Problema călugărului

Noi abordări în rezolvarea problemelor.
Se schimbă teoriile, conceptele și metodele - și matematica se schimbă!

Motto: “Matematica face ca din proprietăți ce nu-i aparțin, să se obțină alte proprietăți ce nu-i aparțin. Utilizatorul de matematică trebuie să asimileze teorii și tehnici noi și subtile pentru a beneficia de marele potențial al calculatorului” Ludwig Wittgenstein (1889-1951)¹ - filozof, inginer, arhitect.
"Matematica este un mod de exprimare a legilor naturale, este cel mai simplu şi cel mai potrivit chip de a înfăţişa o lege generală sau curgerea unui fenomen, este cea mai perfectă limbă în care se poate povesti un fenomen natural." Gheorghe Ţiţeica (1873-1939)
„Matematica e teoretică, iar Informatica e practică” ?
„Matematica e teoretică, iar Informatica e practică”, aceasta este o replica a unui reputat profesor de matematica din Bucuresti, pe care am primit-o dupa ce am sustinut o prezentare la Sesiunea Națională de comunicări "Impactul concursurilor de matematică asupra educației matematice", 21 martie 2015, organizata la București de SSMR -  LINK (pdf).
Atunci, am spus ca e o obisnuinta/traditie ca la Olimpiada de informatica sa se conceapa si sa se rezolve probleme din realitate, din viata obisnuita. In felul acesta, elevii au posibilitatea sa inteleaga si sa poata vedea utilitatea teoriilor si metodelor oferite de matematica si informatica. Procesul invatarii se va schimba, iar prin atractivitatea acestor cautari si aplicatii in rezolvarea problemelor, elevii vor avea o alta perspectiva privind domeniul cunoasterii.

Dar, sa trecem de la vorbe, la fapte.
Problemă. Un călugăr trăiește într-o mănăstire din vârful unui munte. Periodic, dimineața - la o anumită oră, trebuie să coboare pe un drum, într-o localitate de la poalele muntelui, unde va înnopta. Dimineața următoare, la aceeași oră din ziua precedentă, acesta se va întoarce la mănăstire pe același drum. Să se demonstreze că există un loc de pe drumul parcurs de călugăr, prin care trece la aceeași oră, la ducere și la întoarcere. (© M. Vlada, 2016)
REZOLVARE.


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“Mathematicians of the future, however, will be more sensitive and this will (repeatedly) prune mathematical extensions and inventions, since mathematicians will come to recognize that new extensions and creations (e.g., propositions of transfinite cardinal arithmetic) are not well-connected with the solid core of mathematics or with real-world applications. Philosophical clarity will, eventually, enable mathematicians and philosophers to ”.
“Do not agree with me in particular opinions but investigate the matter in the right way. To notice the interesting things … that serve as key if you use them properly”

Source: Wittgenstein's Philosophy of Mathematics, Stanford Encyclopedia of Philosophy, 2011 - http://plato.stanford.edu/

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ISI Web of Science - Web of knowledge

Results: 24 (from Web of Science Core Collection) You searched for: AUTHOR: (Vlada M*) - http://apps.webofknowledge.com

1. ICVL Project, 10 years. The impact of new technologies in education and research By: Vlada, Marin; Albeanu, Grigore; Adascalitei, Adrian Edited by: Vlada, M; Albeanu, G; Adascalitei, A; et al. Conference: 10th International Conference on Virtual Learning Location: Timisoara, ROMANIA Date: OCT 31, 2015 Proceedings of the 10th International Conference on Virtual Learning Book Series: Proceedings of the International Conference on Virtual learning Pages: 27-36 Published: 2015

2. Romanian Informatics Pioneers, Leon Livovschi and Octavian Basca at the University of Bucharest By: Vlada, Marin Edited by: Vlada, M; Albeanu, G; Adascalitei, A; et al. Conference: 10th International Conference on Virtual Learning Location: Timisoara, ROMANIA Date: OCT 31, 2015 Proceedings of the 10th International Conference on Virtual Learning Book Series: Proceedings of the International Conference on Virtual learning Pages: 37-43 Published: 2015

3. COMPUTERS: AS DIGITAL FACILITIES FOR SCIENTIFIC RESEARCH AND AS TOOLS FOR ENHANCED LEARNING IN HIGHER EDUCATION By: Vlada, Marin; Adascalitei, Adrian Edited by: Roceanu, I Conference: 10th International Scientific Conference on eLearning and Software for Education Location: Bucharest, ROMANIA Date: APR 24-25, 2014 LET'S BUILD THE FUTURE THROUGH LEARNING INNOVATION!, VOL. 2 Book Series: eLearning and Software for Education Pages: 537-544 Published: 2014

