ปัญหาการตัดกันของรูปสี่เหลี่ยมคางหมู
In 1980, J.W. Fickett proposed the following conjecture: Assume R, and R2 be congruent rectangular regions in the Euclidean plane whose interiors intersect. Then the ratio between the length of ∂R1 that lies in R2 and the length of ∂R2 that lies in R1 must lie between 1/3 and 3 where ∂R₁ and ∂R2 are...
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| Format: | Senior Project |
| Language: | Thai |
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จุฬาลงกรณ์มหาวิทยาลัย
2018
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| Online Access: | https://digiverse.chula.ac.th/Info/item/dc:10299 |
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| Institution: | Chulalongkorn University |
| Language: | Thai |
| Summary: | In 1980, J.W. Fickett proposed the following conjecture: Assume R, and R2 be congruent rectangular regions in the Euclidean plane whose interiors intersect. Then the ratio between the length of ∂R1 that lies in R2 and the length of ∂R2 that lies in R1 must lie between 1/3 and 3 where ∂R₁ and ∂R2 are the boundary of R₁ and R₂ respectively. Later on, in 2013, C. Nielsen and C. Powers showed that, in the case of R₁ and R₂ are two congruent equilaterals, the ratio has values between ½ and 2. In this study, we are interested in solving the conjecture when R₁ and R₂ are two translative trapezoids. |
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