We present a simple new algorithm for triangulating polygons and planar straightline graphs. It provides \shape" and \size" guarantees: All triangles have a bounded aspect ratio. The number of triangles is within a constant factor of optimal. Such \quality" triangulations are desirable as meshes for the nite element method, in which the running time generally increases with the number of triang...

In grade school, students learn a standard set of Euclidean triangles. Among this set, the usual 45–45–90 and 30–60–90 triangles are the only right triangles with rational angles and side lengths each containing at most one square root. Are there any other such right triangles? We answer this question completely and present an elegant complement called Ailles’ rectangle that deserves to be in e...

Abstract. Monotone triangles are certain triangular arrays of integers, which correspond to n × n alternating sign matrices when prescribing (1, 2, . . . , n) as bottom row of the monotone triangle. In this article we define halved monotone triangles, a specialization of which correspond to vertically symmetric alternating sign matrices. We derive an operator formula for the number of halved mo...

in this paper, we find explicit solution to the operator equation$txs^* -sx^*t^*=a$ in the general setting of the adjointable operators between hilbert $c^*$-modules, when$t,s$ have closed ranges and $s$ is a self adjoint operator.