Radian (English Wikipedia)

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

Last modified: 16:09:23, 10 September 2026 (UTC)

Ref.Un. Ref.Website

Global rank English rank

2920doi.org

2^nd place

2819adsabs.harvard.edu

14^th place

9^th place

2012semanticscholar.org

15^th place

8^th place

1812arxiv.org

49^th place

31^st place

1515bipm.org

1,781^st place

2,481^st place

77web.archive.org

1^st place

76books.google.com

3^rd place

44archive.org

6^th place

22researchgate.net

96^th place

89^th place

22csiro.au

3,457^th place

2,432^nd place

22worldcat.org

4^th place

11loc.gov

63^rd place

47^th place

11iso.org

1,190^th place

1,097^th place

11boost.org

low place

11wolfram.com

1,091^st place

1,169^th place

11st-and.ac.uk

4,765^th place

5,091^st place

1117centurymaths.com

low place

11zenodo.org

737^th place

426^th place

11tripod.com

666^th place

543^rd place

11wikibooks.org

7,048^th place

low place

17centurymaths.com (Global: low place; English: low place)

Euler, Leonhard. Theoria Motus Corporum Solidorum seu Rigidorum [Theory of the motion of solid or rigid bodies] (PDF) (in Latin). Translated by Bruce, Ian. Definition 6, paragraph 316.

adsabs.harvard.edu (Global: 14^th place; English: 9^th place)

ui.adsabs.harvard.edu

Other proposals include the abbreviation "rad" (Brinsmade 1936), the notation $\langle \theta \rangle$ (Romain 1962), and the constants ם (Brownstein 1997), ◁ (Lévy-Leblond 1998), k (Foster 2010), θ_C (Quincey 2021), and ${\cal {C}}={\frac {2\pi }{\Theta }}$ (Mohr et al. 2022). Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Quincey 2016, p. 844: "Also, as alluded to in Mohr & Phillips 2015, the radian can be defined in terms of the area A of a sector ( $A = ⁠ 1 / 2 ⁠ θ r 2$ ), in which case it has the units m²⋅m⁻²." Quincey, Paul (1 April 2016). "The range of options for handling plane angle and solid angle within a system of units". Metrologia. 53 (2): 840–845. Bibcode:2016Metro..53..840Q. doi:10.1088/0026-1394/53/2/840. S2CID 125438811. Mohr, Peter J; Phillips, William D (1 February 2015). "Dimensionless units in the SI". Metrologia. 52 (1): 40–47. arXiv:1409.2794. Bibcode:2015Metro..52...40M. doi:10.1088/0026-1394/52/1/40.
Prando, Giacomo (August 2020). "A spectral unit". Nature Physics. 16 (8): 888. Bibcode:2020NatPh..16..888P. doi:10.1038/s41567-020-0997-3. S2CID 225445454.
Oberhofer, E. S. (March 1992). "What happens to the 'radians'?". The Physics Teacher. 30 (3): 170–171. Bibcode:1992PhTea..30..170O. doi:10.1119/1.2343500.
Aubrecht, Gordon J.; French, Anthony P.; Iona, Mario; Welch, Daniel W. (February 1993). "The radian—That troublesome unit". The Physics Teacher. 31 (2): 84–87. Bibcode:1993PhTea..31...84A. doi:10.1119/1.2343667.
Brinsmade 1936; Romain 1962; Eder 1982; Torrens 1986; Brownstein 1997; Lévy-Leblond 1998; Foster 2010; Mills 2016; Quincey 2021; Leonard 2021; Mohr et al. 2022 Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Eder, W E (January 1982). "A Viewpoint on the Quantity "Plane Angle"". Metrologia. 18 (1): 1–12. Bibcode:1982Metro..18....1E. doi:10.1088/0026-1394/18/1/002. S2CID 250750831. Torrens, A B (1 January 1986). "On Angles and Angular Quantities". Metrologia. 22 (1): 1–7. Bibcode:1986Metro..22....1T. doi:10.1088/0026-1394/22/1/002. S2CID 250801509. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Mills, Ian (1 June 2016). "On the units radian and cycle for the quantity plane angle". Metrologia. 53 (3): 991–997. Bibcode:2016Metro..53..991M. doi:10.1088/0026-1394/53/3/991. S2CID 126032642. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Leonard, B P (1 October 2021). "Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)". Metrologia. 58 (5): 052001. Bibcode:2021Metro..58e2001L. doi:10.1088/1681-7575/abe0fc. S2CID 234036217. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Mohr & Phillips 2015. Mohr, Peter J; Phillips, William D (1 February 2015). "Dimensionless units in the SI". Metrologia. 52 (1): 40–47. arXiv:1409.2794. Bibcode:2015Metro..52...40M. doi:10.1088/0026-1394/52/1/40.
Quincey, Paul; Brown, Richard J C (1 June 2016). "Implications of adopting plane angle as a base quantity in the SI". Metrologia. 53 (3): 998–1002. arXiv:1604.02373. Bibcode:2016Metro..53..998Q. doi:10.1088/0026-1394/53/3/998. S2CID 119294905.
Quincey 2016. Quincey, Paul (1 April 2016). "The range of options for handling plane angle and solid angle within a system of units". Metrologia. 53 (2): 840–845. Bibcode:2016Metro..53..840Q. doi:10.1088/0026-1394/53/2/840. S2CID 125438811.
Torrens 1986. Torrens, A B (1 January 1986). "On Angles and Angular Quantities". Metrologia. 22 (1): 1–7. Bibcode:1986Metro..22....1T. doi:10.1088/0026-1394/22/1/002. S2CID 250801509.
Mohr et al. 2022, p. 6. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Mohr et al. 2022, pp. 8–9. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Quincey 2021. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235.
Quincey, Paul; Brown, Richard J C (1 August 2017). "A clearer approach for defining unit systems". Metrologia. 54 (4): 454–460. arXiv:1705.03765. Bibcode:2017Metro..54..454Q. doi:10.1088/1681-7575/aa7160. S2CID 119418270.
Mohr et al. 2022, p. 3. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
- Muir, Thos. (1910). "The Term "Radian" in Trigonometry". Nature. 83 (2110): 156. Bibcode:1910Natur..83..156M. doi:10.1038/083156a0. S2CID 3958702.
- Quincey, Paul; Mohr, Peter J.; Phillips, William D. (1 August 2019). "Angles are inherently neither length ratios nor dimensionless". Metrologia. 56 (4): 043001. arXiv:1909.08389. Bibcode:2019Metro..56d3001Q. doi:10.1088/1681-7575/ab27d7. S2CID 198428043.
- Nelson, Robert A. (March 1984). "The supplementary units". The Physics Teacher. 22 (3): 188–193. Bibcode:1984PhTea..22..188N. doi:10.1119/1.2341516.
- Kalinin, Mikhail I (1 December 2019). "On the status of plane and solid angles in the International System of Units (SI)". Metrologia. 56 (6): 065009. arXiv:1810.12057. Bibcode:2019Metro..56f5009K. doi:10.1088/1681-7575/ab3fbf. S2CID 53627142.

