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An advanced study of cut locus and related topics

Research Project

Project/Area Number 26400072
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionKumamoto University

Principal Investigator

Itoh Jin-ichi  熊本大学, 教育学部, 教授 (20193493)

Co-Investigator(Kenkyū-buntansha) 清原 一吉  岡山大学, 自然科学研究科, 教授 (80153245)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords測地線 / 最小跡 / 共役跡 / 多面体 / 第一共役跡 / 全曲率 / 全捩率
Outline of Final Research Achievements

This research of cut locus was separated 5 themaes and developed all themaes synthetically. (A) As an extension of Jacobi's last statement in general dimension, we finished the paper and submitted it. As a thread construction of quadric surface, we published the paper. (B) A main paper of series of studies of the structure of cut locus by using graph theory was published. (C) We almost finished the paper of the relation between the number of distance functions such that a point is critical and the topology of orientable surface. (D) We discussed continuous flattening of non-convex polyhedral surface by using cut locus, but we firstly got the result by the other method. (E) We published the paper constructing the Finslerian metric with fractal cut locus.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (62 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (3 results) Journal Article (24 results) (of which Int'l Joint Research: 7 results,  Peer Reviewed: 18 results,  Open Access: 15 results,  Acknowledgement Compliant: 4 results) Presentation (35 results) (of which Int'l Joint Research: 5 results,  Invited: 2 results)

  • [Int'l Joint Research] ルーマニア科学アカデミー数学研究所(ルーマニア)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] マサチューセッツ工科大学(米国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] IMAR(ルーマニアアカデミー数学研究所)(ルーマニア)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Classification of regular complex 2-polyhedra of positive constant excess2017

    • Author(s)
      Jin-ichi Itoh, Fumiko Ohtsuka
    • Journal Title

      Topology and its applications

      Volume: 219 Pages: 43-54

    • DOI

      10.1016/j.topol.2017.01.004

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] The total absolute curvature and the total absolute torsion of open curves in the Euclidean spaces2017

    • Author(s)
      Enomoto, Kazuyuki; Itoh, Jin-ichi
    • Journal Title

      Contemporary Mathematics

      Volume: ?

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Thread construction revisited2017

    • Author(s)
      Itoh, Jin-ichi; Kiyohara, Kazuyoshi
    • Journal Title

      J.

      Volume: ?

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Continuous folding of regular dodecahedra2017

    • Author(s)
      Horiyama, Takashi; Itoh, Jin-ichi; Katoh, Naoki; Kobayashi, Yuki; Nara,
    • Journal Title

      Proc. of JCDCGG2015, Lecture Note of Computer Science

      Volume: ?

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Continuous flattening of orthogonal polyhedra2017

    • Author(s)
      Demaine, Erik; Demaine, Martin; Itoh, Jin-chi, Nara, Chie
    • Journal Title

      Proc. of JCDCGG2015, Lecture Note of Computer Science

      Volume: ?

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Thread construction revisited2016

    • Author(s)
      Jin-ichi Itoh, Kazuyoshi Kiyohara
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 68 Issue: 3 Pages: 917-938

    • DOI

      10.2969/jmsj/06830917

    • NAID

      130005166145

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Continuous flattening of orthogonal polyhedra2016

    • Author(s)
      Erik Demaine, Martin Demaine, Jin-ichi Itoh, Chie Nara
    • Journal Title

      Revised Selected Papers of JCDCGG 2015, J. Akiyama et al. (eds.) LNCS, vol. 9943, Springer-Heidelberg

      Volume: LNCS, vol. 9943 Pages: 85-93

    • DOI

      10.1007/978-3-319-48532-4_8

    • ISBN
      9783319485317, 9783319485324
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] The total absolute curvature and the total absolute torsion of open curves in the Euclidean spaces2016

    • Author(s)
      Enomoto, Kazuyuki; Itoh, Jin-ichi
    • Journal Title

      Contemporary Mathematics

      Volume: 674 Pages: 41-48

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Riemannian and Finslerian spheres with fractal cut locus2016

