Triangle (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Triangle" in English language version.

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mathscinet.ams.org

Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst (2008). "Orthocentric simplices and biregularity". Results in Mathematics. 52 (1–2): 41–50. doi:10.1007/s00025-008-0294-4. MR 2430410. It is well known that the incenter of a Euclidean triangle lies on its Euler line connecting the centroid and the circumcenter if and only if the triangle is isosceles.
Richmond, Bettina; Richmond, Thomas (1997). "Metric spaces in which all triangles are degenerate". The American Mathematical Monthly. 104 (8): 713–719. doi:10.1080/00029890.1997.11990706. JSTOR 2975234. MR 1476755.
Meisters 1975. Meisters, G. H. (1975). "Polygons have ears". The American Mathematical Monthly. 82 (6): 648–651. doi:10.2307/2319703. JSTOR 2319703. MR 0367792.
Chandran & Mount 1992. Chandran, Sharat; Mount, David M. (1992). "A parallel algorithm for enclosed and enclosing triangles". International Journal of Computational Geometry & Applications. 2 (2): 191–214. doi:10.1142/S0218195992000123. MR 1168956.
Chandran & Mount 1992. Chandran, Sharat; Mount, David M. (1992). "A parallel algorithm for enclosed and enclosing triangles". International Journal of Computational Geometry & Applications. 2 (2): 191–214. doi:10.1142/S0218195992000123. MR 1168956.
Ballmann 1995, p. viii+112. Ballmann, Werner (1995). Lectures on spaces of nonpositive curvature. DMV Seminar 25. Basel: Birkhäuser Verlag. pp. viii+112. ISBN 3-7643-5242-6. MR 1377265.

archive.org

Byrne 2013, pp. xx–xxi. Byrne, Oliver (2013) [1847]. The First Six Books of the Elements of Euclid (facsimile ed.). TASCHEN GmbH. ISBN 978-3-8365-4471-9.
Byrne 2013, pp. xx–xxi. Byrne, Oliver (2013) [1847]. The First Six Books of the Elements of Euclid (facsimile ed.). TASCHEN GmbH. ISBN 978-3-8365-4471-9.
Byrne 2013, pp. xx–xxi. Byrne, Oliver (2013) [1847]. The First Six Books of the Elements of Euclid (facsimile ed.). TASCHEN GmbH. ISBN 978-3-8365-4471-9.
Heath 1926, p. 187, Definition 20. Heath, Thomas L. (1926). The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). Cambridge University Press. hdl:2027/uva.x001426155. Dover reprint, 1956. SBN 486-60088-2.
Heath 1926, Definition 20, Definition 21. Heath, Thomas L. (1926). The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). Cambridge University Press. hdl:2027/uva.x001426155. Dover reprint, 1956. SBN 486-60088-2.
Heath 1926, Definition 20, Definition 21. Heath, Thomas L. (1926). The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). Cambridge University Press. hdl:2027/uva.x001426155. Dover reprint, 1956. SBN 486-60088-2.
Cromwell (1997), p. 341. Cromwell, Peter R. (1997). Polyhedra. Cambridge University Press. ISBN 978-0-521-55432-9.
Heath 1926, Proposition 32. Heath, Thomas L. (1926). The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). Cambridge University Press. hdl:2027/uva.x001426155. Dover reprint, 1956. SBN 486-60088-2.
Heath 1926, Propositions 36–41. Heath, Thomas L. (1926). The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). Cambridge University Press. hdl:2027/uva.x001426155. Dover reprint, 1956. SBN 486-60088-2.