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

Hall, Arthur Graham; Frink, Fred Goodrich (January 1909). "Chapter VII. The General Angle [55] Signs and Limitations in Value. Exercise XV.". Written at Ann Arbor, Michigan, USA. Trigonometry. Vol. Part I: Plane Trigonometry. New York, USA: Henry Holt and Company / Norwood Press / J. S. Cushing Co. - Berwick & Smith Co., Norwood, Massachusetts, USA. p. 73. Retrieved 2017-08-12.
Bridgman, Percy Williams (1922). Dimensional analysis. New Haven: Yale University Press. Angular amplitude of swing [...] No dimensions.
Cajori, Florian (1993) [1st Pub. 1929]. History of Mathematical Notations. Vol. 2. Dover Publications. pp. 147–148. ISBN 0-486-67766-4.
A. Macfarlane (1893) "On the definitions of the trigonometric functions", page 9, link at Internet Archive

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

Other proposals include the abbreviation "rad" (Brinsmade 1936), the notation $\langle \theta \rangle$ (Romain 1962), and the constants ם (Brownstein 1997), ◁ (Lévy-Leblond 1998), k (Foster 2010), θ_C (Quincey 2021), and ${\cal {C}}={\frac {2\pi }{\Theta }}$ (Mohr et al. 2022). Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Quincey 2016, p. 844: "Also, as alluded to in Mohr & Phillips 2015, the radian can be defined in terms of the area A of a sector ( $A = ⁠ 1 / 2 ⁠ θ r 2$ ), in which case it has the units m²⋅m⁻²." Quincey, Paul (1 April 2016). "The range of options for handling plane angle and solid angle within a system of units". Metrologia. 53 (2): 840–845. Bibcode:2016Metro..53..840Q. doi:10.1088/0026-1394/53/2/840. S2CID 125438811. Mohr, Peter J; Phillips, William D (1 February 2015). "Dimensionless units in the SI". Metrologia. 52 (1): 40–47. arXiv:1409.2794. Bibcode:2015Metro..52...40M. doi:10.1088/0026-1394/52/1/40.
Brinsmade 1936; Romain 1962; Eder 1982; Torrens 1986; Brownstein 1997; Lévy-Leblond 1998; Foster 2010; Mills 2016; Quincey 2021; Leonard 2021; Mohr et al. 2022 Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Eder, W E (January 1982). "A Viewpoint on the Quantity "Plane Angle"". Metrologia. 18 (1): 1–12. Bibcode:1982Metro..18....1E. doi:10.1088/0026-1394/18/1/002. S2CID 250750831. Torrens, A B (1 January 1986). "On Angles and Angular Quantities". Metrologia. 22 (1): 1–7. Bibcode:1986Metro..22....1T. doi:10.1088/0026-1394/22/1/002. S2CID 250801509. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Mills, Ian (1 June 2016). "On the units radian and cycle for the quantity plane angle". Metrologia. 53 (3): 991–997. Bibcode:2016Metro..53..991M. doi:10.1088/0026-1394/53/3/991. S2CID 126032642. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Leonard, B P (1 October 2021). "Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)". Metrologia. 58 (5): 052001. Bibcode:2021Metro..58e2001L. doi:10.1088/1681-7575/abe0fc. S2CID 234036217. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Mohr & Phillips 2015. Mohr, Peter J; Phillips, William D (1 February 2015). "Dimensionless units in the SI". Metrologia. 52 (1): 40–47. arXiv:1409.2794. Bibcode:2015Metro..52...40M. doi:10.1088/0026-1394/52/1/40.
Quincey, Paul; Brown, Richard J C (1 June 2016). "Implications of adopting plane angle as a base quantity in the SI". Metrologia. 53 (3): 998–1002. arXiv:1604.02373. Bibcode:2016Metro..53..998Q. doi:10.1088/0026-1394/53/3/998. S2CID 119294905.
Mohr et al. 2022, p. 6. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Mohr et al. 2022, pp. 8–9. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Quincey 2021. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235.
Quincey, Paul; Brown, Richard J C (1 August 2017). "A clearer approach for defining unit systems". Metrologia. 54 (4): 454–460. arXiv:1705.03765. Bibcode:2017Metro..54..454Q. doi:10.1088/1681-7575/aa7160. S2CID 119418270.
Mohr et al. 2022, p. 3. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Quincey, Paul; Mohr, Peter J.; Phillips, William D. (1 August 2019). "Angles are inherently neither length ratios nor dimensionless". Metrologia. 56 (4): 043001. arXiv:1909.08389. Bibcode:2019Metro..56d3001Q. doi:10.1088/1681-7575/ab27d7. S2CID 198428043.
Kalinin, Mikhail I (1 December 2019). "On the status of plane and solid angles in the International System of Units (SI)". Metrologia. 56 (6): 065009. arXiv:1810.12057. Bibcode:2019Metro..56f5009K. doi:10.1088/1681-7575/ab3fbf. S2CID 53627142.

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

The International System of Units (PDF), V4.01 (9th ed.), International Bureau of Weights and Measures, Jun 2026, p. 138, ISBN 978-92-822-2272-0: "One radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius."
The International System of Units (PDF), V4.01 (9th ed.), International Bureau of Weights and Measures, Jun 2026, p. 138, ISBN 978-92-822-2272-0: "The radian is the coherent unit for plane angle. ... The radian is also the coherent unit for phase angle."
The International System of Units (PDF), V4.01 (9th ed.), International Bureau of Weights and Measures, Jun 2026, p. 138, ISBN 978-92-822-2272-0
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
International Bureau of Weights and Measures 2019, p. 151: "One radian corresponds to the angle for which $s = r$ " International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021
International Bureau of Weights and Measures 2019, p. 151. International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021
International Bureau of Weights and Measures 2019, p. 151: "One radian corresponds to the angle for which $s = r$ , thus $1 rad = 1$ ." International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021
International Bureau of Weights and Measures 2019, p. 137. International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021
Le Système international d'unités (in French), 1970, p. 12, Pour quelques unités du Système International, la Conférence Générale n'a pas ou n'a pas encore décidé s'il s'agit d'unités de base ou bien d'unités dérivées. [For some units of the SI, the CGPM still hasn't yet decided whether they are base units or derived units.]
Report of the 7th meeting (in French), Consultative Committee for Units, May 1980, pp. 6–7
International Bureau of Weights and Measures 2019, pp. 174–175. International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021
International Bureau of Weights and Measures 2019, p. 179. International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021
Consultative Committee for Units (11–12 June 2013). Report of the 21st meeting to the International Committee for Weights and Measures (Report). pp. 18–20.
Consultative Committee for Units (21–23 September 2021). Report of the 25th meeting to the International Committee for Weights and Measures (Report). pp. 16–17.
"CCU Task Group on angle and dimensionless quantities in the SI Brochure (CCU-TG-ADQSIB)". BIPM. Retrieved 26 June 2022.

