Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/16236
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Santos, José Manuel dos Santos dos | pt |
dc.contributor.author | Breda, Ana | pt |
dc.date.accessioned | 2016-11-02T17:27:43Z | - |
dc.date.available | 2016-11-02T17:27:43Z | - |
dc.date.issued | 2015 | - |
dc.identifier.issn | 2183-1432 | pt |
dc.identifier.uri | http://hdl.handle.net/10773/16236 | - |
dc.description.abstract | The stereographic projection is a bijective smooth map which allows us to think the sphere as the extended complex plane. Among its properties it should be emphasized the remarkable property of being angle conformal that is, it is an angle measure preserving map. Unfortunately, this projection map does not preserve areas. Besides being conformal it has also the property of projecting spherical circles in either circles or straight lines in the plane This type of projection maps seems to have been known since ancient times by Hipparchus (150 BC), being Ptolemy (AD 140) who, in his work entitled "The Planisphaerium", provided a detailed description of such a map. Nonetheless, it is worthwhile to mention that the property of the invariance of angle measure has only been established much later, in the seventeenth century, by Thomas Harriot. In fact, it was exactly in that century that the Jesuit François d’Aguilon introduced the terminology "stereographic projection" for this type of maps, which remained up to our days. Here, we shall show how we create in GeoGebra, the PRiemannz tool and its potential concerning the visualization and analysis of the properties of the stereographic projection, in addition to the viewing of the amazing relations between Möbius Transformations and stereographic projections. | pt |
dc.language.iso | eng | pt |
dc.publisher | InED – Centro de Investigação e Inovação em Educação, Escola Superior de Educação, Instituto Politécnico do Porto | pt |
dc.relation | CIDMA/FCT - PEst-OE/MAT/UI4106/2014 | pt |
dc.rights | openAccess | por |
dc.subject | Mathematics | pt |
dc.subject | GeoGebra | pt |
dc.subject | Riemann Sphere | pt |
dc.subject | Möbius Transformations | pt |
dc.subject | Stereographic Projections | pt |
dc.title | The Riemann sphere in GeoGebra | pt |
dc.type | article | pt |
dc.peerreviewed | yes | pt |
ua.distribution | national | pt |
degois.publication.issue | 1 | pt |
degois.publication.title | Sensos-e: Revista Multimédia de Investigação em Educação | pt |
degois.publication.volume | II | pt |
dc.relation.publisherversion | http://sensos-e.ese.ipp.pt/?p=7997 | pt |
Appears in Collections: | CIDMA - Artigos AGG - Artigos |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
The Riemann Sphere in Geogebra -.pdf | Main article | 2.91 MB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.