books.google.com

Lang & Murrow 1988, p. 4. Lang, Serge; Murrow, Gene (1988). Geometry: A High School Course (2nd ed.). Springer. doi:10.1007/978-1-4757-2022-8. ISBN 978-1-4757-2022-8.
Stahl 2003, p. 37. Stahl, Saul (2003). Geometry from Euclid to Knots. Prentice-Hall. ISBN 0-13-032927-4.
Stahl 2003, p. 37. Stahl, Saul (2003). Geometry from Euclid to Knots. Prentice-Hall. ISBN 0-13-032927-4.
Stahl 2003, p. 37. Stahl, Saul (2003). Geometry from Euclid to Knots. Prentice-Hall. ISBN 0-13-032927-4.
Guillermo (2012), p. 161. Guillermo, Artemio R. (2012). Historical Dictionary of the Philippines. Scarecrow Press. ISBN 978-0810872462.
Montroll (2009), p. 4. Montroll, John (2009). Origami Polyhedra Design. A K Peters. ISBN 9781439871065.
Montroll (2009), p. 4. Montroll, John (2009). Origami Polyhedra Design. A K Peters. ISBN 9781439871065.
Holme 2010, p. 210. Holme, A. (2010). Geometry: Our Cultural Heritage. Springer. doi:10.1007/978-3-642-14441-7. ISBN 978-3-642-14441-7.
Holme 2010, p. 143. Holme, A. (2010). Geometry: Our Cultural Heritage. Springer. doi:10.1007/978-3-642-14441-7. ISBN 978-3-642-14441-7.
Lang & Murrow 1988, p. 126–127. Lang, Serge; Murrow, Gene (1988). Geometry: A High School Course (2nd ed.). Springer. doi:10.1007/978-1-4757-2022-8. ISBN 978-1-4757-2022-8.
Lang & Murrow 1988, p. 128. Lang, Serge; Murrow, Gene (1988). Geometry: A High School Course (2nd ed.). Springer. doi:10.1007/978-1-4757-2022-8. ISBN 978-1-4757-2022-8.
Anglin & Lambek 1995, p. 30. Anglin, W. S.; Lambek, J. (1995). The Heritage of Thales. Springer. doi:10.1007/978-1-4612-0803-7. ISBN 978-1-4612-0803-7.
Ryan 2008, p. 105. Ryan, Mark (2008). Geometry For Dummies. John Wiley & Sons. ISBN 978-0-470-08946-0.
Ryan 2008, p. 105. Ryan, Mark (2008). Geometry For Dummies. John Wiley & Sons. ISBN 978-0-470-08946-0.
King 2021, p. 153. King, James R. (2021). Geometry Transformed: Euclidean Plane Geometry Based on Rigid Motions. American Mathematical Society. ISBN 9781470464431.
Ryan 2008, p. 106. Ryan, Mark (2008). Geometry For Dummies. John Wiley & Sons. ISBN 978-0-470-08946-0.
Ryan 2008, p. 104. Ryan, Mark (2008). Geometry For Dummies. John Wiley & Sons. ISBN 978-0-470-08946-0.
King 2021, p. 155. King, James R. (2021). Geometry Transformed: Euclidean Plane Geometry Based on Rigid Motions. American Mathematical Society. ISBN 9781470464431.
Schattschneider, Doris; King, James (1997). Geometry Turned On: Dynamic Software in Learning, Teaching, and Research. The Mathematical Association of America. pp. 3–4. ISBN 978-0883850992.
Ryan 2008, p. 102. Ryan, Mark (2008). Geometry For Dummies. John Wiley & Sons. ISBN 978-0-470-08946-0.
Holme 2010, p. 240. Holme, A. (2010). Geometry: Our Cultural Heritage. Springer. doi:10.1007/978-3-642-14441-7. ISBN 978-3-642-14441-7.
Ramsay & Richtmyer 1995, p. 38. Ramsay, Arlan; Richtmyer, Robert D. (1995). Introduction to Hyperbolic Geometry. Springer. doi:10.1007/978-1-4757-5585-5. ISBN 978-1-4757-5585-5.
Young 2017, p. 27. Young, Cynthia (2017). Trigonometry (4th ed.). John Wiley & Sons. ISBN 978-1-119-32113-2.
Axler 2012, p. 634. Axler, Sheldon (2012). Algebra and Trigonometry. John Wiley & Sons. ISBN 978-0470-58579-5.
Ryan 2008, p. 98. Ryan, Mark (2008). Geometry For Dummies. John Wiley & Sons. ISBN 978-0-470-08946-0.
Jordan & Smith 2010, p. 834. Jordan, D. W.; Smith, P. (2010). Mathematical Techniques: An Introduction for the Engineering, Physical, and Mathematical Sciences (4th ed.). Oxford University Press. ISBN 978-0-19-928201-2.
Vahedi & van der Stappen 2008, p. 73. Vahedi, Mostafa; van der Stappen, A. Frank (2008). "Caging Polygons with Two and Three Fingers". In Akella, Srinivas; Amato, Nancy M.; Huang, Wesley; Mishra, Bud (eds.). Algorithmic Foundation of Robotics VII: Selected Contributions of the Seventh International Workshop on the Algorithmic Foundations of Robotics. doi:10.1007/978-3-540-68405-3. ISBN 978-3-540-68405-3.
Pocchiola & Vegter 1999, p. 259. Pocchiola, Michel; Vegter, Gert (1999). "On Polygonal Covers". In Chazelle, Bernard; Goodman, Jacob E.; Pollack, Richard (eds.). Advances in Discrete and Computational Geometry: Proceedings of the 1996 AMS-IMS-SIAM Joint Summer Research Conference, Discrete and Computational Geometry—Ten Years Later, July 14-18, 1996, Mount Holyoke College. American Mathematical Soc. ISBN 978-0-8218-0674-6.
Devadoss & O'Rourke 2011, p. 93. Devadoss, Satyan L.; O'Rourke, Joseph (2011). Discrete and Computational Geometry. Princeton University Press. ISBN 978-0-691-14553-2.
Nielsen 2021, p. 154. Nielsen, Frank (2021). "On Geodesic Triangles with Right Angles in a Dually Flat Space". In Nielsen, Frank (ed.). Progress in Information Geometry: Theory and Applications. Signals and Communication Technology. Springer. doi:10.1007/978-3-030-65459-7. ISBN 978-3-030-65458-0.
Frame, Michael; Urry, Amelia (21 June 2016). Fractal Worlds: Grown, Built, and Imagined. Yale University Press. p. 21. ISBN 978-0-300-22070-4.