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

Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3. National Aeronautics and Space Administration, Goddard Space Flight Center. 2002. p. 12.
Leonard, William J. (1999). Minds-on Physics: Advanced topics in mechanics. Kendall Hunt. p. 262. ISBN 978-0-7872-5412-4.
Roche, John J. (21 December 1998). The Mathematics of Measurement: A Critical History. Springer Science & Business Media. p. 134. ISBN 978-0-387-91581-4.
Cotes, Roger (1722). "Editoris notæ ad Harmoniam mensurarum". In Smith, Robert (ed.). Harmonia mensurarum (in Latin). Cambridge, England. pp. 94–95. In Canone Logarithmico exhibetur Systema quoddam menfurarum numeralium, quæ Logarithmi dicuntur: atque hujus systematis Modulus is est Logarithmus, qui metitur Rationem Modularem in Corol. 6. definitam. Similiter in Canone Trigonometrico finuum & tangentium, exhibetur Systema quoddam menfurarum numeralium, quæ Gradus appellantur: atque hujus systematis Modulus is est Numerus Graduum, qui metitur Angulum Modularem modo definitun, hoc est, qui continetur in arcu Radio æquali. Eft autem hic Numerus ad Gradus 180 ut Circuli Radius ad Semicircuinferentiam, hoc eft ut 1 ad 3.141592653589 &c. Unde Modulus Canonis Trigonometrici prodibit 57.2957795130 &c. Cujus Reciprocus eft 0.0174532925 &c. Hujus moduli subsidio (quem in chartula quadam Auctoris manu descriptum inveni) commodissime computabis mensuras angulares, queinadmodum oftendam in Nota III. [In the Logarithmic Canon there is presented a certain system of numerical measures called Logarithms: and the Modulus of this system is the Logarithm, which measures the Modular Ratio as defined in Corollary 6. Similarly, in the Trigonometrical Canon of sines and tangents, there is presented a certain system of numerical measures called Degrees: and the Modulus of this system is the Number of Degrees which measures the Modular Angle defined in the manner defined, that is, which is contained in an equal Radius arc. Now this Number is equal to 180 Degrees as the Radius of a Circle to the Semicircumference, this is as 1 to 3.141592653589 &c. Hence the Modulus of the Trigonometric Canon will be 57.2957795130 &c. Whose Reciprocal is 0.0174532925 &c. With the help of this modulus (which I found described in a note in the hand of the Author) you will most conveniently calculate the angular measures, as mentioned in Note III.]
Gowing, Ronald (27 June 2002). Roger Cotes - Natural Philosopher. Cambridge University Press. ISBN 978-0-521-52649-4.
Isaac Todhunter, Plane Trigonometry: For the Use of Colleges and Schools, p. 10, Cambridge and London: MacMillan, 1864 OCLC 500022958

boost.org (Global: low place; English: low place)

Schabel, Matthias C.; Watanabe, Steven. "Boost.Units FAQ – 1.79.0". www.boost.org. Retrieved 5 May 2022. Angles are treated as units

csiro.au (Global: 3,457^th place; English: 2,432^nd place)

