Apollonius' problems in grammar school

Conic tangency equations and Apollonius problems in biochemistry and pharmacology

The Apollonius Circle Problem dates to Greek antiquity, circa 250 BC. Given three circles in the plane, find or construct a circle tangent to all three. This was generalized by replacing some circles with straight lines. Vieta [19] (or Viète) solved the problem using circle inversions before 1580. Two generations later, Descartes considered a special case in which all four circles are mutually ...

Apollonius Solutions in Rd

Voronoi and related diagrams have technological applications, for example, in motion planning and surface reconstruction, and also find significant use in materials science, molecular biology, and crystallography. Apollonius diagrams arguably provide the most natural division of space for many materials and technology problems, but compared to Voronoi and power diagrams, their use has been limi...

Conflict Management: Apollonius in airspace design

Conflict detection is the process by which potential collisions between aircraft are identified. Developing efficient detection methods is an engineering priority since the prevention of a mid-air collision is a major safety constraint for all airspace design. Proximity between two aircraft each flying with instantaneous uniform straight motion is re-examined. The Apollonius theorem for constru...

Iranian EFL High School Students’ Perceptions Regarding Written Grammar Feedback

This paper reports on a study thatinvestigated Iranian EFL high school students’ perceptions of written grammar feedback to specify their reasons for preferring comprehensive or selective feedback and choosing some feedback strategies. A questionnaire was administered to 100 EFL intermediate high school students who were selected based on their scores on a proficiency test. Moreover, semi-struc...

Constraint-Based Heuristics for Grammar School Timetabling