On the Diameter of a Circle to Hold a Cube
It is proved that a circle of diameter d can hold a cube of unit edge if and only if $\sqrt2\le d< 1.53477...$ . Similarly, it can be proved that a circle of diameter d can hold a regular octahedron of unit edge if and only if 1 ≤ d < 1.1066...
Saved in:
| Published in | Computational Geometry, Graphs and Applications Vol. 7033; pp. 147 - 153 |
|---|---|
| Main Author | |
| Format | Book Chapter |
| Language | English |
| Published |
Germany
Springer Berlin / Heidelberg
2011
Springer Berlin Heidelberg |
| Series | Lecture Notes in Computer Science |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9783642249822 3642249825 |
| ISSN | 0302-9743 1611-3349 |
| DOI | 10.1007/978-3-642-24983-9_15 |
Cover
| Abstract | It is proved that a circle of diameter d can hold a cube of unit edge if and only if $\sqrt2\le d< 1.53477...$ . Similarly, it can be proved that a circle of diameter d can hold a regular octahedron of unit edge if and only if 1 ≤ d < 1.1066... |
|---|---|
| AbstractList | It is proved that a circle of diameter d can hold a cube of unit edge if and only if $\sqrt2\le d< 1.53477...$ . Similarly, it can be proved that a circle of diameter d can hold a regular octahedron of unit edge if and only if 1 ≤ d < 1.1066... |
| Author | Maehara, Hiroshi |
| Author_xml | – sequence: 1 givenname: Hiroshi surname: Maehara fullname: Maehara, Hiroshi email: maehara@tokai-u.jp organization: RIED, Tokai University, Shibuya-ku, Japan |
| BookMark | eNqNkE9PwzAMxQMMxDb2DTj0jBRw4vxpjmgDhjRpFzhHSZayQWlL231_0g0444ulZ_8svzcho6quIiHXDG4ZgL4zOqdIleCUC5MjNZbJEzLBpBwEPCVjphijiMKckVna_51xPiJjQODUaIEXZMJAKaaNMHBJZl33DqkUGNRiTG7WVdZvY7bYuc_Yxzari8xl810bypj1dbasy80g7H28IueFK7s4--lT8vr48DJf0tX66Xl-v6INB5SUbQrQ6Q-MOvi4Ae-F8rmUSmtupA-MBS0iA8eRC6dC8Kh4EVQB3POicDgl_Hi3a9pd9RZb6-v6o7MM7BCNTVYt2mTWHpKwQzQJEkeoaeuvfex6GwcqxKpvXRm2rknmOqsQNCSesYH6NyZlLrUUf9g32Rhy2A |
| ContentType | Book Chapter |
| Copyright | Springer-Verlag Berlin Heidelberg 2011 |
| Copyright_xml | – notice: Springer-Verlag Berlin Heidelberg 2011 |
| DBID | FFUUA |
| DEWEY | 004/.36 |
| DOI | 10.1007/978-3-642-24983-9_15 |
| DatabaseName | ProQuest Ebook Central - Book Chapters - Demo use only |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Computer Science |
| EISBN | 3642249833 9783642249839 |
| EISSN | 1611-3349 |
| Editor | Kano, Mikio Bo, Jiang Akiyama, Jin Tan, Xuehou |
| Editor_xml | – sequence: 1 fullname: Kano, Mikio – sequence: 2 fullname: Bo, Jiang – sequence: 3 fullname: Akiyama, Jin – sequence: 4 fullname: Tan, Xuehou |
| EndPage | 153 |
| ExternalDocumentID | EBC6307078_119_155 EBC5585754_119_155 |
| GroupedDBID | 0D6 0DA 2HV 38. AABBV AAJYQ AAMFE AATVQ ABBUY ABBVZ ABCYT ABFCV ABMNI ACDTA ACDUY AECAB AECMQ AEDXK AEGQK AEHEY AEJLV AEKFX AETDV AEZAY AHNNE ALMA_UNASSIGNED_HOLDINGS ANXAN ATJMZ AZZ BBABE C9S C9V CZZ FFUUA I4C IEZ IX- MA. MW~ SBO TCUKC TPJZQ TSXQS Z81 Z83 Z88 -DT -GH -~X 1SB 29L 2HA 5QI 875 AASHB ACGFS ADCXD AEFIE EJD F5P FEDTE HVGLF LAS LDH P2P RNI RSU SVGTG VI1 ~02 |
