Angle (English Wikipedia)

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

refsWebsite

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11books.google.com

3^rd place

10doi.org

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9archive.org

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4wolfram.com

513^th place

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3web.archive.org

1^st place

3arxiv.org

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2handle.net

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2bipm.org

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1sanu.ac.rs

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1berkeley.edu

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1encyclopediaofmath.org

3,863^rd place

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1nist.gov

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1amesa.org.za

low place

1usp.br

2,069^th place

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1ubc.ca

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1sciendo.com

low place

1umich.edu

459^th place

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1st-andrews.ac.uk

1,547^th place

1,410^th place

1iso.org

629^th place

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1utexas.edu

916^th place

706^th place

1ed.gov

576^th place

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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, 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: 69^th place; English: 59^th 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: 580^th place; English: 462^nd place)

math.berkeley.edu

Hilbert, David, The Foundations of Geometry (PDF), p. 9

bipm.org (Global: 641^st place; English: 955^th 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), V3.01 (9th ed.), International Bureau of Weights and Measures, Aug 2024, 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
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
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, 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, retrieved 2025-08-08

ed.gov (Global: 576^th place; English: 352^nd 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, retrieved 2025-08-08

encyclopediaofmath.org (Global: 3,863^rd place; English: 2,637^th place)

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

handle.net (Global: 102^nd place; English: 76^th place)

hdl.handle.net

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, 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: 629^th place; English: 610^th place)

"ISO 80000-3:2006 Quantities and Units - Space and Time", 2017

nist.gov (Global: 355^th place; English: 454^th place)

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

sanu.ac.rs (Global: 9,183^rd place; English: low 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: 1,547^th place; English: 1,410^th place)

mathshistory.st-andrews.ac.uk

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

ubc.ca (Global: 1,997^th place; English: 1,295^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, 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: 459^th place; English: 360^th place)

name.umdl.umich.edu

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

usp.br (Global: 2,069^th place; English: 5,287^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: 916^th place; English: 706^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
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
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

wolfram.com (Global: 513^th place; English: 537^th place)

mathworld.wolfram.com

Weisstein, Eric W., "Angle", mathworld.wolfram.com, retrieved 2025-06-13
Weisstein, Eric W., "Degree", mathworld.wolfram.com, retrieved 2025-06-14
Weisstein, Eric W., "Radian", mathworld.wolfram.com, 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: 69th place; English: 59th place)

berkeley.edu (Global: 580th place; English: 462nd place)

math.berkeley.edu

bipm.org (Global: 641st place; English: 955th place)

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

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

ed.gov (Global: 576th place; English: 352nd place)

files.eric.ed.gov

encyclopediaofmath.org (Global: 3,863rd place; English: 2,637th place)

handle.net (Global: 102nd place; English: 76th place)

hdl.handle.net

iso.org (Global: 629th place; English: 610th place)

nist.gov (Global: 355th place; English: 454th place)

sanu.ac.rs (Global: 9,183rd place; English: low place)

elib.mi.sanu.ac.rs

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

st-andrews.ac.uk (Global: 1,547th place; English: 1,410th place)

mathshistory.st-andrews.ac.uk

ubc.ca (Global: 1,997th place; English: 1,295th place)

open.library.ubc.ca

umich.edu (Global: 459th place; English: 360th place)

name.umdl.umich.edu

usp.br (Global: 2,069th place; English: 5,287th place)

ime.usp.br

utexas.edu (Global: 916th place; English: 706th place)

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

wolfram.com (Global: 513th place; English: 537th place)

mathworld.wolfram.com

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

arxiv.org (Global: 69^th place; English: 59^th place)

berkeley.edu (Global: 580^th place; English: 462^nd place)

bipm.org (Global: 641^st place; English: 955^th place)

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

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

ed.gov (Global: 576^th place; English: 352^nd place)

encyclopediaofmath.org (Global: 3,863^rd place; English: 2,637^th place)

handle.net (Global: 102^nd place; English: 76^th place)

iso.org (Global: 629^th place; English: 610^th place)

nist.gov (Global: 355^th place; English: 454^th place)

sanu.ac.rs (Global: 9,183^rd place; English: low place)

st-andrews.ac.uk (Global: 1,547^th place; English: 1,410^th place)

ubc.ca (Global: 1,997^th place; English: 1,295^th place)

umich.edu (Global: 459^th place; English: 360^th place)

usp.br (Global: 2,069^th place; English: 5,287^th place)

utexas.edu (Global: 916^th place; English: 706^th place)

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

wolfram.com (Global: 513^th place; English: 537^th place)