given temperature. This distribution in turn governs numerous chemical phenomena, including… (More)

- J Mareš, E Friedman, A Gal, B K Jennings
- 2008

Strong interaction level shifts and widths in Σ − atoms are analyzed by using a Σ nucleus optical potential constructed within the relativistic mean field approach. The analysis leads to potentials with a repulsive real part in the nuclear interior. The data are sufficient to establish the size of the isovector meson–hyperon coupling. Implications to Σ… (More)