publications.csiro.au

Other proposals include the abbreviation "rad" (Brinsmade 1936), the notation $\langle \theta \rangle$ (Romain 1962), and the constants ם (Brownstein 1997), ◁ (Lévy-Leblond 1998), k (Foster 2010), θ_C (Quincey 2021), and ${\cal {C}}={\frac {2\pi }{\Theta }}$ (Mohr et al. 2022). Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Brinsmade 1936; Romain 1962; Eder 1982; Torrens 1986; Brownstein 1997; Lévy-Leblond 1998; Foster 2010; Mills 2016; Quincey 2021; Leonard 2021; Mohr et al. 2022 Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Eder, W E (January 1982). "A Viewpoint on the Quantity "Plane Angle"". Metrologia. 18 (1): 1–12. Bibcode:1982Metro..18....1E. doi:10.1088/0026-1394/18/1/002. S2CID 250750831. Torrens, A B (1 January 1986). "On Angles and Angular Quantities". Metrologia. 22 (1): 1–7. Bibcode:1986Metro..22....1T. doi:10.1088/0026-1394/22/1/002. S2CID 250801509. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Mills, Ian (1 June 2016). "On the units radian and cycle for the quantity plane angle". Metrologia. 53 (3): 991–997. Bibcode:2016Metro..53..991M. doi:10.1088/0026-1394/53/3/991. S2CID 126032642. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Leonard, B P (1 October 2021). "Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)". Metrologia. 58 (5): 052001. Bibcode:2021Metro..58e2001L. doi:10.1088/1681-7575/abe0fc. S2CID 234036217. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.

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

Other proposals include the abbreviation "rad" (Brinsmade 1936), the notation $\langle \theta \rangle$ (Romain 1962), and the constants ם (Brownstein 1997), ◁ (Lévy-Leblond 1998), k (Foster 2010), θ_C (Quincey 2021), and ${\cal {C}}={\frac {2\pi }{\Theta }}$ (Mohr et al. 2022). Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Quincey 2016, p. 844: "Also, as alluded to in Mohr & Phillips 2015, the radian can be defined in terms of the area A of a sector ( $A = ⁠ 1 / 2 ⁠ θ r 2$ ), in which case it has the units m²⋅m⁻²." Quincey, Paul (1 April 2016). "The range of options for handling plane angle and solid angle within a system of units". Metrologia. 53 (2): 840–845. Bibcode:2016Metro..53..840Q. doi:10.1088/0026-1394/53/2/840. S2CID 125438811. Mohr, Peter J; Phillips, William D (1 February 2015). "Dimensionless units in the SI". Metrologia. 52 (1): 40–47. arXiv:1409.2794. Bibcode:2015Metro..52...40M. doi:10.1088/0026-1394/52/1/40.
Prando, Giacomo (August 2020). "A spectral unit". Nature Physics. 16 (8): 888. Bibcode:2020NatPh..16..888P. doi:10.1038/s41567-020-0997-3. S2CID 225445454.
French, Anthony P. (May 1992). "What happens to the 'radians'? (comment)". The Physics Teacher. 30 (5): 260–261. doi:10.1119/1.2343535.
Oberhofer, E. S. (March 1992). "What happens to the 'radians'?". The Physics Teacher. 30 (3): 170–171. Bibcode:1992PhTea..30..170O. doi:10.1119/1.2343500.
Aubrecht, Gordon J.; French, Anthony P.; Iona, Mario; Welch, Daniel W. (February 1993). "The radian—That troublesome unit". The Physics Teacher. 31 (2): 84–87. Bibcode:1993PhTea..31...84A. doi:10.1119/1.2343667.
