Pohlke theorem: demonstration and graphical solution

Gimena Ramos, Faustino; Gimena Ramos, Lázaro; Goñi Garatea, Mikel; Gonzaga Vélez, Pedro

Publication:
Pohlke theorem: demonstration and graphical solution

dc.contributor.author	Gimena Ramos, Faustino
dc.contributor.author	Gimena Ramos, Lázaro
dc.contributor.author	Goñi Garatea, Mikel
dc.contributor.author	Gonzaga Vélez, Pedro
dc.contributor.department	Proyectos e Ingeniería Rural	es_ES
dc.contributor.department	Landa Ingeniaritza eta Proiektuak	eu
dc.date.accessioned	2023-09-12T09:42:05Z
dc.date.available	2023-09-12T09:42:05Z
dc.date.issued	2017
dc.date.updated	2023-09-12T09:37:38Z
dc.description.abstract	It is known that the axonometric defined by Pohlke, is geometrically known as a means of representing the figures of space using a cylindrical projec-tion and proportions. His theorem says that the three unit vectors orthogonal axes of the basis in the space can be transformed into three arbitrary vectors with com-mon origin located in the frame plane. Another way of expressing this theorem is given in three segments mismatched and incidents at one point in a plane, there is a trirectangular unitary thriedra in the space that can be transformed in these three segments. This paper presents a graphical procedure to demonstrate a solution of Pohlke¿s theorem. To do this, we start from previous work by the authors on the axonometric perspective. Graphic constructions that allow a single joint invariant description of relationships between an orthogonal axonometric oblique axono-metric system and systems associated thereby. At a same time of the geometric lo-cus generated by the diagonal magnitude positioned at any direction in the plane of the picture. This magnitude is the square root of the sum of the squares of the projection of the three segments representing axonometric on arbitrary magnitude.	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	Gonzaga, P., Gimena, F., Gimena, L., Goñi, M. (2017) Pohlke theorem: demonstration and graphical solution. En Eynard, B., Nigrelli, V., Oliveri, S. M., Peris-Fajarnes, G., Rizzuti S. (Eds.), Advances on Mechanics, Design Engineering and Manufacturing: proceedings of the International Joint Conference on Mechanics, Design Engineering & Advanced Manufacturing (JCM 2016) (pp. 981-988). Springer. https://doi.org/10.1007/978-3-319-45781-9_98.	en
dc.identifier.doi	10.1007/978-3-319-45781-9_98
dc.identifier.isbn	978-3-319-45780-2
dc.identifier.uri	https://academica-e.unavarra.es/handle/2454/46312
dc.language.iso	eng	en
dc.publisher	Springer	en
dc.relation.ispartof	Eynard, B.; Nigrelli, V.; Oliveri, S. M.; Peris-Fajarnes, G.; Rizzuti, S. (Eds.). Advances on Mechanics, Design Engineering and Manufacturing: proceedings of the International Joint Conference on Mechanics, Design Engineering & Advanced Manufacturing (JCM 2016). Berlín: Springer; 2017. p.981-988 978-3-319-45780-2	en
dc.relation.publisherversion	https://doi.org/10.1007/978-3-319-45781-9_98
dc.rights	© 2017 Springer International Publishing AG	en
dc.rights.accessRights	Acceso abierto / Sarbide irekia	es
dc.rights.accessRights	info:eu-repo/semantics/openAccess	en
dc.subject	Axonometric system	en
dc.subject	Descriptive geometry	en
dc.subject	Pohlke theorem	en
dc.title	Pohlke theorem: demonstration and graphical solution	en
dc.type	Contribución a congreso / Biltzarrerako ekarpena	es
dc.type	info:eu-repo/semantics/conferenceObject	en
dc.type.version	Versión aceptada / Onetsi den bertsioa	es
dc.type.version	info:eu-repo/semantics/acceptedVersion	en
dspace.entity.type	Publication
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