Angle (English Wikipedia)

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

Last modified: 09:53:04, 21 August 2026 (UTC)

Ref.Un. Ref.Website

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1715web.archive.org

1^st place

1311books.google.com

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119archive.org

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1010doi.org

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44wolfram.com

1,091^st place

1,169^th place

33arxiv.org

49^th place

31^st place

32bipm.org

1,781^st place

2,481^st place

31usp.br

1,596^th place

3,629^th place

22hdl.handle.net

66^th place

34^th place

21berkeley.edu

621^st place

429^th place

21umich.edu

429^th place

307^th place

11sanu.ac.rs

4,702^nd place

8,136^th place

11encyclopediaofmath.org

7,049^th place

5,456^th place

11nist.gov

708^th place

742^nd place

11amesa.org.za

low place

11ubc.ca

1,820^th place

998^th place

11sciendo.com

low place

11st-andrews.ac.uk

1,053^rd place

1,274^th place

11iso.org

1,190^th place

1,097^th place

11utexas.edu

868^th place

634^th place

11ed.gov

318^th place

138^th place

amesa.org.za (Global: low place; English: low place)

De, Villiers (2020), "The Value of using Signed Quantities in Geometry" (PDF), Learning and Teaching Mathematics, 29 (2020): 30–34, hdl:10520/ejc-amesal_n29_a8.pdf-v29-n2020-a8, archived (PDF) from the original on 2025-08-16, retrieved 2025-08-08

archive.org (Global: 6^th place; English: 6^th place)

Heath, Thomas Little; Heiberg, J. L. (Johan Ludvig) (1908), The thirteen books of Euclid's Elements, Cambridge, The University Press, p. 176, A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
Moser 1971, p. 41. Moser, James M. (1971), Modern Elementary Geometry, Prentice-Hall
Godfrey & Siddons 1919, p. 9. Godfrey, Charles; Siddons, A. W. (1919), Elementary geometry: practical and theoretical (3rd ed.), Cambridge University Press
Moser 1971, p. 71. Moser, James M. (1971), Modern Elementary Geometry, Prentice-Hall
Rhoad, Richard; Milauskas, George; Whipple, Robert; McDougal Littell (1991), Geometry for enjoyment and challenge, Internet Archive, Evanston, Ill. : McDougal, Littell, p. 67, ISBN 978-0-86609-965-3
Willis, Clarence Addison (1922), Plane Geometry, Blakiston's Son, p. 8
Serra, Michael (2008), Discovering geometry : an investigative approach, Emeryville, CA : Key Curriculum Press, ISBN 978-1-55953-882-4
Alexander, Daniel C. (2006), Elementary geometry for college students, Internet Archive, Boston, MA : Houghton Mifflin, ISBN 978-0-618-64525-1
Robert Baldwin Hayward (1892) The Algebra of Coplanar Vectors and Trigonometry, chapter six

arxiv.org (Global: 49^th place; English: 31^st place)

Quincey, Paul; Mohr, Peter J.; Phillips, William D. (2019), "Angles are inherently neither length ratios nor dimensionless", Metrologia, 56 (4): 043001, arXiv:1909.08389, doi:10.1088/1681-7575/ab27d7
Quincey, Paul; Brown, Richard J C (2016), "Implications of adopting plane angle as a base quantity in the SI", Metrologia, 53 (3): 998–1002, arXiv:1604.02373, doi:10.1088/0026-1394/53/3/998
Quincey, Paul (2021), "Angles in the SI: a detailed proposal for solving the problem", Metrologia, 58 (5): 053002, arXiv:2108.05704, doi:10.1088/1681-7575/ac023f

berkeley.edu (Global: 621^st place; English: 429^th place)

math.berkeley.edu

Hilbert, David, The Foundations of Geometry (PDF), p. 9, archived (PDF) from the original on 2025-06-16, retrieved 2025-05-22

bipm.org (Global: 1,781^st place; English: 2,481^st place)

International Bureau of Weights and Measures (2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived from the original on 2021-10-18
The International System of Units (PDF), V4.01 (9th ed.), International Bureau of Weights and Measures, Jun 2026, p. 137, ISBN 978-92-822-2272-0

books.google.com (Global: 3^rd place; English: 3^rd place)