4. NEUTROSOPHIC APPROACHES IN E-LEARNING ASSESSMENT By: Albeanu, Grigore; Vlada, Marin Edited by: Roceanu, I Conference: 10th International Scientific Conference on eLearning and Software for Education Location: Bucharest, ROMANIA Date: APR 24-25, 2014 LET'S BUILD THE FUTURE THROUGH LEARNING INNOVATION!, VOL III Book Series: eLearning and Software for Education Pages: 435-441 Published: 2014

5. NONLINEAR MODELS. THEORY, SOFTWARE AND APPLICATIONS By: Vlada, Marin Edited by: Roceanu, I; Stanescu, I; Barbieru, D Conference: 9th International Conference eLearning and Software for Education Location: Bucharest, ROMANIA Date: APR 25-26, 2013 Sponsor(s): Games & Learn Alliance; intuitext Grup SOFTWIN; ASCENDIA DESIGN; SAP; INSOFT Dev & Consult; MAGUAY; Adv Technol Syst; PLAGIAT QUALITY AND EFFICIENCY IN E-LEARNING, VOL 2 Book Series: eLearning and Software for Education Pages: 494-501 Published: 2013

6. FROM THE ALGORITHMIC THINKING TO THE CONCEPT OF PROJECT - In memory of Walter Zorn By: Vlada, Marin Edited by: Frunzeti, T; Popescu, V; Jugureanu, R; et al. Conference: 7th International Scientific Conference eLearning and Software for Education Location: Bucharest, ROMANIA Date: APR 28-29, 2011 ANYWHERE, ANYTIME - EDUCATION ON DEMAND, VOL I Book Series: eLearning and Software for Education Pages: 97-104 Published: 2011

7. The Romanian Projects for e-Learning Technologies By: Vlada, Marin; Jugureanu, Radu; Albeanu, Grigore Edited by: Vlada, M; Albeanu, G; Popovici, DM Conference: 6th International Conference on Virtual Learning, ICVL 2011 Location: Babes Bolyai Univ Cluj Napoca, Cluj Napoca, ROMANIA Date: OCT 28-29, 2011 Sponsor(s): Univ Bucharest; Babes Bolyai Univ Cluj Napoca PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON VIRTUAL LEARNING, ICVL 2011 Book Series: Proceedings of the International Conference on Virtual learning Pages: 71-77 Published: 2011

8. Case Study: Using Drupal platform for eContent Management By: Vlada, Marin; Adascalitei, Adrian Edited by: Vlada, M; Albeanu, G; Popovici, DM Conference: 6th International Conference on Virtual Learning, ICVL 2011 Location: Babes Bolyai Univ Cluj Napoca, Cluj Napoca, ROMANIA Date: OCT 28-29, 2011 Sponsor(s): Univ Bucharest; Babes Bolyai Univ Cluj Napoca PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON VIRTUAL LEARNING, ICVL 2011 Book Series: Proceedings of the International Conference on Virtual learning Pages: 98-104 Published: 2011

9. CNIV AND ICVL PROJECTS-NEWS TECHNOLOGIES IN EDUCATION AND RESEARCH By: Vlada, Marin; Adascalitei, Adrian; Jugureanu, Radu; et al. Edited by: Popescu, V; Jugureanu, R; Stefan, V; et al. Conference: 6th International Scientific Conference on eLearning and Software for Education Location: Bucharest, ROMANIA Date: APR 15-16, 2010 Sponsor(s): Siveco; Adv Distributed Learning; Altfactor; ComputerLand; AVITECH; Expert Trade Co; Adv Technol Syst ADVANCED DISTRIBUTED LEARNING IN EDUCATION AND TRAINING TRANSFORMATION Pages: 301-312 Published: 2010

10. The Professional Network for Education, Research and Training "Learning-Knowledge-Development" By: Vlada, Marin; Nica, Adriana Sarah Edited by: Rodrigues, S Conference: 2nd European Conference on Intellectual Capital Location: Lisbon, PORTUGAL Date: MAR 29-30, 2010 Sponsor(s): ISCTE Lisbon Univ Inst; Polytechn Inst Leiria PROCEEDINGS OF THE 2ND EUROPEAN CONFERENCE ON INTELLECTUAL CAPITAL Pages: 612-621 Published: 2010