Brinsmade 1936; Romain 1962; Eder 1982; Torrens 1986; Brownstein 1997; Lévy-Leblond 1998; Foster 2010; Mills 2016; Quincey 2021; Leonard 2021; Mohr et al. 2022 Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Eder, W E (January 1982). "A Viewpoint on the Quantity "Plane Angle"". Metrologia. 18 (1): 1–12. Bibcode:1982Metro..18....1E. doi:10.1088/0026-1394/18/1/002. S2CID 250750831. Torrens, A B (1 January 1986). "On Angles and Angular Quantities". Metrologia. 22 (1): 1–7. Bibcode:1986Metro..22....1T. doi:10.1088/0026-1394/22/1/002. S2CID 250801509. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Mills, Ian (1 June 2016). "On the units radian and cycle for the quantity plane angle". Metrologia. 53 (3): 991–997. Bibcode:2016Metro..53..991M. doi:10.1088/0026-1394/53/3/991. S2CID 126032642. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Leonard, B P (1 October 2021). "Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)". Metrologia. 58 (5): 052001. Bibcode:2021Metro..58e2001L. doi:10.1088/1681-7575/abe0fc. S2CID 234036217. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Mohr & Phillips 2015. Mohr, Peter J; Phillips, William D (1 February 2015). "Dimensionless units in the SI". Metrologia. 52 (1): 40–47. arXiv:1409.2794. Bibcode:2015Metro..52...40M. doi:10.1088/0026-1394/52/1/40.
Quincey, Paul; Brown, Richard J C (1 June 2016). "Implications of adopting plane angle as a base quantity in the SI". Metrologia. 53 (3): 998–1002. arXiv:1604.02373. Bibcode:2016Metro..53..998Q. doi:10.1088/0026-1394/53/3/998. S2CID 119294905.
Quincey 2016. Quincey, Paul (1 April 2016). "The range of options for handling plane angle and solid angle within a system of units". Metrologia. 53 (2): 840–845. Bibcode:2016Metro..53..840Q. doi:10.1088/0026-1394/53/2/840. S2CID 125438811.
Torrens 1986. Torrens, A B (1 January 1986). "On Angles and Angular Quantities". Metrologia. 22 (1): 1–7. Bibcode:1986Metro..22....1T. doi:10.1088/0026-1394/22/1/002. S2CID 250801509.
Mohr et al. 2022, p. 6. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Mohr et al. 2022, pp. 8–9. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Quincey 2021. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235.
Quincey, Paul; Brown, Richard J C (1 August 2017). "A clearer approach for defining unit systems". Metrologia. 54 (4): 454–460. arXiv:1705.03765. Bibcode:2017Metro..54..454Q. doi:10.1088/1681-7575/aa7160. S2CID 119418270.
Mohr et al. 2022, p. 3. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
- Muir, Thos. (1910). "The Term "Radian" in Trigonometry". Nature. 83 (2110): 156. Bibcode:1910Natur..83..156M. doi:10.1038/083156a0. S2CID 3958702.
- Quincey, Paul; Mohr, Peter J.; Phillips, William D. (1 August 2019). "Angles are inherently neither length ratios nor dimensionless". Metrologia. 56 (4): 043001. arXiv:1909.08389. Bibcode:2019Metro..56d3001Q. doi:10.1088/1681-7575/ab27d7. S2CID 198428043.
- Nelson, Robert A. (March 1984). "The supplementary units". The Physics Teacher. 22 (3): 188–193. Bibcode:1984PhTea..22..188N. doi:10.1119/1.2341516.
- Kalinin, Mikhail I (1 December 2019). "On the status of plane and solid angles in the International System of Units (SI)". Metrologia. 56 (6): 065009. arXiv:1810.12057. Bibcode:2019Metro..56f5009K. doi:10.1088/1681-7575/ab3fbf. S2CID 53627142.

