A CONCEPT OF PARABOLA IN TAXICAB GEOMETRY BASED ON PERPENDICULAR BISECTOR AS ITS DIRECTRIX
Taxicab Geometry is a non-Euclidean geometry in which distance is defined differently, i.e. (( ) ( )) | | | | for any two points ( ) and ( ). In Euclidean geometry, lines can also be defined as perpendicular bisectors. Since perpendicular bisectors can be defined solely based on distance, we use...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/34238 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Taxicab Geometry is a non-Euclidean geometry in which distance is
defined differently, i.e. (( ) ( )) | | | | for any two
points ( ) and ( ). In Euclidean geometry, lines can also be defined as
perpendicular bisectors. Since perpendicular bisectors can be defined solely based
on distance, we use it to define lines in this particular study of taxicab geometry.
Furthermore, we develop concept of parabolas using perpendicular bisector as
directrix. We find that lines defined as perpendicular bisector consists of single
Euclidean line or two line segment of gradient ?1 and two rays or four rays. Each
parabola in Euclidean geometry is an open curve whereas in a taxicab geometry,
to a specific directrix, a parabola is a closed curve. Each parabola consists of a
vertical or horizontal ray and a line segment with gradient
, , or |
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