Θεώρημα του Πικ (Greek Wikipedia)
Analysis of information sources in references of the Wikipedia article "Θεώρημα του Πικ" in Greek language version.
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ams.org
- Grünbaum, Branko; Shephard, G. C. (February 1993). «Pick's theorem». The American Mathematical Monthly 100 (2): 150–161. doi:. .
- Steinhaus, H. (1950). Mathematical Snapshots. Oxford University Press. σελ. 76. MR 0036005.
- Beck, Matthias· Robins, Sinai (2015). «2.6 Pick's theorem». Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra. Undergraduate Texts in Mathematics (2nd έκδοση). Springer. σελίδες 40–43. doi:10.1007/978-1-4939-2969-6. ISBN 978-1-4939-2968-9. MR 3410115.
- Ball, Keith (2003). «Chapter 2: Counting Dots». Strange Curves, Counting Rabbits, and Other Mathematical Explorations. Princeton University Press, Princeton, NJ. σελίδες 25–40. ISBN 0-691-11321-1. MR 2015451.
- Martin, George Edward (1982). Transformation geometry. Undergraduate Texts in Mathematics. Springer-Verlag. Theorem 12.1, page 120. doi:10.1007/978-1-4612-5680-9. ISBN 0-387-90636-3. MR 0718119.
- Ram Murty, M.; Thain, Nithum (2007). «Pick's theorem via Minkowski's theorem». The American Mathematical Monthly 114 (8): 732–736. doi:. .
- Funkenbusch, W. W. (June–July 1974). «From Euler's formula to Pick's formula using an edge theorem». The American Mathematical Monthly 81 (6): 647–648. doi:. .
- DeTemple, Duane; Robertson, Jack M. (March 1974). «The equivalence of Euler's and Pick's theorems». The Mathematics Teacher 67 (3): 222–226. doi:. .
- Varberg, Dale E. (1985). «Pick's theorem revisited». The American Mathematical Monthly 92 (8): 584–587. doi:. .
- Diaz, Ricardo; Robins, Sinai (1995). «Pick's formula via the Weierstrass -function». The American Mathematical Monthly 102 (5): 431–437. doi:. .
- Brandolini, L.; Colzani, L.; Robins, S.; Travaglini, G. (2021). «Pick's theorem and convergence of multiple Fourier series». The American Mathematical Monthly 128 (1): 41–49. doi:. .
- Rosenholtz, Ira (1979). «Calculating surface areas from a blueprint». Mathematics Magazine 52 (4): 252–256. doi:. .
- Reeve, J. E. (1957). «On the volume of lattice polyhedra». Proceedings of the London Mathematical Society. Third Series 7: 378–395. doi:. .
- Diaz, Ricardo; Robins, Sinai (1997). «The Ehrhart polynomial of a lattice polytope». Annals of Mathematics. Second Series 145 (3): 503–518. doi:. .
- Olds, C. D.· Lax, Anneli· Davidoff, Giuliana P. (2000). «Chapter 9: A new principle in the geometry of numbers». The Geometry of Numbers. Anneli Lax New Mathematical Library. 41. Mathematical Association of America, Washington, DC. σελίδες 119–127. ISBN 0-88385-643-3. MR 1817689.
- Guy, Richard K. (2004). «F1: Gauß's lattice point problem». Unsolved Problems in Number Theory. Problem Books in Mathematics. 1 (3rd έκδοση). New York: Springer-Verlag. σελίδες 365–367. doi:10.1007/978-0-387-26677-0. ISBN 0-387-20860-7. MR 2076335.
- Barvinok, Alexander (2008). Integer Points In Polyhedra. Zurich Lectures in Advanced Mathematics. Zürich: European Mathematical Society. doi:10.4171/052. ISBN 978-3-03719-052-4. MR 2455889.
- Bellhouse, D. R. (1981). «Area estimation by point-counting techniques». Biometrics 37 (2): 303–312. doi:. . https://archive.org/details/sim_biometrics_1981-06_37_2/page/303.
- Bruckheimer, Maxim; Arcavi, Abraham (1995). «Farey series and Pick's area theorem». The Mathematical Intelligencer 17 (4): 64–67. doi:. .
archive.org
- Steinhaus, H. (1950). Mathematical Snapshots. Oxford University Press. σελ. 76. MR 0036005.
- Bellhouse, D. R. (1981). «Area estimation by point-counting techniques». Biometrics 37 (2): 303–312. doi:. . https://archive.org/details/sim_biometrics_1981-06_37_2/page/303.
biodiversitylibrary.org
- Pick, Georg (1899). «Geometrisches zur Zahlenlehre». Sitzungsberichte des deutschen naturwissenschaftlich-medicinischen Vereines für Böhmen "Lotos" in Prag. (Neue Folge) 19: 311–319. https://www.biodiversitylibrary.org/item/50207#page/327. CiteBank:47270
books.google.com
- Martin, George Edward (1982). Transformation geometry. Undergraduate Texts in Mathematics. Springer-Verlag. Theorem 12.1, page 120. doi:10.1007/978-1-4612-5680-9. ISBN 0-387-90636-3. MR 0718119.
citebank.org
- Pick, Georg (1899). «Geometrisches zur Zahlenlehre». Sitzungsberichte des deutschen naturwissenschaftlich-medicinischen Vereines für Böhmen "Lotos" in Prag. (Neue Folge) 19: 311–319. https://www.biodiversitylibrary.org/item/50207#page/327. CiteBank:47270
doi.org
dx.doi.org
- Grünbaum, Branko; Shephard, G. C. (February 1993). «Pick's theorem». The American Mathematical Monthly 100 (2): 150–161. doi:. .