11. 2010: Year of Mathematics in Romania and Centenary of Romanian Mathematical Society. An unique Journal in the world: Mathematical Gazette at 115 anniversary By: Vlada, Marin Edited by: Vlada, M; Albeanu, G; Popovici, DM Conference: 5th International Conference on Virtual Learning Location: Univ Med & Pharm Targu Mures, Targu Mures, ROMANIA Date: OCT 29-31, 2010 Sponsor(s): INTUITION Consortium Network Excellence Europe; Univ Bucharest; Natl Authority Sci Res; Autoritatea Natl Cercetare Stiintif; Univ Med Pharm Targu Mures; Siveco Romania; Intel Co PROCEEDINGS OF THE 5TH INTERNATIONAL CONFERENCE ON VIRTUAL LEARNING, ICVL 2010 Book Series: Proceedings of the International Conference on Virtual learning Pages: 27-37 Published: 2010

12. The Potential of Collaborative Augmented Reality in Education By: Vlada, Marin; Albeanu, Grigore Edited by: Vlada, M; Albeanu, G; Popovici, DM Conference: 5th International Conference on Virtual Learning Location: Univ Med & Pharm Targu Mures, Targu Mures, ROMANIA Date: OCT 29-31, 2010 Sponsor(s): INTUITION Consortium Network Excellence Europe; Univ Bucharest; Natl Authority Sci Res; Autoritatea Natl Cercetare Stiintif; Univ Med Pharm Targu Mures; Siveco Romania; Intel Co PROCEEDINGS OF THE 5TH INTERNATIONAL CONFERENCE ON VIRTUAL LEARNING, ICVL 2010 Book Series: Proceedings of the International Conference on Virtual learning Pages: 38-43 Published: 2010

13. ABBYY recognition technologies - ideal alternative to manual data entry. Automating processing of exam tests. By: Vlada, Marin; Babiy, Ivan; Ivanescu, Octav Edited by: Vlada, M; Albeanu, G; Popovici, DM Conference: 5th International Conference on Virtual Learning Location: Univ Med & Pharm Targu Mures, Targu Mures, ROMANIA Date: OCT 29-31, 2010 Sponsor(s): INTUITION Consortium Network Excellence Europe; Univ Bucharest; Natl Authority Sci Res; Autoritatea Natl Cercetare Stiintif; Univ Med Pharm Targu Mures; Siveco Romania; Intel Co PROCEEDINGS OF THE 5TH INTERNATIONAL CONFERENCE ON VIRTUAL LEARNING, ICVL 2010 Book Series: Proceedings of the International Conference on Virtual learning Pages: 263-268 Published: 2010

14. Using statistical software and Web Technologies in analyzing information on detection and monitoring of somatic and psycho-behavioural deficiencies in children and adolescents By: Vlada, Marin; Nica, Adriana Sarah Edited by: Vlada, M; Albeanu, G; Popovici, DM Conference: 5th International Conference on Virtual Learning Location: Univ Med & Pharm Targu Mures, Targu Mures, ROMANIA Date: OCT 29-31, 2010 Sponsor(s): INTUITION Consortium Network Excellence Europe; Univ Bucharest; Natl Authority Sci Res; Autoritatea Natl Cercetare Stiintif; Univ Med Pharm Targu Mures; Siveco Romania; Intel Co PROCEEDINGS OF THE 5TH INTERNATIONAL CONFERENCE ON VIRTUAL LEARNING, ICVL 2010 Book Series: Proceedings of the International Conference on Virtual learning Pages: 455-466 Published: 2010

15. E-Learning and Educational Software. Educational Projects and Experience of Implementation in Romania By: Vlada, Marin; Jugureanu, Radu; Istrate, Olimpius Edited by: Vlada, M; Albeanu, G; Popovici, DM Conference: 4th International Conference on Virtual Learning Location: Jassy, ROMANIA Date: OCT 30-NOV 01, 2009 Sponsor(s): European Year of Creativ & Innovat 2009; Intuit Consortium Network Excellence Europe ICVL 2009 - PROCEEDINGS OF THE 4TH INTERNATIONAL CONFERENCE ON VIRTUAL LEARNING Pages: 25-39 Published: 2009

16. Scientific Knowledge and Solving Problems Modelling, Representation and Processing By: Vlada, Marin Edited by: Vlada, M; Albeanu, G; Popovici, DM Conference: 4th International Conference on Virtual Learning Location: Jassy, ROMANIA Date: OCT 30-NOV 01, 2009 Sponsor(s): European Year of Creativ & Innovat 2009; Intuit Consortium Network Excellence Europe ICVL 2009 - PROCEEDINGS OF THE 4TH INTERNATIONAL CONFERENCE ON VIRTUAL LEARNING Pages: 40-51 Published: 2009

