The Arrangement of the Osteons and Kepler’s Conjecture
The studies of bone tissue have mainly highlighted the morphometrical characteristics of the osteons, rather than their spatial distribution. This work aimed to verify if the topographical distribution of the osteons responds to geometrical order. From an analysis of hundreds of bone sections of dom...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/8/5170 |
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| author | Marco Zedda |
| author_facet | Marco Zedda |
| author_sort | Marco Zedda |
| collection | DOAJ |
| description | The studies of bone tissue have mainly highlighted the morphometrical characteristics of the osteons, rather than their spatial distribution. This work aimed to verify if the topographical distribution of the osteons responds to geometrical order. From an analysis of hundreds of bone sections of domestic and wild mammals collected over 60 years, it is evident that the spatial distribution of osteons varies from a random arrangement in the irregular Haversian tissue to an ordered geometric arrangement in the dense Haversian tissue. In this work, a new method of classification of Haversian bone tissue was introduced based on the number of points of contact that the perimeter of an osteon has with neighboring osteons. When the functional commitment of the bone is maximum to resist biomechanical stresses, the osteons are smaller and crammed adjacent to each other as if to occupy less space. Their spatial arrangement, in this case, reminds us of Kepler’s conjecture, which predicts the ideal arrangement that spheres must have to occupy as little space as possible. The conjecture was elaborated by Kepler in the Seventeenth Century to solve the practical problem linked to the need to transport the largest number of cannonballs in warships. |
| first_indexed | 2024-03-11T05:16:17Z |
| format | Article |
| id | doaj.art-bd1fab39afe24a8e928342a535cf2ab1 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-11T05:16:17Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-bd1fab39afe24a8e928342a535cf2ab12023-11-17T18:14:37ZengMDPI AGApplied Sciences2076-34172023-04-01138517010.3390/app13085170The Arrangement of the Osteons and Kepler’s ConjectureMarco Zedda0Department of Veterinary Medicine, University of Sassari, 07100 Sassari, ItalyThe studies of bone tissue have mainly highlighted the morphometrical characteristics of the osteons, rather than their spatial distribution. This work aimed to verify if the topographical distribution of the osteons responds to geometrical order. From an analysis of hundreds of bone sections of domestic and wild mammals collected over 60 years, it is evident that the spatial distribution of osteons varies from a random arrangement in the irregular Haversian tissue to an ordered geometric arrangement in the dense Haversian tissue. In this work, a new method of classification of Haversian bone tissue was introduced based on the number of points of contact that the perimeter of an osteon has with neighboring osteons. When the functional commitment of the bone is maximum to resist biomechanical stresses, the osteons are smaller and crammed adjacent to each other as if to occupy less space. Their spatial arrangement, in this case, reminds us of Kepler’s conjecture, which predicts the ideal arrangement that spheres must have to occupy as little space as possible. The conjecture was elaborated by Kepler in the Seventeenth Century to solve the practical problem linked to the need to transport the largest number of cannonballs in warships.https://www.mdpi.com/2076-3417/13/8/5170bone tissueosteonHaversian tissueinterosteonal areaKepler’s conjecture |
| spellingShingle | Marco Zedda The Arrangement of the Osteons and Kepler’s Conjecture Applied Sciences bone tissue osteon Haversian tissue interosteonal area Kepler’s conjecture |
| title | The Arrangement of the Osteons and Kepler’s Conjecture |
| title_full | The Arrangement of the Osteons and Kepler’s Conjecture |
| title_fullStr | The Arrangement of the Osteons and Kepler’s Conjecture |
| title_full_unstemmed | The Arrangement of the Osteons and Kepler’s Conjecture |
| title_short | The Arrangement of the Osteons and Kepler’s Conjecture |
| title_sort | arrangement of the osteons and kepler s conjecture |
| topic | bone tissue osteon Haversian tissue interosteonal area Kepler’s conjecture |
| url | https://www.mdpi.com/2076-3417/13/8/5170 |
| work_keys_str_mv | AT marcozedda thearrangementoftheosteonsandkeplersconjecture AT marcozedda arrangementoftheosteonsandkeplersconjecture |