To Be Presented in the 11th Asian Technology Conference in Mathematics December 12-16, 2006, Hong Kong SAR, China |
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## The Third Motivation for Spherical GeometryYoichi Maedamaeda@keyaki.cc.u-tokai.ac.jpDepartment of Mathematics Tokai University Japan
## Abstract Historically, spherical geometry has developed mainly on the terrestrial
globe and the celestial globe. In this paper, we will introduce
the third globe ˇ§visual globeˇ¨ centered at our eyes.
When we see the external world, we are under an illusion that our
view screen is a plane. Locally it is true, however, globally it
is more natural to think that our view screen is a sphere centered
at our eyes. In this concept, we will study ˇ§visual anglesˇ¨
of a rectangle in the space. An angle in the space changes its visual
angle according to our viewpoint. This visual angle is easily measured
on the visual globe and there is a very simple relation among the
visual angles of a rectangle. We will also realize the visual angle
on a two dimensional Euclidean plane along with the dynamic geometry
software Cabri II Plus. Furthermore, we will find out that the simple
relation above is also true in hyperbolic geometry. |
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