- Ram Murty, M.; Thain, Nithum (2007). «Pick's theorem via Minkowski's theorem». The American Mathematical Monthly 114 (8): 732–736. doi:. .
- Funkenbusch, W. W. (June–July 1974). «From Euler's formula to Pick's formula using an edge theorem». The American Mathematical Monthly 81 (6): 647–648. doi:. .
- DeTemple, Duane; Robertson, Jack M. (March 1974). «The equivalence of Euler's and Pick's theorems». The Mathematics Teacher 67 (3): 222–226. doi:. .
- Varberg, Dale E. (1985). «Pick's theorem revisited». The American Mathematical Monthly 92 (8): 584–587. doi:. .
- Trainin, J. (November 2007). «An elementary proof of Pick's theorem». The Mathematical Gazette 91 (522): 536–540. doi:.
- Diaz, Ricardo; Robins, Sinai (1995). «Pick's formula via the Weierstrass -function». The American Mathematical Monthly 102 (5): 431–437. doi:. .
- Brandolini, L.; Colzani, L.; Robins, S.; Travaglini, G. (2021). «Pick's theorem and convergence of multiple Fourier series». The American Mathematical Monthly 128 (1): 41–49. doi:. .
- Rosenholtz, Ira (1979). «Calculating surface areas from a blueprint». Mathematics Magazine 52 (4): 252–256. doi:. .
- Sankar, P. V.; Krishnamurthy, E. V. (August 1978). «On the compactness of subsets of digital pictures». Computer Graphics and Image Processing 8 (1): 136–143. doi:.
- Reeve, J. E. (1957). «On the volume of lattice polyhedra». Proceedings of the London Mathematical Society. Third Series 7: 378–395. doi:. .
- Diaz, Ricardo; Robins, Sinai (1997). «The Ehrhart polynomial of a lattice polytope». Annals of Mathematics. Second Series 145 (3): 503–518. doi:. .
- Bellhouse, D. R. (1981). «Area estimation by point-counting techniques». Biometrics 37 (2): 303–312. doi:. . https://archive.org/details/sim_biometrics_1981-06_37_2/page/303.
- Bruckheimer, Maxim; Arcavi, Abraham (1995). «Farey series and Pick's area theorem». The Mathematical Intelligencer 17 (4): 64–67. doi:. .
- Braden, Bart (1986). «The surveyor's area formula». The College Mathematics Journal 17 (4): 326–337. doi:. Αρχειοθετήθηκε από το πρωτότυπο στις 2015-04-06. https://web.archive.org/web/20150406152731/http://www.maa.org/sites/default/files/pdf/pubs/Calc_Articles/ma063.pdf. Ανακτήθηκε στις 2024-07-10.
doi.org
- Aigner, Martin· Ziegler, Günter M. (2018). «Three applications of Euler's formula: Pick's theorem». Proofs from THE BOOK (6th έκδοση). Springer. σελίδες 93–94. doi:10.1007/978-3-662-57265-8. ISBN 978-3-662-57265-8.
- Beck, Matthias· Robins, Sinai (2015). «2.6 Pick's theorem». Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra. Undergraduate Texts in Mathematics (2nd έκδοση). Springer. σελίδες 40–43. doi:10.1007/978-1-4939-2969-6. ISBN 978-1-4939-2968-9. MR 3410115.
- Martin, George Edward (1982). Transformation geometry. Undergraduate Texts in Mathematics. Springer-Verlag. Theorem 12.1, page 120. doi:10.1007/978-1-4612-5680-9. ISBN 0-387-90636-3. MR 0718119.
- Guy, Richard K. (2004). «F1: Gauß's lattice point problem». Unsolved Problems in Number Theory. Problem Books in Mathematics. 1 (3rd έκδοση). New York: Springer-Verlag. σελίδες 365–367. doi:10.1007/978-0-387-26677-0. ISBN 0-387-20860-7. MR 2076335.