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

"ISO 80000-3:2006 Quantities and Units - Space and Time". 17 January 2017.

loc.gov (Global: 63^rd place; English: 47^th place)

lccn.loc.gov

Protter, Murray H.; Morrey, Charles B. Jr. (1970), College Calculus with Analytic Geometry (2nd ed.), Reading: Addison-Wesley, p. APP-4, LCCN 76087042

researchgate.net (Global: 96^th place; English: 89^th place)

Other proposals include the abbreviation "rad" (Brinsmade 1936), the notation $\langle \theta \rangle$ (Romain 1962), and the constants ם (Brownstein 1997), ◁ (Lévy-Leblond 1998), k (Foster 2010), θ_C (Quincey 2021), and ${\cal {C}}={\frac {2\pi }{\Theta }}$ (Mohr et al. 2022). Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Brinsmade 1936; Romain 1962; Eder 1982; Torrens 1986; Brownstein 1997; Lévy-Leblond 1998; Foster 2010; Mills 2016; Quincey 2021; Leonard 2021; Mohr et al. 2022 Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Eder, W E (January 1982). "A Viewpoint on the Quantity "Plane Angle"". Metrologia. 18 (1): 1–12. Bibcode:1982Metro..18....1E. doi:10.1088/0026-1394/18/1/002. S2CID 250750831. Torrens, A B (1 January 1986). "On Angles and Angular Quantities". Metrologia. 22 (1): 1–7. Bibcode:1986Metro..22....1T. doi:10.1088/0026-1394/22/1/002. S2CID 250801509. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Mills, Ian (1 June 2016). "On the units radian and cycle for the quantity plane angle". Metrologia. 53 (3): 991–997. Bibcode:2016Metro..53..991M. doi:10.1088/0026-1394/53/3/991. S2CID 126032642. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Leonard, B P (1 October 2021). "Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)". Metrologia. 58 (5): 052001. Bibcode:2021Metro..58e2001L. doi:10.1088/1681-7575/abe0fc. S2CID 234036217. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Other proposals include the abbreviation "rad" (Brinsmade 1936), the notation $\langle \theta \rangle$ (Romain 1962), and the constants ם (Brownstein 1997), ◁ (Lévy-Leblond 1998), k (Foster 2010), θ_C (Quincey 2021), and ${\cal {C}}={\frac {2\pi }{\Theta }}$ (Mohr et al. 2022). Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Quincey 2016, p. 844: "Also, as alluded to in Mohr & Phillips 2015, the radian can be defined in terms of the area A of a sector ( $A = ⁠ 1 / 2 ⁠ θ r 2$ ), in which case it has the units m²⋅m⁻²." Quincey, Paul (1 April 2016). "The range of options for handling plane angle and solid angle within a system of units". Metrologia. 53 (2): 840–845. Bibcode:2016Metro..53..840Q. doi:10.1088/0026-1394/53/2/840. S2CID 125438811. Mohr, Peter J; Phillips, William D (1 February 2015). "Dimensionless units in the SI". Metrologia. 52 (1): 40–47. arXiv:1409.2794. Bibcode:2015Metro..52...40M. doi:10.1088/0026-1394/52/1/40.
Prando, Giacomo (August 2020). "A spectral unit". Nature Physics. 16 (8): 888. Bibcode:2020NatPh..16..888P. doi:10.1038/s41567-020-0997-3. S2CID 225445454.
