We show that the best possible positive constant k in a certain geometric inequality of third order lies in the interval [0.14119, 0.14364], which improves upon a previous known result where k = 0. We also consider a comparable question concerning a fourth order version of the inequality.

background and aims. panoramic radiographs are used for surgical planning of unerupted third molars. the major problems associated with panoramic radiography include unequal magnification and geometric distortion of the image. the purpose of this study was the clinical evaluation of the effect of radiographic distortion on the position and classification of unerpted mandibular third molars. mat...

In algebraic approaches to geometric computing, the general procedure is as follows [11]: first, the geometric configuration, including both the hypotheses and the conclusion, is translated into an algebraic formulation in a prerequisite algebraic language; second, algebraic computations are carried out to the conclusion by utilizing the computational rules of the algebra and the given hypothes...

In this paper we study the difference between algebraic and geometric solutions of the hyperbolic Dehn filling equations (see Definition 3.6) for ideally triangulated 3-manifolds. We show that any geometric solution is an algebraic one, and we prove the uniqueness of the geometric solutions. Then we do explicit calculations for three interesting examples. With the first two examples we see that...