Evgrafov, M. A. (1966), Analytic Functions, W. B. Saunders, ISBN 978-0-486-84366-7
Papadopoulos, Athanase (2012), Strasbourg Master Class on Geometry, European Mathematical Society, ISBN 978-3-03719-105-7
D'Andrea, Francesco (2023), A Guide to Penrose Tilings, Springer, ISBN 978-3-031-28428-1, archived from the original on 2025-08-14, retrieved 2025-02-24
Bulboacǎ, Teodor; Joshi, Santosh B.; Goswami, Pranay (2019), Complex Analysis: Theory and Applications, Walter de Gruyter GmbH & Co KG, ISBN 978-3-11-065803-3
Redei, L. (2014), Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein, Elsevier, ISBN 978-1-4832-8270-1, archived from the original on 2025-03-19, retrieved 2025-02-24
Aboughantous 2010, p. 18. Aboughantous, Charles H. (2010), A High School First Course in Euclidean Plane Geometry, Universal Publishers, ISBN 978-1-59942-822-2
Halsted, George Bruce (1899), Elementary Synthetic Geometry, Wiley, p. 7
Todhunter, Isaac (1864), Plane Trigonometry: For the Use of Colleges and Schools. With Numerous Examples, MacMillan and Company
Leonard, William J. (1999), Minds-on Physics: Advanced topics in mechanics, Kendall Hunt, p. 262, ISBN 978-0-7872-5412-4
Chisholm 1911; Heiberg 1908, p. 178 Heiberg, Johan Ludvig (1908), Heath, T. L. (ed.), Euclid, The Thirteen Books of Euclid's Elements, vol. 1, Cambridge: Cambridge University Press.
Chisholm 1911; Heiberg 1908, pp. 177–178 Heiberg, Johan Ludvig (1908), Heath, T. L. (ed.), Euclid, The Thirteen Books of Euclid's Elements, vol. 1, Cambridge: Cambridge University Press.

doi.org (Global: 2^nd place; English: 2^nd place)

Linton, John Alexander (1973), Phase and amplitude variation of Chandler wobble (Thesis), University of British Columbia, doi:10.14288/1.0052929, archived from the original on 2025-08-15, retrieved 2025-08-08, The latitude of a point on earth is defined as the conjugate of the angle between the point where the rotation axis pierces the celestial sphere (celestial pole) and the point where the local vertical pierces the same sphere (zenith).
Grötschel, Martin; Hanche-Olsen, Harald; Holden, Helge; Krystek, Michael P. (2022), "On Angular Measures in Axiomatic Euclidean Planar Geometry", Measurement Science Review, 22 (4): 152–159, doi:10.2478/msr-2022-0019, hdl:11250/3033842
Quincey, Paul; Mohr, Peter J.; Phillips, William D. (2019), "Angles are inherently neither length ratios nor dimensionless", Metrologia, 56 (4): 043001, arXiv:1909.08389, doi:10.1088/1681-7575/ab27d7
French, Anthony P. (1992), "What happens to the 'radians'? (comment)", The Physics Teacher, 30 (5): 260–261, doi:10.1119/1.2343535
Prando, Giacomo (2020), "A spectral unit", Nature Physics, 16 (8): 888, doi:10.1038/s41567-020-0997-3
Oberhofer, E. S. (1992), "What happens to the 'radians'?", The Physics Teacher, 30 (3): 170–171, doi:10.1119/1.2343500
Quincey, Paul; Brown, Richard J C (2016), "Implications of adopting plane angle as a base quantity in the SI", Metrologia, 53 (3): 998–1002, arXiv:1604.02373, doi:10.1088/0026-1394/53/3/998
Quincey, Paul (2021), "Angles in the SI: a detailed proposal for solving the problem", Metrologia, 58 (5): 053002, arXiv:2108.05704, doi:10.1088/1681-7575/ac023f
Aubrecht, Gordon J.; French, Anthony P.; Iona, Mario; Welch, Daniel W. (1993), "The radian—That troublesome unit", The Physics Teacher, 31 (2): 84–87, doi:10.1119/1.2343667
Jackson, Stanley B. (1967), "Congruence and measurement" (PDF), The Arithmetic Teacher, 14 (2): 94–102, doi:10.5951/AT.14.2.0094, archived (PDF) from the original on 2025-08-16, retrieved 2025-08-08

ed.gov (Global: 318^th place; English: 138^th place)

files.eric.ed.gov

Jackson, Stanley B. (1967), "Congruence and measurement" (PDF), The Arithmetic Teacher, 14 (2): 94–102, doi:10.5951/AT.14.2.0094, archived (PDF) from the original on 2025-08-16, retrieved 2025-08-08

encyclopediaofmath.org (Global: 7,049^th place; English: 5,456^th place)

