Cutting solid figures by plane � analytical solution and spreadsheet implementation

Autores: Jan Benacka
Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 43, Nº. 5, 2012, págs. 647-654
Idioma: inglés
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Resumen
- In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras� theorem, trigonometric functions, and sine and cosine rules. The basic problem is to find the section of the figure by a plane that is defined by three points related to the figure. In this article, a formula is derived that gives the positions of the intersection points of such a plane and the figure edges, that is, the vertices of the section polygon. Spreadsheet implementations of the formula for cuboid and right rectangular pyramids are presented. The user can check his/her graphical solution, or proceed if he/she is not able to complete the section.