A Research of Conics from Five Elements

• Main Authors: Wei-Hung Wu, 吳偉弘
• Other Authors: Jen-Chung Chuan
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/83034231122989768689

碩士 === 國立清華大學 === 數學系 === 91 === We know that a conic is determined by five points. With help of Pascal's theorem, we can construct only one conic from given five ordinary points. The study of this research is focused on pointwise constructions of conics from given "any" five elements---no matter points or straight lines. After introducing the constructions of the double elements of the involution, which plays an important role in the constructions of conics, we construct conics from five given ordinary points or straight lines based on the deductions of Pascal's theorem, Brianchon's theorem, Desargues' involution theorem and its dual theorem. Then we analyze the constructions assuming that the ordinary point is the point at infinity or that the ordinary straight line is the line at infinity, etc…. At last, through the interactive dynamic software of geometry, Cabri Geometry II, fifty-three cases of constructions of conics from given any five elements are explicated and concluded.