| ID | FETCH-LOGICAL-p2035-1df072493e7cbed0bb46b855677295bc11c74e10a2324a6ccb362fc6f02b2ffa3 |
| ISBN | 9783642249822 3642249825 |
| ISSN | 0302-9743 |
| IngestDate | Wed Sep 17 03:10:39 EDT 2025 Tue Oct 21 02:11:04 EDT 2025 Tue Oct 21 02:32:44 EDT 2025 |
| IsPeerReviewed | false |
| IsScholarly | false |
| LCCallNum | QA76.9.A43QA76.9.M35 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-p2035-1df072493e7cbed0bb46b855677295bc11c74e10a2324a6ccb362fc6f02b2ffa3 |
| Notes | Original Abstract: It is proved that a circle of diameter d can hold a cube of unit edge if and only if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt2\le d< 1.53477...$\end{document}. Similarly, it can be proved that a circle of diameter d can hold a regular octahedron of unit edge if and only if 1 ≤ d < 1.1066.... |
| OCLC | 1066179490 |
| PQID | EBC5585754_119_155 |
| PageCount | 7 |
| ParticipantIDs | springer_books_10_1007_978_3_642_24983_9_15 proquest_ebookcentralchapters_6307078_119_155 proquest_ebookcentralchapters_5585754_119_155 |
| PublicationCentury | 2000 |
| PublicationDate | 2011 |
| PublicationDateYYYYMMDD | 2011-01-01 |
| PublicationDate_xml | – year: 2011 text: 2011 |
| PublicationDecade | 2010 |
| PublicationPlace | Germany |
| PublicationPlace_xml | – name: Germany – name: Berlin, Heidelberg |
| PublicationSeriesTitle | Lecture Notes in Computer Science |
| PublicationSubtitle | International Conference,CGGA 2010, Dalian, China, November 3-6, 2010, Revised, Selected Papers |
| PublicationTitle | Computational Geometry, Graphs and Applications |
| PublicationYear | 2011 |
| Publisher | Springer Berlin / Heidelberg Springer Berlin Heidelberg |
| Publisher_xml | – name: Springer Berlin / Heidelberg – name: Springer Berlin Heidelberg |
| RelatedPersons | Kleinberg, Jon M. Mattern, Friedemann Nierstrasz, Oscar Steffen, Bernhard Kittler, Josef Vardi, Moshe Y. Weikum, Gerhard Sudan, Madhu Naor, Moni Mitchell, John C. Terzopoulos, Demetri Pandu Rangan, C. Kanade, Takeo Hutchison, David Tygar, Doug |
| RelatedPersons_xml | – sequence: 1 givenname: David surname: Hutchison fullname: Hutchison, David organization: Lancaster University, Lancaster, UK – sequence: 2 givenname: Takeo surname: Kanade fullname: Kanade, Takeo organization: Carnegie Mellon University, Pittsburgh, USA – sequence: 3 givenname: Josef surname: Kittler fullname: Kittler, Josef organization: University of Surrey, Guildford, UK – sequence: 4 givenname: Jon M. surname: Kleinberg fullname: Kleinberg, Jon M. organization: Cornell University, Ithaca, USA – sequence: 5 givenname: Friedemann surname: Mattern fullname: Mattern, Friedemann organization: ETH Zurich, Zurich, Switzerland – sequence: 6 givenname: John C. surname: Mitchell fullname: Mitchell, John C. organization: Stanford University, Stanford, USA – sequence: 7 givenname: Moni surname: Naor fullname: Naor, Moni organization: Weizmann Institute of Science, Rehovot, Israel – sequence: 8 givenname: Oscar surname: Nierstrasz fullname: Nierstrasz, Oscar organization: University of Bern, Bern, Switzerland – sequence: 9 givenname: