The variance of a weighted collection of points is used to prove classical theorems of geometry concerning homogeneous quadratic functions of length (Apollonius, Feuerbach, Ptolemy, Stewart) and to deduce some of the theory of major triangle centers. We also show how a formula for the distance of the incenter to the reflection of the centroid in the nine-point center enables one to simplify Eul...

In 1907 Hagge constructed a circle associated with each cevian point P of triangle ABC. If P is on the circumcircle this circle degenerates to a straight line through the orthocenter which is parallel to the Wallace-Simson line of P . We give a new proof of Hagge’s result by a method based on reflections. We introduce an axis associated with the construction, and (via an areal analysis) a conic...

Hough transform (HT) has been the most common method for circle detection exhibiting robustness but adversely demanding a considerable computational load and large storage. Alternative approaches include heuristic methods that employ iterative optimization procedures for detecting multiple circles under the inconvenience that only one circle can be marked at each optimization cycle demanding a ...

Background and objective: The circle of Willis (COW) supports adequate blood supply to the brain. The cardiovascular system, in the current study, is modeled using an equivalent electronic system focusing on the COW.Method: In our previous study we used 42 compartments to model whole car- diovascular system. In the current study, nevertheless, we extended our model by using 63 compartments to m...

This article describes a straightforward method to measure the dimensions and identify morphological variations in the cerebral arterial circle using the general-purpose software program Osiris. This user-friendly and portable program displays, manipulates, and analyzes medical digital images, and it has the capability to determine morphometric properties of selected blood vessels (or other ana...