cambridge.org

Kimberling, Clark (March 2008). "Twenty-one points on the nine-point circle". The Mathematical Gazette. 92 (523): 29–38. doi:10.1017/S002555720018249X. ISSN 0025-5572.

cuny.edu

math.csi.cuny.edu

Polking, John C. (25 April 1999). "The area of a spherical triangle. Girard's Theorem". Geometry of the Sphere. Retrieved 19 August 2024.

doi.org

Lang & Murrow 1988, p. 4. Lang, Serge; Murrow, Gene (1988). Geometry: A High School Course (2nd ed.). Springer. doi:10.1007/978-1-4757-2022-8. ISBN 978-1-4757-2022-8.
Cundy (1952). Cundy, H. Martyn (1952). "Deltahedra". Mathematical Gazette. 36 (318): 263–266. doi:10.2307/3608204. JSTOR 3608204.
Holme 2010, p. 210. Holme, A. (2010). Geometry: Our Cultural Heritage. Springer. doi:10.1007/978-3-642-14441-7. ISBN 978-3-642-14441-7.
Holme 2010, p. 143. Holme, A. (2010). Geometry: Our Cultural Heritage. Springer. doi:10.1007/978-3-642-14441-7. ISBN 978-3-642-14441-7.
Lang & Murrow 1988, p. 126–127. Lang, Serge; Murrow, Gene (1988). Geometry: A High School Course (2nd ed.). Springer. doi:10.1007/978-1-4757-2022-8. ISBN 978-1-4757-2022-8.
Lang & Murrow 1988, p. 128. Lang, Serge; Murrow, Gene (1988). Geometry: A High School Course (2nd ed.). Springer. doi:10.1007/978-1-4757-2022-8. ISBN 978-1-4757-2022-8.
Anglin & Lambek 1995, p. 30. Anglin, W. S.; Lambek, J. (1995). The Heritage of Thales. Springer. doi:10.1007/978-1-4612-0803-7. ISBN 978-1-4612-0803-7.
Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst (2008). "Orthocentric simplices and biregularity". Results in Mathematics. 52 (1–2): 41–50. doi:10.1007/s00025-008-0294-4. MR 2430410. It is well known that the incenter of a Euclidean triangle lies on its Euler line connecting the centroid and the circumcenter if and only if the triangle is isosceles.
Holme 2010, p. 240. Holme, A. (2010). Geometry: Our Cultural Heritage. Springer. doi:10.1007/978-3-642-14441-7. ISBN 978-3-642-14441-7.
Ramsay & Richtmyer 1995, p. 38. Ramsay, Arlan; Richtmyer, Robert D. (1995). Introduction to Hyperbolic Geometry. Springer. doi:10.1007/978-1-4757-5585-5. ISBN 978-1-4757-5585-5.
Richmond, Bettina; Richmond, Thomas (1997). "Metric spaces in which all triangles are degenerate". The American Mathematical Monthly. 104 (8): 713–719. doi:10.1080/00029890.1997.11990706. JSTOR 2975234. MR 1476755.
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 29 June 2014.
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 29 June 2014.
Meisters 1975. Meisters, G. H. (1975). "Polygons have ears". The American Mathematical Monthly. 82 (6): 648–651. doi:10.2307/2319703. JSTOR 2319703. MR 0367792.