C. surname: Pandu Rangan fullname: Pandu Rangan, C. organization: Indian Institute of Technology, Madras, India – sequence: 10 givenname: Bernhard surname: Steffen fullname: Steffen, Bernhard organization: University of Dortmund, Dortmund, Germany – sequence: 11 givenname: Madhu surname: Sudan fullname: Sudan, Madhu organization: Massachusetts Institute of Technology, USA – sequence: 12 givenname: Demetri surname: Terzopoulos fullname: Terzopoulos, Demetri organization: University of California, Los Angeles, USA – sequence: 13 givenname: Doug surname: Tygar fullname: Tygar, Doug organization: University of California, Berkeley, USA – sequence: 14 givenname: Moshe Y. surname: Vardi fullname: Vardi, Moshe Y. organization: Rice University, Houston, USA – sequence: 15 givenname: Gerhard surname: Weikum fullname: Weikum, Gerhard organization: Max-Planck Institute of Computer Science, Saarbrücken, Germany |
| SSID | ssj0000609374 ssj0002792 |
| Score | 1.3791609 |
| Snippet | It is proved that a circle of diameter d can hold a cube of unit edge if and only if $\sqrt2\le d< 1.53477...$ . Similarly, it can be proved that a circle of... |
| SourceID | springer proquest |
| SourceType | Publisher |
| StartPage | 147 |
| SubjectTerms | 52A15 52B10 52C99 Algorithms & data structures cube Discrete mathematics Graphics programming holding circle octahedron |
| Title | On the Diameter of a Circle to Hold a Cube |
| URI | http://ebookcentral.proquest.com/lib/SITE_ID/reader.action?docID=5585754&ppg=155 http://ebookcentral.proquest.com/lib/SITE_ID/reader.action?docID=6307078&ppg=155 http://link.springer.com/10.1007/978-3-642-24983-9_15 |
| Volume | 7033 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PT9swFLZGd2E7jDGm8VM-IA4gI6eO3XJkpVChAReYuFm2Ywuk0XRtuPDX856TtGlVCcElSp6c6CWf5Tw_-_seIfvmxHMRnGNJSDss9c4yq4JggmeJCyLzPCBR-OpaDe7Sy3t5Pyv3F9klhT12L0t5JR9BFWyAK7Jk34Hs9KFggHPAF46AMBwXgt_5NGupKxDrMdS5vAufP_liXPFOzOih1F4-baxPN3vHTbm78ezRPOF-mJIl2XscQyfCaHSQ_8vQ8Gx9My0QyXHNtECdFjyqVLNQA32ZclZkcaTwH0cdv-aoCCOBWDrENndVKOT2wK2CneiSlTmvaJ3IBWP8cfZ_95SIMkMw_8Ab5cHoP8NCYLhgXlVFWSEr4FqLfD7tX_75O02bccUhoMJiXVO3ZamjNHuNBkNymZtzc4mF5e8YVdyuka_INKFIAQHHv5NPfrhOvtV1Nmg17K6TL1dTbd3JD3J4M6RwSWvsaB6ooSV2tMgpYocGwG6D3J33b3sDVlW8YKM2aocmWeAd8FT4jrM-49amynalVDgHktYlieukPuEG42CjnLMQfwSnAm_bdghG_CStYT70vwjNusYbgeGxgSCRJ92uynxmLYSrSGZubxJWfwUd1-WrzcCufOeJlhKLt6Y1RG-2X4B0kxzVn1Zj84muBbIBEy00YKIjJhqbb73z6dtkddbpd0irGD_7XYgOC7tX9ZhXaJRcoQ |
| linkProvider | Library Specific Holdings |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.title=Computational+Geometry%2C+Graphs+and+Applications&rft.atitle=On+the+Diameter+of+a+Circle+to+Hold+a+Cube&rft.date=2011-01-01&rft.pub=Springer+Berlin+%2F+Heidelberg&rft.isbn=9783642249822&rft.volume=7033&rft_id=info:doi/10.1007%2F978-3-642-24983-9_15&rft.externalDBID=155&rft.externalDocID=EBC6307078_119_155 |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Febookcentral.proquest.com%2Fcovers%2F5585754-l.jpg http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Febookcentral.proquest.com%2Fcovers%2F6307078-l.jpg |