On tiling rectangles with rectangles
The thesis is taken from the article Tiling Rectangles with Rectangles by F.R.K. Chung, E.N. Gilbert, R.L. Graham, J.B. Shearer and J.H. van Lint. This thesis concerns two main problem, namely, to determine the number of elements for which a simple rectangle tiling can be form, and the lower bound o...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
2001
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/17159 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | The thesis is taken from the article Tiling Rectangles with Rectangles by F.R.K. Chung, E.N. Gilbert, R.L. Graham, J.B. Shearer and J.H. van Lint. This thesis concerns two main problem, namely, to determine the number of elements for which a simple rectangle tiling can be form, and the lower bound of the average area of the elements in any simple rectangle tiling with n number of elements.
A computer program illustrates the theorem which shows that for all n < 7, there exists a simple rectangle tiling with n elements.
For the second problem, it is shown that the average area of the elements in a simple tiling is strictly greater than 11/6. Moreover, there is only one simple rectangle tiling of the plane up to rotations, reflections and translations. |
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