- Barvinok, Alexander (2008). Integer Points In Polyhedra. Zurich Lectures in Advanced Mathematics. Zürich: European Mathematical Society. doi:10.4171/052. ISBN 978-3-03719-052-4. MR 2455889.
maa.org
- Braden, Bart (1986). «The surveyor's area formula». The College Mathematics Journal 17 (4): 326–337. doi:. Αρχειοθετήθηκε από το πρωτότυπο στις 2015-04-06. https://web.archive.org/web/20150406152731/http://www.maa.org/sites/default/files/pdf/pubs/Calc_Articles/ma063.pdf. Ανακτήθηκε στις 2024-07-10.
ox.ac.uk
maths.ox.ac.uk
- Kiradjiev, Kristian (October 2018). «Connecting the dots with Pick's theorem». Mathematics Today: 212–214. http://www.maths.ox.ac.uk/system/files/attachments/ECMPick.pdf.
ru.nl
cs.ru.nl
- Wiedijk, Freek. «Formalizing 100 Theorems». Radboud University Institute for Computing and Information Sciences. Ανακτήθηκε στις 20 Φεβρουαρίου 2024.
web.archive.org
- Braden, Bart (1986). «The surveyor's area formula». The College Mathematics Journal 17 (4): 326–337. doi:. Αρχειοθετήθηκε από το πρωτότυπο στις 2015-04-06. https://web.archive.org/web/20150406152731/http://www.maa.org/sites/default/files/pdf/pubs/Calc_Articles/ma063.pdf. Ανακτήθηκε στις 2024-07-10.
wikipedia.org
en.wikipedia.org
- Pick, Georg (1899). «Geometrisches zur Zahlenlehre». Sitzungsberichte des deutschen naturwissenschaftlich-medicinischen Vereines für Böhmen "Lotos" in Prag. (Neue Folge) 19: 311–319. https://www.biodiversitylibrary.org/item/50207#page/327. CiteBank:47270
- Grünbaum, Branko; Shephard, G. C. (February 1993). «Pick's theorem». The American Mathematical Monthly 100 (2): 150–161. doi:. .
- Steinhaus, H. (1950). Mathematical Snapshots. Oxford University Press. σελ. 76. MR 0036005.
- Aigner, Martin· Ziegler, Günter M. (2018). «Three applications of Euler's formula: Pick's theorem». Proofs from THE BOOK (6th έκδοση). Springer. σελίδες 93–94. doi:10.1007/978-3-662-57265-8. ISBN 978-3-662-57265-8.
- Ball, Keith (2003). «Chapter 2: Counting Dots». Strange Curves, Counting Rabbits, and Other Mathematical Explorations. Princeton University Press, Princeton, NJ. σελίδες 25–40. ISBN 0-691-11321-1. MR 2015451.
- Ram Murty, M.; Thain, Nithum (2007). «Pick's theorem via Minkowski's theorem». The American Mathematical Monthly 114 (8): 732–736. doi:. .
- Funkenbusch, W. W. (June–July 1974). «From Euler's formula to Pick's formula using an edge theorem». The American Mathematical Monthly 81 (6): 647–648. doi:. .
- DeTemple, Duane; Robertson, Jack M. (March 1974). «The equivalence of Euler's and Pick's theorems». The Mathematics Teacher 67 (3): 222–226. doi:. .
- Varberg, Dale E. (1985). «Pick's theorem revisited». The American Mathematical Monthly 92 (8): 584–587. doi:. .
- Trainin, J. (November 2007). «An elementary proof of Pick's theorem». The Mathematical Gazette 91 (522): 536–540. doi:.
- Diaz, Ricardo; Robins, Sinai (1995). «Pick's formula via the Weierstrass -function». The American Mathematical Monthly 102 (5): 431–437. doi:. .
- Brandolini, L.; Colzani, L.; Robins, S.; Travaglini, G. (2021). «Pick's theorem and convergence of multiple Fourier series». The American Mathematical Monthly 128 (1): 41–49. doi:. .
- Rosenholtz, Ira (1979). «Calculating surface areas from a blueprint». Mathematics Magazine 52 (4): 252–256. doi:. .
- Reeve, J. E. (1957). «On the volume of lattice polyhedra». Proceedings of the London Mathematical Society. Third Series 7: 378–395. doi:. .
- Diaz, Ricardo; Robins, Sinai (1997). «The Ehrhart polynomial of a lattice polytope». Annals of Mathematics. Second Series 145 (3): 503–518. doi:. .
- Olds, C. D.· Lax, Anneli· Davidoff, Giuliana P. (2000). «Chapter 9: A new principle in the geometry of numbers». The Geometry of Numbers. Anneli Lax New Mathematical Library. 41. Mathematical Association of America, Washington, DC. σελίδες 119–127. ISBN 0-88385-643-3. MR 1817689.
- Guy, Richard K. (2004). «F1: Gauß's lattice point problem». Unsolved Problems in Number Theory. Problem Books in Mathematics. 1 (3rd έκδοση). New York: Springer-Verlag. σελίδες 365–367. doi:10.1007/978-0-387-26677-0. ISBN 0-387-20860-7. MR 2076335.
- Barvinok, Alexander (2008). Integer Points In Polyhedra. Zurich Lectures in Advanced Mathematics. Zürich: European Mathematical Society. doi:10.4171/052. ISBN 978-3-03719-052-4. MR 2455889.
- Bruckheimer, Maxim; Arcavi, Abraham (1995). «Farey series and Pick's area theorem». The Mathematical Intelligencer 17 (4): 64–67. doi:. .