Analysing Student Work Involving Geometric Concepts

Hyunyi Jung reflects on why students struggle to understand trigonometry

Some Effects of Wing Planform on Sonic Boom

A wind-tunnel investigation was conducted to determine the effect of wing planform on sonic boom at Mach numbers of 1.7, 2.0, and 2.7. The results of the investigation show that the wing leading-edge sweep is one of the primary planform variables affecting the overpressure characteristics

A geometric constraint over k-dimensional objects and shapes subject to business rules

This report presents a global constraint that enforces rules written in a language based on arithmetic and first-order logic to hold among a set of objects. In a first step, the rules are rewritten to Quantifier-Free Presburger Arithmetic (QFPA) formulas. Secondly, such formulas are compiled to generators of k-dimensional forbidden sets. Such generators are a generalization of the indexicals of cc(FD). Finally, the forbidden sets generated by such indexicals are aggregated by a sweep-based algorithm and used for filtering. The business rules allow to express a great variety of packing and placement constraints, while admitting efficient and effective filtering of the domain variables of the k-dimensional object, without the need to use spatial data structures. The constraint was used to directly encode the packing knowledge of a major car manufacturer and tested on a set of real packing problems under these rules, as well as on a packing-unpacking problem