Brinsmade 1936; Romain 1962; Eder 1982; Torrens 1986; Brownstein 1997; Lévy-Leblond 1998; Foster 2010; Mills 2016; Quincey 2021; Leonard 2021; Mohr et al. 2022 Brinsmade, J. B. (December 1936). "Plane and Solid Angles. Their Pedagogic Value When Introduced Explicitly". American Journal of Physics. 4 (4): 175–179. Bibcode:1936AmJPh...4..175B. doi:10.1119/1.1999110. Romain, Jacques E. (July 1962). "Angle as a fourth fundamental quantity". Journal of Research of the National Bureau of Standards Section B. 66B (3): 97. doi:10.6028/jres.066B.012. Eder, W E (January 1982). "A Viewpoint on the Quantity "Plane Angle"". Metrologia. 18 (1): 1–12. Bibcode:1982Metro..18....1E. doi:10.1088/0026-1394/18/1/002. S2CID 250750831. Torrens, A B (1 January 1986). "On Angles and Angular Quantities". Metrologia. 22 (1): 1–7. Bibcode:1986Metro..22....1T. doi:10.1088/0026-1394/22/1/002. S2CID 250801509. Brownstein, K. R. (July 1997). "Angles—Let's treat them squarely". American Journal of Physics. 65 (7): 605–614. Bibcode:1997AmJPh..65..605B. doi:10.1119/1.18616. Lévy-Leblond, Jean-Marc (September 1998). "Dimensional angles and universal constants". American Journal of Physics. 66 (9): 814–815. Bibcode:1998AmJPh..66..814L. doi:10.1119/1.18964. Foster, Marcus P (1 December 2010). "The next 50 years of the SI: a review of the opportunities for the e-Science age". Metrologia. 47 (6): R41–R51. doi:10.1088/0026-1394/47/6/R01. S2CID 117711734. Mills, Ian (1 June 2016). "On the units radian and cycle for the quantity plane angle". Metrologia. 53 (3): 991–997. Bibcode:2016Metro..53..991M. doi:10.1088/0026-1394/53/3/991. S2CID 126032642. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235. Leonard, B P (1 October 2021). "Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)". Metrologia. 58 (5): 052001. Bibcode:2021Metro..58e2001L. doi:10.1088/1681-7575/abe0fc. S2CID 234036217. Mohr, Peter J; Shirley, Eric L; Phillips, William D; Trott, Michael (23 June 2022). "On the dimension of angles and their units". Metrologia. 59 (5): 053001. arXiv:2203.12392. Bibcode:2022Metro..59e3001M. doi:10.1088/1681-7575/ac7bc2.
Quincey, Paul; Brown, Richard J C (1 June 2016). "Implications of adopting plane angle as a base quantity in the SI". Metrologia. 53 (3): 998–1002. arXiv:1604.02373. Bibcode:2016Metro..53..998Q. doi:10.1088/0026-1394/53/3/998. S2CID 119294905.
Quincey 2016. Quincey, Paul (1 April 2016). "The range of options for handling plane angle and solid angle within a system of units". Metrologia. 53 (2): 840–845. Bibcode:2016Metro..53..840Q. doi:10.1088/0026-1394/53/2/840. S2CID 125438811.
Torrens 1986. Torrens, A B (1 January 1986). "On Angles and Angular Quantities". Metrologia. 22 (1): 1–7. Bibcode:1986Metro..22....1T. doi:10.1088/0026-1394/22/1/002. S2CID 250801509.
Quincey 2021. Quincey, Paul (1 October 2021). "Angles in the SI: a detailed proposal for solving the problem". Metrologia. 58 (5): 053002. arXiv:2108.05704. Bibcode:2021Metro..58e3002Q. doi:10.1088/1681-7575/ac023f. S2CID 236547235.
Quincey, Paul; Brown, Richard J C (1 August 2017). "A clearer approach for defining unit systems". Metrologia. 54 (4): 454–460. arXiv:1705.03765. Bibcode:2017Metro..54..454Q. doi:10.1088/1681-7575/aa7160. S2CID 119418270.
- Muir, Thos. (1910). "The Term "Radian" in Trigonometry". Nature. 83 (2110): 156. Bibcode:1910Natur..83..156M. doi:10.1038/083156a0. S2CID 3958702.
- Quincey, Paul; Mohr, Peter J.; Phillips, William D. (1 August 2019). "Angles are inherently neither length ratios nor dimensionless". Metrologia. 56 (4): 043001. arXiv:1909.08389. Bibcode:2019Metro..56d3001Q. doi:10.1088/1681-7575/ab27d7. S2CID 198428043.
- Kalinin, Mikhail I (1 December 2019). "On the status of plane and solid angles in the International System of Units (SI)". Metrologia. 56 (6): 065009. arXiv:1810.12057. Bibcode:2019Metro..56f5009K. doi:10.1088/1681-7575/ab3fbf. S2CID 53627142.

