Dancing Dorsal Quadrilaterals

Characterizations of Orthodiagonal Quadrilaterals

We prove ten necessary and sufficient conditions for a convex quadrilateral to have perpendicular diagonals. One of these is a quite new eight point circle theorem and three of them are metric conditions concerning the nonoverlapping triangles formed by the diagonals. 1. A well known characterization An orthodiagonal quadrilateral is a convex quadrilateral with perpendicular diagonals. The most...

Dancing eyes and dancing feet syndrome.

133 Introduction Opsoclonus-myoclonus is a rare neurological disorder characterised by intention tremor, unsteady gait, myoclonus and opsoclonus. Lethargy and irritability are also described. The abnormal eye movements are distinctive, being multidirectional and of high amplitude. Its recognition helps in the diagnosis of this clinical syndrome, the correct identification of which leads to the ...

Properties of Equidiagonal Quadrilaterals

We prove eight necessary and sufficient conditions for a convex quadrilateral to have congruent diagonals, and one dual connection between equidiagonal and orthodiagonal quadrilaterals. Quadrilaterals with both congruent and perpendicular diagonals are also discussed, including a proposal for what they may be called and how to calculate their area in several ways. Finally we derive a cubic equa...

Spectral method on quadrilaterals

In this paper, we investigate the spectral method on quadrilaterals. We introduce an orthogonal family of functions induced by Legendre polynomials, and establish some results on the corresponding orthogonal approximation. These results play important roles in the spectral method for partial differential equations defined on quadrilaterals. As examples of applications, we provide spectral schem...

Dancing medicine.