Sidorov 2001 Sidorov, L. A. (2001) [1994], "Angle", Encyclopedia of Mathematics, EMS Press

hdl.handle.net (Global: 66^th place; English: 34^th place)

De, Villiers (2020), "The Value of using Signed Quantities in Geometry" (PDF), Learning and Teaching Mathematics, 29 (2020): 30–34, hdl:10520/ejc-amesal_n29_a8.pdf-v29-n2020-a8, archived (PDF) from the original on 2025-08-16, retrieved 2025-08-08
Grötschel, Martin; Hanche-Olsen, Harald; Holden, Helge; Krystek, Michael P. (2022), "On Angular Measures in Axiomatic Euclidean Planar Geometry", Measurement Science Review, 22 (4): 152–159, doi:10.2478/msr-2022-0019, hdl:11250/3033842

iso.org (Global: 1,190^th place; English: 1,097^th place)

"ISO 80000-3:2006 Quantities and Units - Space and Time", 2017, archived from the original on 2016-03-03, retrieved 2025-08-08

nist.gov (Global: 708^th place; English: 742^nd place)

"NIST Guide to the SI, Chapter 7: Rules and Style Conventions for Expressing Values of Quantities", NIST, 2016, archived from the original on 2025-08-05, retrieved 2025-08-08, α is a quantity symbol for plane angle.

sanu.ac.rs (Global: 4,702^nd place; English: 8,136^th place)

elib.mi.sanu.ac.rs

This approach requires, however, an additional proof that the measure of the angle does not change with changing radius $r$ , in addition to the issue of "measurement units chosen". A smoother approach is to measure the angle by the length of the corresponding unit circle arc. Here "unit" can be chosen to be dimensionless in the sense that it is the real number 1 associated with the unit segment on the real line. See Dimitrić (2012), for instance. Dimitrić, Radoslav M. (2012), "On Angles and Angle Measurements" (PDF), The Teaching of Mathematics, XV (2): 133–140, archived (PDF) from the original on 2019-01-17, retrieved 2019-08-06

sciendo.com (Global: low place; English: low place)

Grötschel, Martin; Hanche-Olsen, Harald; Holden, Helge; Krystek, Michael P. (2022), "On Angular Measures in Axiomatic Euclidean Planar Geometry", Measurement Science Review, 22 (4): 152–159, doi:10.2478/msr-2022-0019, hdl:11250/3033842

st-andrews.ac.uk (Global: 1,053^rd place; English: 1,274^th place)

mathshistory.st-andrews.ac.uk

"Earliest Known Uses of Some of the Words of Mathematics (R)", Maths History, archived from the original on 2025-08-14, retrieved 2025-08-01

ubc.ca (Global: 1,820^th place; English: 998^th place)

open.library.ubc.ca

Linton, John Alexander (1973), Phase and amplitude variation of Chandler wobble (Thesis), University of British Columbia, doi:10.14288/1.0052929, archived from the original on 2025-08-15, retrieved 2025-08-08, The latitude of a point on earth is defined as the conjugate of the angle between the point where the rotation axis pierces the celestial sphere (celestial pole) and the point where the local vertical pierces the same sphere (zenith).

umich.edu (Global: 429^th place; English: 307^th place)

name.umdl.umich.edu

Loney, Sidney Luxton (1893), Plane trigonometry, p. 5

usp.br (Global: 1,596^th place; English: 3,629^th place)

ime.usp.br

Moise, Edwin E. (1990), Elementary geometry from an advanced standpoint (PDF) (3rd ed.), Addison-Wesley Publishing Company

utexas.edu (Global: 868^th place; English: 634^th place)

Slocum 2007 Slocum, Jonathan (2007), Preliminary Indo-European lexicon — Pokorny PIE data, University of Texas research department: linguistics research center, archived from the original on 2010-06-27, retrieved 2010-02-02

web.archive.org (Global: 1^st place; English: 1^st place)