    • Author(s)
      Itoh, Jin-ichi; Sabau, Sorin
    • Journal Title

      Diff. Geometry and its Applications

      Volume: 49 Pages: 43-64

    • DOI

      10.1016/j.difgeo.2017.07.004

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 生徒に考えさせるテクノロジーを用いた数学教材の研究2016

    • Author(s)
      伊藤仁一, 堀尾直文
    • Journal Title

      熊本大学教育学部紀要

      Volume: 65 Pages: 229-236

    • NAID

      110010061537

    • Related Report
      2016 Annual Research Report
    • Open Access
  • [Journal Article] Continuous flattening of truncated tetrahedra2016

    • Author(s)
      Itoh, Jin-ichi; Nara, Chie
    • Journal Title

      J. Geometry

      Volume: 107 Issue: 1 Pages: 61-75

    • DOI

      10.1007/s00022-015-0274-2

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] ICTを用いた平面幾何学の発見的学習に関するいくつかの事例2016

    • Author(s)
      伊藤仁一; 中尾温
    • Journal Title

      日本教科内容学会誌

      Volume: 2 Pages: 111-118

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Every graph is a cut locus2015

    • Author(s)
      Itoh, Jin-ichi; Vilcu, Costin
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 67 Issue: 3 Pages: 1227-1238

    • DOI

      10.2969/jmsj/06731227

    • NAID

      130005094189

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] On the theorem of the three perpendiculars2015

    • Author(s)
      Itoh, Jin-ichi; Rouyer, Joel; Vilcu, Costin
    • Journal Title

      Elem. Math.

      Volume: 70 Issue: 2 Pages: 71-78

    • DOI

      10.4171/em/277

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Costin Moderate smoothness of most Alexandrov surfaces2015

    • Author(s)
      Itoh, Jin-ichi; Rouyer, Joel; Vilcu, Costin
    • Journal Title

      Internat. J. Math.

      Volume: 26 Issue: 04 Pages: 1540004-1540004

    • DOI

      10.1142/s0129167x15400042

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Continuously flattening polyhedra using straight skeletons2015

    • Author(s)
      Abel, Zachary; Demaine, Erik D.; Itoh, Jin-ichi; Lubiw, Anna; Nara, Chie; O'Rourke, Joseph
    • Journal Title

      Computational geometry (SoCG'14)

      Volume: ? Pages: 396-405

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] 幾何学の発見的学習に関するいくつかの考察2015

    • Author(s)
      伊藤仁一; 中尾温
    • Journal Title

      熊本大学教 育学部紀要

      Volume: 64 Pages: 311-316

    • NAID

      110009987787

    • Related Report
      2015 Research-status Report
    • Open Access
  • [Journal Article] Thread construction revisited2015

    • Author(s)
      Jin-ichi Itoh, Kazuyoshi Kiyohara
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 未定

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Moderate smoothness of most Alexandrov surfaces2015

    • Author(s)
      Jin-ichi Itoh, Jo¨el Rouyer, Costin Vilcu
    • Journal Title

      International Journal of Mathematics

      Volume: 未定

    • Related Report
      2014 Research-status Report
  • [Journal Article] Continuously Flattening Polyhedra Using Straight Skeletons2015

    • Author(s)
      Zachary Abel, Erik D. Demaine, Martin Demaine, Jin-Ichi Itoh, Anna Lubiw, Chie Nara and Joseph O'Rourke
    • Journal Title

      Proceeding of SoCG

      Volume: 未定

    • Related Report
      2014 Research-status Report
  • [Journal Article] 円織面 ,直角双曲線織面としての二次曲面2015

    • Author(s)
      山下雄太郎,伊藤仁一
    • Journal Title

      日本教科内容学会誌

      Volume: 1 Pages: 41-52

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the Theorem of the Three Perpendiculars2014

    • Author(s)
      Jin-ichi Itoh, Jo¨el Rouyer and Costin Vilcu
    • Journal Title