Oldknow 1995. Oldknow, Adrian (1995). "Computer Aided Research into Triangle Geometry". The Mathematical Gazette. 79 (485 =): 263–274. doi:10.2307/3618298. JSTOR 3618298.
Oldknow 1995. Oldknow, Adrian (1995). "Computer Aided Research into Triangle Geometry". The Mathematical Gazette. 79 (485 =): 263–274. doi:10.2307/3618298. JSTOR 3618298.
Kalman 2008. Kalman, Dan (2008). "An Elementary Proof of Marden's Theorem". American Mathematical Monthly. 115 (4): 330–338. doi:10.1080/00029890.2008.11920532.
Allaire, Zhou & Yao 2012. Allaire, Patricia R.; Zhou, Junmin; Yao, Haishen (2012). "Proving a nineteenth century ellipse identity"". Mathematical Gazette. 96: 161–165. doi:10.1017/S0025557200004277.
Kimberling, Clark (March 2008). "Twenty-one points on the nine-point circle". The Mathematical Gazette. 92 (523): 29–38. doi:10.1017/S002555720018249X. ISSN 0025-5572.
Smith, Geoff; Leversha, Gerry (November 2007). "Euler and triangle geometry". Mathematical Gazette. 91 (522): 436–452. doi:10.1017/S0025557200182087. JSTOR 40378417.
Silvester, John R. (March 2017). "Extremal area ellipses of a convex quadrilateral". The Mathematical Gazette. 101 (550): 11–26. doi:10.1017/mag.2017.2.
Eddy, R. H.; Fritsch, R. (1994). "The Conics of Ludwig Kiepert: A Comprehensive Lesson in the Geometry of the Triangle". Mathematics Magazine. 67 (3): 188–205. doi:10.1080/0025570X.1994.11996212.
Chandran & Mount 1992. Chandran, Sharat; Mount, David M. (1992). "A parallel algorithm for enclosed and enclosing triangles". International Journal of Computational Geometry & Applications. 2 (2): 191–214. doi:10.1142/S0218195992000123. MR 1168956.
Chandran & Mount 1992. Chandran, Sharat; Mount, David M. (1992). "A parallel algorithm for enclosed and enclosing triangles". International Journal of Computational Geometry & Applications. 2 (2): 191–214. doi:10.1142/S0218195992000123. MR 1168956.
Vahedi & van der Stappen 2008, p. 73. Vahedi, Mostafa; van der Stappen, A. Frank (2008). "Caging Polygons with Two and Three Fingers". In Akella, Srinivas; Amato, Nancy M.; Huang, Wesley; Mishra, Bud (eds.). Algorithmic Foundation of Robotics VII: Selected Contributions of the Seventh International Workshop on the Algorithmic Foundations of Robotics. doi:10.1007/978-3-540-68405-3. ISBN 978-3-540-68405-3.
Nielsen 2021, p. 154. Nielsen, Frank (2021). "On Geodesic Triangles with Right Angles in a Dually Flat Space". In Nielsen, Frank (ed.). Progress in Information Geometry: Theory and Applications. Signals and Communication Technology. Springer. doi:10.1007/978-3-030-65459-7. ISBN 978-3-030-65458-0.
Berger 2002, pp. 134–139. Berger, Marcel (2002). A panoramic view of Riemannian geometry. Springer. doi:10.1007/978-3-642-18245-7. ISBN 978-3-642-18245-7.