This approach requires, however, an additional proof that the measure of the angle does not change with changing radius $r$ , in addition to the issue of "measurement units chosen". A smoother approach is to measure the angle by the length of the corresponding unit circle arc. Here "unit" can be chosen to be dimensionless in the sense that it is the real number 1 associated with the unit segment on the real line. See Dimitrić (2012), for instance. Dimitrić, Radoslav M. (2012), "On Angles and Angle Measurements" (PDF), The Teaching of Mathematics, XV (2): 133–140, archived (PDF) from the original on 2019-01-17, retrieved 2019-08-06
Hilbert, David, The Foundations of Geometry (PDF), p. 9, archived (PDF) from the original on 2025-06-16, retrieved 2025-05-22
D'Andrea, Francesco (2023), A Guide to Penrose Tilings, Springer, ISBN 978-3-031-28428-1, archived from the original on 2025-08-14, retrieved 2025-02-24
Redei, L. (2014), Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein, Elsevier, ISBN 978-1-4832-8270-1, archived from the original on 2025-03-19, retrieved 2025-02-24
"NIST Guide to the SI, Chapter 7: Rules and Style Conventions for Expressing Values of Quantities", NIST, 2016, archived from the original on 2025-08-05, retrieved 2025-08-08, α is a quantity symbol for plane angle.
De, Villiers (2020), "The Value of using Signed Quantities in Geometry" (PDF), Learning and Teaching Mathematics, 29 (2020): 30–34, hdl:10520/ejc-amesal_n29_a8.pdf-v29-n2020-a8, archived (PDF) from the original on 2025-08-16, retrieved 2025-08-08
Weisstein, Eric W., "Angle", mathworld.wolfram.com, archived from the original on 2023-03-26, retrieved 2025-06-13
Weisstein, Eric W., "Degree", mathworld.wolfram.com, archived from the original on 2025-06-12, retrieved 2025-06-14
Weisstein, Eric W., "Radian", mathworld.wolfram.com, archived from the original on 2021-02-13, retrieved 2025-06-14
Linton, John Alexander (1973), Phase and amplitude variation of Chandler wobble (Thesis), University of British Columbia, doi:10.14288/1.0052929, archived from the original on 2025-08-15, retrieved 2025-08-08, The latitude of a point on earth is defined as the conjugate of the angle between the point where the rotation axis pierces the celestial sphere (celestial pole) and the point where the local vertical pierces the same sphere (zenith).
International Bureau of Weights and Measures (2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived from the original on 2021-10-18
"Earliest Known Uses of Some of the Words of Mathematics (R)", Maths History, archived from the original on 2025-08-14, retrieved 2025-08-01
"ISO 80000-3:2006 Quantities and Units - Space and Time", 2017, archived from the original on 2016-03-03, retrieved 2025-08-08
Slocum 2007 Slocum, Jonathan (2007), Preliminary Indo-European lexicon — Pokorny PIE data, University of Texas research department: linguistics research center, archived from the original on 2010-06-27, retrieved 2010-02-02
Jackson, Stanley B. (1967), "Congruence and measurement" (PDF), The Arithmetic Teacher, 14 (2): 94–102, doi:10.5951/AT.14.2.0094, archived (PDF) from the original on 2025-08-16, retrieved 2025-08-08

wolfram.com (Global: 1,091^st place; English: 1,169^th place)

mathworld.wolfram.com

Weisstein, Eric W., "Angle", mathworld.wolfram.com, archived from the original on 2023-03-26, retrieved 2025-06-13
Weisstein, Eric W., "Degree", mathworld.wolfram.com, archived from the original on 2025-06-12, retrieved 2025-06-14
Weisstein, Eric W., "Radian", mathworld.wolfram.com, archived from the original on 2021-02-13, retrieved 2025-06-14
D. Zwillinger, ed. (1995), CRC Standard Mathematical Tables and Formulae, Boca Raton, FL: CRC Press, p. 270 as cited in Weisstein, Eric W., "Exterior Angle", MathWorld

Angle (English Wikipedia)

amesa.org.za (Global: low place; English: low place)

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 49th place; English: 31st place)

berkeley.edu (Global: 621st place; English: 429th place)

math.berkeley.edu

bipm.org (Global: 1,781st place; English: 2,481st place)

books.google.com (Global: 3rd place; English: 3rd place)

doi.org (Global: 2nd place; English: 2nd place)

ed.gov (Global: 318th place; English: 138th place)

files.eric.ed.gov

encyclopediaofmath.org (Global: 7,049th place; English: 5,456th place)

hdl.handle.net (Global: 66th place; English: 34th place)

iso.org (Global: 1,190th place; English: 1,097th place)

nist.gov (Global: 708th place; English: 742nd place)

sanu.ac.rs (Global: 4,702nd place; English: 8,136th place)