      Elemente der Mathematik

      Volume: 69 Pages: 1-8

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 円織面に関するいくつかの考察2014

    • Author(s)
      伊藤仁一,山下雄太郎
    • Journal Title

      熊本大学教育学部紀要

      Volume: 63 Pages: 347-356

    • NAID

      110009864052

    • Related Report
      2014 Research-status Report
    • Open Access
  • [Journal Article] 教育学部及び教育学研究科における数学研究の事例2014

    • Author(s)
      伊藤仁一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1920 Pages: 137-149

    • Related Report
      2014 Research-status Report
  • [Presentation] 直交多面体の連続的平坦折りたたみ2017

    • Author(s)
      奈良知恵; 伊藤仁一; Demaine, Erik; Demaine, Martin
    • Organizer
      日本数学会年会
    • Place of Presentation
      首都大学東京南大沢キャンパス
    • Year and Date
      2017-03-24
    • Related Report
      2016 Annual Research Report
  • [Presentation] Some considerations of Maehara's reversing of a polyhedral surface2017

    • Author(s)
      Itoh, Jin-ichi
    • Organizer
      The 6th Workshop on combinatorial rigidity theory and polyhedra
    • Place of Presentation
      Hong Kong City Univ.( China)
    • Year and Date
      2017-03-17
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 最小跡と直観幾何学2017

    • Author(s)
      伊藤仁一
    • Organizer
      測地線及び関連する諸問題
    • Place of Presentation
      熊本大学
    • Year and Date
      2017-01-07
    • Related Report
      2016 Annual Research Report
  • [Presentation] Applications of cut locus and Intuitive geometry -continuous flattening of polyhedra-2016

    • Author(s)
      Itoh, Jin-ichi
    • Organizer
      ICMMA2016: Origami-Based Mathematical Modeling and Analysis
    • Place of Presentation
      明治大学中野キャンパス
    • Year and Date
      2016-11-12
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] With respect to whom are you critical?2016

    • Author(s)
      Itoh, Jin-ichi
    • Organizer
      The cut locus -A bridge over differential geometry, optimal control and transport-
    • Place of Presentation
      KMITL Bangkok(Tailand)
    • Year and Date
      2016-08-04
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The cut locus of Liouville surfaces and manifolds2016

    • Author(s)
      Kiyohara, Kazuyoshi
    • Organizer
      The cut locus -A bridge over differential geometry, optimal control and transport-
    • Place of Presentation
      KMITL Bangkok(Tailand)
    • Year and Date
      2016-08-03
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Some studies of heuristic learning of plane geometry with ICT2016

    • Author(s)
      Itoh, Jin-ichi ; Nakao, Atsushi
    • Organizer
      Intern. Congress of Mathematical Education ICME 13
    • Place of Presentation
      Hamburg(Germany)
    • Year and Date
      2016-07-29
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 直観幾何学と数学教師教育の展望2016

    • Author(s)
      伊藤仁一
    • Organizer
      RIMS共同研究「直観幾何学を用いた数学教師に必要な数学能力開発の研究」
    • Place of Presentation
      京都大学数理解析研究助
    • Year and Date
      2016-07-21
    • Related Report
      2016 Annual Research Report
  • [Presentation] flexatube 及び動く教材の紹介2016

    • Author(s)
      伊藤仁一
    • Organizer
      RIMS共同研究「直観幾何学を用いた数学教師に必要な数学能力開発の研究」
    • Place of Presentation
      京都大学数理解析研究助
    • Year and Date
      2016-07-20
    • Related Report
      2016 Annual Research Report
  • [Presentation] 動く模型を用いた教材のいくつかの事例2016

    • Author(s)
      伊藤仁一, 中尾温, 堀尾直文
    • Organizer
      日本教科内容学会第3回研究大会
    • Place of Presentation
      上越教育大学
    • Year and Date
      2016-07-03
    • Related Report
      2016 Annual Research Report
  • [Presentation] 直観幾何学と数学教育の現状と今後の展望2015

