Pick's theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Pick's theorem" in English language version.

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Grünbaum, Branko; Shephard, G. C. (February 1993). "Pick's theorem". The American Mathematical Monthly. 100 (2): 150–161. doi:10.2307/2323771. JSTOR 2323771. MR 1212401.
Steinhaus, H. (1950). Mathematical Snapshots. Oxford University Press. p. 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 ed.). Springer. pp. 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. pp. 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:10.1080/00029890.2007.11920465. JSTOR 27642309. MR 2354443. S2CID 38855683.
Funkenbusch, W. W. (June–July 1974). "From Euler's formula to Pick's formula using an edge theorem". Classroom Notes. The American Mathematical Monthly. 81 (6): 647–648. doi:10.2307/2319224. JSTOR 2319224. MR 1537447.
DeTemple, Duane; Robertson, Jack M. (March 1974). "The equivalence of Euler's and Pick's theorems". The Mathematics Teacher. 67 (3): 222–226. doi:10.5951/mt.67.3.0222. JSTOR 27959631. MR 0444503.
Varberg, Dale E. (1985). "Pick's theorem revisited". The American Mathematical Monthly. 92 (8): 584–587. doi:10.2307/2323172. JSTOR 2323172. MR 0812105.
Diaz, Ricardo; Robins, Sinai (1995). "Pick's formula via the Weierstrass $\wp$ -function". The American Mathematical Monthly. 102 (5): 431–437. doi:10.2307/2975035. JSTOR 2975035. MR 1327788.
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:10.1080/00029890.2021.1839241. MR 4200451. S2CID 231624428.
Rosenholtz, Ira (1979). "Calculating surface areas from a blueprint". Mathematics Magazine. 52 (4): 252–256. doi:10.1080/0025570X.1979.11976797. JSTOR 2689425. MR 1572312.
Reeve, J. E. (1957). "On the volume of lattice polyhedra". Proceedings of the London Mathematical Society. Third Series. 7: 378–395. doi:10.1112/plms/s3-7.1.378. MR 0095452.
Diaz, Ricardo; Robins, Sinai (1997). "The Ehrhart polynomial of a lattice polytope". Annals of Mathematics. Second Series. 145 (3): 503–518. doi:10.2307/2951842. JSTOR 2951842. MR 1454701.
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. Vol. 41. Mathematical Association of America, Washington, DC. pp. 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. Vol. 1 (3rd ed.). New York: Springer-Verlag. pp. 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. Vol. 11. 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:10.2307/2530419. JSTOR 2530419. MR 0673040.
Bruckheimer, Maxim; Arcavi, Abraham (1995). "Farey series and Pick's area theorem". The Mathematical Intelligencer. 17 (4): 64–67. doi:10.1007/BF03024792. MR 1365013. S2CID 55051527.

biodiversitylibrary.org

Pick, Georg (1899). "Geometrisches zur Zahlenlehre". Sitzungsberichte des deutschen naturwissenschaftlich-medicinischen Vereines für Böhmen "Lotos" in Prag. (Neue Folge). 19: 311–319. JFM 33.0216.01. 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. JFM 33.0216.01. CiteBank:47270

doi.org

Grünbaum, Branko; Shephard, G. C. (February 1993). "Pick's theorem". The American Mathematical Monthly. 100 (2): 150–161. doi:10.2307/2323771. JSTOR 2323771. MR 1212401.
Aigner, Martin; Ziegler, Günter M. (2018). "Three applications of Euler's formula: Pick's theorem". Proofs from THE BOOK (6th ed.). Springer. pp. 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 ed.). Springer. pp. 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.
Ram Murty, M.; Thain, Nithum (2007). "Pick's theorem via Minkowski's theorem". The American Mathematical Monthly. 114 (8): 732–736. doi:10.1080/00029890.2007.11920465. JSTOR 27642309. MR 2354443. S2CID 38855683.
Funkenbusch, W. W. (June–July 1974). "From Euler's formula to Pick's formula using an edge theorem". Classroom Notes. The American Mathematical Monthly. 81 (6): 647–648. doi:10.2307/2319224. JSTOR 2319224. MR 1537447.
DeTemple, Duane; Robertson, Jack M. (March 1974). "The equivalence of Euler's and Pick's theorems". The Mathematics Teacher. 67 (3): 222–226. doi:10.5951/mt.67.3.0222. JSTOR 27959631. MR 0444503.
Varberg, Dale E. (1985). "Pick's theorem revisited". The American Mathematical Monthly. 92 (8): 584–587. doi:10.2307/2323172. JSTOR 2323172. MR 0812105.
Trainin, J. (November 2007). "An elementary proof of Pick's theorem". The Mathematical Gazette. 91 (522): 536–540. doi:10.1017/S0025557200182270. JSTOR 40378436. S2CID 124831432.
Diaz, Ricardo; Robins, Sinai (1995). "Pick's formula via the Weierstrass $\wp$ -function". The American Mathematical Monthly. 102 (5): 431–437. doi:10.2307/2975035. JSTOR 2975035. MR 1327788.
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:10.1080/00029890.2021.1839241. MR 4200451. S2CID 231624428.
Rosenholtz, Ira (1979). "Calculating surface areas from a blueprint". Mathematics Magazine. 52 (4): 252–256. doi:10.1080/0025570X.1979.11976797. JSTOR 2689425. MR 1572312.
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:10.1016/s0146-664x(78)80021-5.
Reeve, J. E. (1957). "On the volume of lattice polyhedra". Proceedings of the London Mathematical Society. Third Series. 7: 378–395. doi:10.1112/plms/s3-7.1.378. MR 0095452.
Diaz, Ricardo; Robins, Sinai (1997). "The Ehrhart polynomial of a lattice polytope". Annals of Mathematics. Second Series. 145 (3): 503–518. doi:10.2307/2951842. JSTOR 2951842. MR 1454701.
Guy, Richard K. (2004). "F1: Gauß's lattice point problem". Unsolved Problems in Number Theory. Problem Books in Mathematics. Vol. 1 (3rd ed.). New York: Springer-Verlag. pp. 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. Vol. 11. 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:10.2307/2530419. JSTOR 2530419. MR 0673040.
Bruckheimer, Maxim; Arcavi, Abraham (1995). "Farey series and Pick's area theorem". The Mathematical Intelligencer. 17 (4): 64–67. doi:10.1007/BF03024792. MR 1365013. S2CID 55051527.
Braden, Bart (1986). "The surveyor's area formula" (PDF). The College Mathematics Journal. 17 (4): 326–337. doi:10.2307/2686282. JSTOR 2686282. Archived from the original (PDF) on 2015-04-06. Retrieved 2021-07-04.

