Computer simulation of the arrangement of pears in the dryer

Abstract

Classical formulations of problems about dense packing of objects on a plane mainly consider the arrangement of circles or polygons in areas with a contour in the form of a circle, polygon or strip. In this article, for the first time (as far as the authors know), various models of the arrangement of pear lobes in the dryer are studied and the transition to tighter packaging is discussed. For drying, the pear is first cut into pieces. Sections along the center line and perpendicular to the center line are considered. The simplest model of a pear plate, the contour of which consists of two arcs of circles and two segments, has been studied in detail. One line is part of the common tangent of the circles, and the other is part of the center line. Next, mathematical models for the arrangement of pears on a rectangular tray and in a cylindrical dryer are considered. The optimal arrangement in a cylindrical dryer is discussed. A computer program in PascalABC language is provided. The study can serve as the basis for developing a project on mathematical and computer modeling for secondary school students with in-depth study of mathematics and informatics. Research topics are available to high school students, and the solution of research problems in discrete geometry can be continued by a high school student or university student.