    • Author(s)
      伊藤仁一
    • Organizer
      研究会「直観幾何学の 数学教育への有用性の研究」
    • Place of Presentation
      キャンパスプラザ京都
    • Year and Date
      2015-11-22
    • Related Report
      2015 Research-status Report
  • [Presentation] 最小跡と多面体の連続的平坦折り畳み2015

    • Author(s)
      伊藤仁一
    • Organizer
      文部科学省 現象数理学共 同利用・共同研究拠点研究集会「文理融合を目指した折紙科学研究」
    • Place of Presentation
      明治大学中野キャンパ ス
    • Year and Date
      2015-11-13
    • Related Report
      2015 Research-status Report
  • [Presentation] 多面体の連続的平坦折り畳みーひし形の特殊折をベースにー2015

    • Author(s)
      奈良知恵
    • Organizer
      文部科学省 現象数理学共 同利用・共同研究拠点研究集会「文理融合を目指した折紙科学研究」
    • Place of Presentation
      明治大学中野キャンパ ス
    • Year and Date
      2015-11-12
    • Related Report
      2015 Research-status Report
  • [Presentation] 多面体の連続的平坦折り畳み2015

    • Author(s)
      奈良知恵
    • Organizer
      第19回折り紙の科学・数学・教育  研究集会
    • Place of Presentation
      石川県教育会館(金沢市)
    • Year and Date
      2015-11-07
    • Related Report
      2015 Research-status Report
  • [Presentation] 円織面,直角双曲線織面としての二次曲面2015

    • Author(s)
      伊藤仁一
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-16
    • Related Report
      2015 Research-status Report
  • [Presentation] Moderate smoothness of most Alexandrov2015

    • Author(s)
      伊藤仁一
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-16
    • Related Report
      2015 Research-status Report
  • [Presentation] Continuous folding of regular dodecahedra2015

    • Author(s)
      Nara, Chie
    • Organizer
      JCDCG^2
    • Place of Presentation
      京都大学百周年記念会館
    • Year and Date
      2015-09-15
    • Related Report
      2015 Research-status Report
  • [Presentation] Continuous flattening of orthogonal polyhedra2015

    • Author(s)
      Demaine, Erik
    • Organizer
      JCDCG^2
    • Place of Presentation
      京都大学百周年記念会館
    • Year and Date
      2015-09-15
    • Related Report
      2015 Research-status Report
  • [Presentation] 数学が苦手な生徒による予期せぬ発見「末永ライン」さらには「末 永サーフェス」2015

    • Author(s)
      堀尾直史
    • Organizer
      The 19th T^3 Japan annual meeting
    • Place of Presentation
      東京理科大学神楽坂キャンパス
    • Year and Date
      2015-08-23
    • Related Report
      2015 Research-status Report
  • [Presentation] Quadratic surfaces as the surfaces generated by circles or rectangular hyperbolas2015

    • Author(s)
      Itoh, Jin-ichi
    • Organizer
      Intuitive Geometry
    • Place of Presentation
      Budapest(Hungary)
    • Year and Date
      2015-06-26
    • Related Report
      2015 Research-status Report
  • [Presentation] 平面幾何の発見的学習に関するいくつかの事例2015

    • Author(s)
      伊藤仁一
    • Organizer
      日本教科内容学会第2回研究大会
    • Place of Presentation
      聖徳大学(千葉県松戸市)
    • Year and Date
      2015-05-17
    • Related Report
      2015 Research-status Report
  • [Presentation] On the cut locus of a family of Finsler manifolds2015

    • Author(s)
      Sorin Sabau
    • Organizer
      日本数学会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] ICT活用の図形学習の授業における生徒の発見とその一般化2015

    • Author(s)
      伊藤仁一
    • Organizer
      数学教育学会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-21 – 2015-03-23
    • Related Report
      2014 Research-status Report
  • [Presentation] 多面体の連続折りたたみ―種々の方法と課題―2015