jstor.org

Grünbaum, Branko; Shephard, G. C. (February 1993). "Pick's theorem". The American Mathematical Monthly. 100 (2): 150–161. doi:10.2307/2323771. JSTOR 2323771. MR 1212401.
Ram Murty, M.; Thain, Nithum (2007). "Pick's theorem via Minkowski's theorem". The American Mathematical Monthly. 114 (8): 732–736. doi:10.1080/00029890.2007.11920465. JSTOR 27642309. MR 2354443. S2CID 38855683.
Funkenbusch, W. W. (June–July 1974). "From Euler's formula to Pick's formula using an edge theorem". Classroom Notes. The American Mathematical Monthly. 81 (6): 647–648. doi:10.2307/2319224. JSTOR 2319224. MR 1537447.
DeTemple, Duane; Robertson, Jack M. (March 1974). "The equivalence of Euler's and Pick's theorems". The Mathematics Teacher. 67 (3): 222–226. doi:10.5951/mt.67.3.0222. JSTOR 27959631. MR 0444503.
Varberg, Dale E. (1985). "Pick's theorem revisited". The American Mathematical Monthly. 92 (8): 584–587. doi:10.2307/2323172. JSTOR 2323172. MR 0812105.
Trainin, J. (November 2007). "An elementary proof of Pick's theorem". The Mathematical Gazette. 91 (522): 536–540. doi:10.1017/S0025557200182270. JSTOR 40378436. S2CID 124831432.
Diaz, Ricardo; Robins, Sinai (1995). "Pick's formula via the Weierstrass $\wp$ -function". The American Mathematical Monthly. 102 (5): 431–437. doi:10.2307/2975035. JSTOR 2975035. MR 1327788.
Rosenholtz, Ira (1979). "Calculating surface areas from a blueprint". Mathematics Magazine. 52 (4): 252–256. doi:10.1080/0025570X.1979.11976797. JSTOR 2689425. MR 1572312.
Diaz, Ricardo; Robins, Sinai (1997). "The Ehrhart polynomial of a lattice polytope". Annals of Mathematics. Second Series. 145 (3): 503–518. doi:10.2307/2951842. JSTOR 2951842. MR 1454701.
Bellhouse, D. R. (1981). "Area estimation by point-counting techniques". Biometrics. 37 (2): 303–312. doi:10.2307/2530419. JSTOR 2530419. MR 0673040.
Braden, Bart (1986). "The surveyor's area formula" (PDF). The College Mathematics Journal. 17 (4): 326–337. doi:10.2307/2686282. JSTOR 2686282. Archived from the original (PDF) on 2015-04-06. Retrieved 2021-07-04.

maa.org

Braden, Bart (1986). "The surveyor's area formula" (PDF). The College Mathematics Journal. 17 (4): 326–337. doi:10.2307/2686282. JSTOR 2686282. Archived from the original (PDF) on 2015-04-06. Retrieved 2021-07-04.

ox.ac.uk

maths.ox.ac.uk

Kiradjiev, Kristian (October 2018). "Connecting the dots with Pick's theorem" (PDF). Mathematics Today. pp. 212–214.

ru.nl

cs.ru.nl

Wiedijk, Freek. "Formalizing 100 Theorems". Radboud University Institute for Computing and Information Sciences. Retrieved 2024-02-20.

semanticscholar.org

api.semanticscholar.org

Ram Murty, M.; Thain, Nithum (2007). "Pick's theorem via Minkowski's theorem". The American Mathematical Monthly. 114 (8): 732–736. doi:10.1080/00029890.2007.11920465. JSTOR 27642309. MR 2354443. S2CID 38855683.
Trainin, J. (November 2007). "An elementary proof of Pick's theorem". The Mathematical Gazette. 91 (522): 536–540. doi:10.1017/S0025557200182270. JSTOR 40378436. S2CID 124831432.
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:10.1080/00029890.2021.1839241. MR 4200451. S2CID 231624428.
Bruckheimer, Maxim; Arcavi, Abraham (1995). "Farey series and Pick's area theorem". The Mathematical Intelligencer. 17 (4): 64–67. doi:10.1007/BF03024792. MR 1365013. S2CID 55051527.

web.archive.org

Braden, Bart (1986). "The surveyor's area formula" (PDF). The College Mathematics Journal. 17 (4): 326–337. doi:10.2307/2686282. JSTOR 2686282. Archived from the original (PDF) on 2015-04-06. Retrieved 2021-07-04.

zbmath.org

Pick, Georg (1899). "Geometrisches zur Zahlenlehre". Sitzungsberichte des deutschen naturwissenschaftlich-medicinischen Vereines für Böhmen "Lotos" in Prag. (Neue Folge). 19: 311–319. JFM 33.0216.01. CiteBank:47270