The mathematics of amputation and inscription in rasmi
Rasmi is the projection of a star polygon onto the surface of a rotating solid. The term is adopted from a form of stellar vault but as expanded through this research proves to be a mathematical phenomenon whose scientific reality exceeds the architectural manifestations. Existing knowledge on rasmi...
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| Format: | Thesis |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/35867/5/RezaHashemiNikPFAB2013ABS.pdf |
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| Summary: | Rasmi is the projection of a star polygon onto the surface of a rotating solid. The term is adopted from a form of stellar vault but as expanded through this research proves to be a mathematical phenomenon whose scientific reality exceeds the architectural manifestations. Existing knowledge on rasmi comes from two groups of unrelated sources, hence traditional builders and mathematical scholars. This isolation has left many areas of knowledge undocumented in the science of rasmi. The objective of this research is to initiate this scientific exploration into the mathematical criteria raised by the procedures and phenomena in the field of rasmi. The significance of this research is that it is the first of its kind. The main problems of the research have been formulated into seven mathematical questions within three areas of interest in the analysis of star polygons as the planar manifestations of rasmi. These questions are elaborated under two subchapters over Chapter 1 and Chapter 3, and relate to the sum of internal angles and the total number of sequels as the first two, and five other questions on the inscription of rasmis into regular polygons, rectangles and trapezoids. Research data has been generated through AutoCAD for all polygram sequels between five and forty-eight. The method adopted by the research comprises of the successive stages of data regrouping, pattern detection, observation, pattern analysis, examination, mathematical redefinition, and formulation. The formula is then tested for universality, the result of which produces a universal or local formula. This research has produced two mathematical axioms, two local formulae for the sum of internal angles for odd and even rasmis each, two local formulae for the number of sequels for odd and even rasmis each, one universal formula for regular inscriptions, three local formulae for rectangles, and four local formulae for trapezoids. |
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