    • Author(s)
      奈良知恵
    • Organizer
      直観幾何学
    • Place of Presentation
      熊本大学
    • Year and Date
      2015-03-09 – 2015-03-10
    • Related Report
      2014 Research-status Report
  • [Presentation] 円織面と2次曲面,ICT活用の授業での生徒の発見(末永ライン)--教育学部・教育学研究科における研究課題--2015

    • Author(s)
      伊藤仁一
    • Organizer
      教員養成数学教育研究会
    • Place of Presentation
      南九州大学
    • Year and Date
      2015-02-15 – 2015-02-16
    • Related Report
      2014 Research-status Report
  • [Presentation] リウヴィル多様体上のヤコビ場と 2次超曲面の射影同値2015

    • Author(s)
      清原一吉
    • Organizer
      測地線及び関連する諸問題
    • Place of Presentation
      熊本大学
    • Year and Date
      2015-01-10 – 2015-01-11
    • Related Report
      2014 Research-status Report
  • [Presentation] The total absolute torsion of open curves in E^32014

    • Author(s)
      Kazuyuki Enomoto
    • Organizer
      AMS Fall Western Meeting
    • Place of Presentation
      San Francisco State University, USA
    • Year and Date
      2014-10-25 – 2014-10-26
    • Related Report
      2014 Research-status Report
  • [Presentation] 楕円体上の共役跡に現れる特異点について2014

    • Author(s)
      清原一吉
    • Organizer
      広島幾何学研究集会2014
    • Place of Presentation
      広島大学
    • Year and Date
      2014-10-08 – 2014-10-10
    • Related Report
      2014 Research-status Report
  • [Presentation] Flattening Polyhedra with Two Adjacent Rigid Faces -Part II-2014

    • Author(s)
      Chie Nara
    • Organizer
      The 17th Japan Conference on Discrete and Computational Geometry and Graphs
    • Place of Presentation
      東京理科大学
    • Year and Date
      2014-09-15 – 2014-09-16
    • Related Report
      2014 Research-status Report
  • [Presentation] Optimally Bracing Frameworks of Union of Space-filling Convex Polyhedra2014

    • Author(s)
      Yoshihiko Ito
    • Organizer
      The 17th Japan Conference on Discrete and Computational Geometry and Graphs
    • Place of Presentation
      東京理科大学
    • Year and Date
      2014-09-15 – 2014-09-16
    • Related Report
      2014 Research-status Report
  • [Presentation] 楕円体上の共役跡と D_4^+ ラグランジュ特異点2014

    • Author(s)
      清原一吉
    • Organizer
      日本数学会秋季総合文科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-15 – 2014-09-16
    • Related Report
      2014 Research-status Report
  • [Presentation] Total torsion and curvature of open curves2014

    • Author(s)
      Jin-ichi Itoh
    • Organizer
      Geometry Conference TZ-70
    • Place of Presentation
      Univ. Haute-Alsace, Mulouse, France
    • Year and Date
      2014-09-07 – 2014-09-11
    • Related Report
      2014 Research-status Report
  • [Presentation] Total absolute torsion of open curves in E^32014

    • Author(s)
      Kazuyuki Enomoto
    • Organizer
      International Congress of Mathematicians, Seoul 2014
    • Place of Presentation
      Seoul, Korea
    • Year and Date
      2014-08-13 – 2014-08-21
    • Related Report
      2014 Research-status Report
  • [Presentation] Flattening Polyhedra with Two Adjacent Rigid Faces2014

    • Author(s)
      Chie Nara
    • Organizer
      The 6th International Meeting on Origami in Science, Mathematics and Education
    • Place of Presentation
      東京大学
    • Year and Date
      2014-08-10 – 2014-08-13
    • Related Report
      2014 Research-status Report
  • [Presentation] Continuously Flattening Polyhedra Using Straight Skeletons2014

    • Author(s)
      Erik Demaine
    • Organizer
      The 30th Annual Dymposium on Computational Geometry
    • Place of Presentation
      京都大学百周年会館
    • Year and Date
      2014-06-08 – 2014-06-11
    • Related Report
      2014 Research-status Report

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Published: 2014-04-04   Modified: 2022-02-16  

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