handle.net

hdl.handle.net

Heath 1926, p. 187, Definition 20. Heath, Thomas L. (1926). The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). Cambridge University Press. hdl:2027/uva.x001426155. Dover reprint, 1956. SBN 486-60088-2.
Heath 1926, Definition 20, Definition 21. Heath, Thomas L. (1926). The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). Cambridge University Press. hdl:2027/uva.x001426155. Dover reprint, 1956. SBN 486-60088-2.
Heath 1926, Definition 20, Definition 21. Heath, Thomas L. (1926). The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). Cambridge University Press. hdl:2027/uva.x001426155. Dover reprint, 1956. SBN 486-60088-2.
Heath 1926, Proposition 32. Heath, Thomas L. (1926). The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). Cambridge University Press. hdl:2027/uva.x001426155. Dover reprint, 1956. SBN 486-60088-2.
Heath 1926, Propositions 36–41. Heath, Thomas L. (1926). The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). Cambridge University Press. hdl:2027/uva.x001426155. Dover reprint, 1956. SBN 486-60088-2.

heldermann-verlag.de

Moses, Peter; Kimberling, Charles (2009). "Reflection-Induced Perspectivities Among Triangles" (PDF). Journal for Geometry and Graphics. 13 (1): 15–24.
Moses, Peter; Kimberling, Charles (2009). "Reflection-Induced Perspectivities Among Triangles" (PDF). Journal for Geometry and Graphics. 13 (1): 15–24.

jstor.org

Cundy (1952). Cundy, H. Martyn (1952). "Deltahedra". Mathematical Gazette. 36 (318): 263–266. doi:10.2307/3608204. JSTOR 3608204.
Richmond, Bettina; Richmond, Thomas (1997). "Metric spaces in which all triangles are degenerate". The American Mathematical Monthly. 104 (8): 713–719. doi:10.1080/00029890.1997.11990706. JSTOR 2975234. MR 1476755.
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 29 June 2014.
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 29 June 2014.
Meisters 1975. Meisters, G. H. (1975). "Polygons have ears". The American Mathematical Monthly. 82 (6): 648–651. doi:10.2307/2319703. JSTOR 2319703. MR 0367792.
Oldknow 1995. Oldknow, Adrian (1995). "Computer Aided Research into Triangle Geometry". The Mathematical Gazette. 79 (485 =): 263–274. doi:10.2307/3618298. JSTOR 3618298.
Oldknow 1995. Oldknow, Adrian (1995). "Computer Aided Research into Triangle Geometry". The Mathematical Gazette. 79 (485 =): 263–274. doi:10.2307/3618298. JSTOR 3618298.
Smith, Geoff; Leversha, Gerry (November 2007). "Euler and triangle geometry". Mathematical Gazette. 91 (522): 436–452. doi:10.1017/S0025557200182087. JSTOR 40378417.

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 29 June 2014.
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 29 June 2014.

mathdl.maa.org

Kalman 2008. Kalman, Dan (2008). "An Elementary Proof of Marden's Theorem". American Mathematical Monthly. 115 (4): 330–338. doi:10.1080/00029890.2008.11920532.

proquest.com

Alonso, Orlando Braulio (2009). Making sense of definitions in geometry: Metric-combinatorial approaches to classifying triangles and quadrilaterals (PhD thesis). Teachers College, Columbia University. p. 57. ProQuest 304870039.
Alonso, Orlando Braulio (2009). Making sense of definitions in geometry: Metric-combinatorial approaches to classifying triangles and quadrilaterals (PhD thesis). Teachers College, Columbia University. p. 57. ProQuest 304870039.

st-andrews.ac.uk

mathshistory.st-andrews.ac.uk

O'Connor, John J.; Robertson, Edmund F., "Heron of Alexandria", MacTutor History of Mathematics Archive, University of St Andrews

uic.edu

homepages.math.uic.edu

Wood, John. "LAS 100 — Freshman Seminar — Fall 1996: Reasoning with shape and quantity". Retrieved 19 August 2024.

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 29 June 2014.
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 29 June 2014.

worldcat.org

search.worldcat.org

Kimberling, Clark (March 2008). "Twenty-one points on the nine-point circle". The Mathematical Gazette. 92 (523): 29–38. doi:10.1017/S002555720018249X. ISSN 0025-5572.