17. Languages and Knowledge Versus Modeling and Processing By: Vlada, Marin; Nica, Adriana Sarah Edited by: Bolisani, E; Scarso, E Conference: 10th European Conference on Knowledge Management Location: Univ Degli Studi Padova, Vicenza, ITALY Date: SEP 03-04, 2009 PROCEEDINGS OF THE 10TH EUROPEAN CONFERENCE ON KNOWLEDGE MANAGEMENT , VOLS 1 AND 2 Pages: 879-887 Published: 2009

18. SVG Language (Scalable Vector Graphics) For 2D Graphics in XML and Applications By: Vlada, Marin Edited by: Vlada, M; Albeanu, G; Popovici, D Conference: 3rd International Conference on Virtual Learning Location: Constanta, ROMANIA Date: OCT 31-NOV 02, 2008 Sponsor(s): Univ Bucharest; SIVECO Romania SA; Intel Corp; MEdR, Natl Author Sci Res; Agora Media; Int Journal Comp, Commun & Control; Market Watch, IT & C; Modern Professors Portal; MEdC, SEI Educ Portal; CNCSIS PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON VIRTUAL LEARNING Book Series: Proceedings of the International Conference on Virtual learning Pages: 297-306 Published: 2008

19. The application of laser beam diffraction and scattering methods in the measurement of shape and determination of material parameters By: Milesa, Sreckovic Z.; Eljka, Tomic; Stank, Ostoji M.; et al. LASERS IN ENGINEERING Volume: 17 Issue: 3-4 Pages: 179-196 Published: 2007

20. E-Learning Technologies - Achievements and Perspectives By: Vlada, Marin; Jugureanu, Radu Edited by: Vlada, M; Albeanu, G; Popovici, D Conference: 2nd International Conference on Virtual Learning Location: Constanta, ROMANIA Date: OCT 26-28, 2007 Sponsor(s): Univ Bucharest; Ovidius Univ Constanta, Fac Math & Comp Sci; Minist Educ & Res, Natl Author Sci Res; SIVECO Romania; Agora Media; International Journal Comp, Commun & Control; Market Watch, IT & C; Modern Professors Portal; MEdC, SEI Educ Portal; CNCSIS PROCEEDINGS OF THE 2ND INTERNATIONAL CONFERENCE ON VIRTUAL LEARNING: VIRTUAL LEARNING - VIRTUAL REALITY: MODELS & METHODOLOGIES, TECHNOLOGIES, SOFTWARE SOLUTIONS Book Series: Proceedings of the International Conference on Virtual learning Pages: 35-46 Published: 2007

21. Information Society Technologies - The four waves of information technologies By: Vlada, Marin; Tugui, Alexandru Edited by: Vlada, M; Albeanu, G; Popovici, D Conference: 1st International Conference on Virtual Learning Location: Bucharest, ROMANIA Date: OCT 27-29, 2006 Sponsor(s): Univ Bucharest, Fac Math & Comp Sci; SIVECO Romania; MEd, Natl Author Sci Res; Coca Cola; COMENIUS Hands Sci; ARRE; Agora Media; Market Watch, IT & C; Modern Professors Portal; MEdC, SEI Educ Portal; CNCSIS PROCEEDINGS OF THE 1ST INTERNATIONAL CONFERENCE ON VIRTUAL LEARNING: VIRTUAL LEARNING - VIRTUAL REALITY: MODELS & METHODOLOGIES, TECHNOLOGIES, SOFTWARE SOLUTIONS Book Series: Proceedings of the International Conference on Virtual learning Pages: 69-82 Published: 2006

22. Algorithms for testing satisfiability formulas By: Vlada, M ARTIFICIAL INTELLIGENCE REVIEW Volume: 15 Issue: 3 Pages: 153-163 Published: MAY 2001

23. Investigation of the experimental response of a biamperometric detector operating in flow conditions By: David, V; Vlada, M REVUE ROUMAINE DE CHIMIE Volume: 44 Issue: 10 Pages: 955-962 Published: OCT 1999

24. An efficient algorithm for testing propositional formulas By: Vlada, M COMPUTERS AND ARTIFICIAL INTELLIGENCE Volume: 17 Issue: 4 Pages: 383-391 Published: 1998

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