st-and.ac.uk (Global: 4,765^th place; English: 5,091^st place)

www-groups.dcs.st-and.ac.uk

O'Connor, J. J.; Robertson, E. F. (February 2005). "Biography of Roger Cotes". The MacTutor History of Mathematics. Archived from the original on 2012-10-19. Retrieved 2006-04-21.

tripod.com (Global: 666^th place; English: 543^rd place)

jeff560.tripod.com

Miller, Jeff (Nov 23, 2009). "Earliest Known Uses of Some of the Words of Mathematics". Retrieved Sep 30, 2011.

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

International Bureau of Weights and Measures 2019, p. 151: "One radian corresponds to the angle for which $s = r$ " International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021
International Bureau of Weights and Measures 2019, p. 151. International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021
International Bureau of Weights and Measures 2019, p. 151: "One radian corresponds to the angle for which $s = r$ , thus $1 rad = 1$ ." International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021
International Bureau of Weights and Measures 2019, p. 137. International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021
O'Connor, J. J.; Robertson, E. F. (February 2005). "Biography of Roger Cotes". The MacTutor History of Mathematics. Archived from the original on 2012-10-19. Retrieved 2006-04-21.
International Bureau of Weights and Measures 2019, pp. 174–175. International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021
International Bureau of Weights and Measures 2019, p. 179. International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived (PDF) from the original on 8 May 2021

wikibooks.org (Global: 7,048^th place; English: low place)

en.wikibooks.org

Geometry/Unified Angles at Wikibooks

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

reference.wolfram.com

"UnityDimensions—Wolfram Language Documentation". reference.wolfram.com. Retrieved 1 July 2022.

worldcat.org (Global: 4^th place; English: 4^th place)

Isaac Todhunter, Plane Trigonometry: For the Use of Colleges and Schools, p. 10, Cambridge and London: MacMillan, 1864 OCLC 500022958
Frederick Sparks, Longmans' School Trigonometry, p. 6, London: Longmans, Green, and Co., 1890 OCLC 877238863 (1891 edition)

zenodo.org (Global: 737^th place; English: 426^th place)

- Muir, Thos. (1910). "The Term "Radian" in Trigonometry". Nature. 83 (2110): 156. Bibcode:1910Natur..83..156M. doi:10.1038/083156a0. S2CID 3958702.

Radian (English Wikipedia)

17centurymaths.com (Global: low place; English: low place)

adsabs.harvard.edu (Global: 14th place; English: 9th place)

ui.adsabs.harvard.edu

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

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

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

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

boost.org (Global: low place; English: low place)

csiro.au (Global: 3,457th place; English: 2,432nd place)

publications.csiro.au

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

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

loc.gov (Global: 63rd place; English: 47th place)

lccn.loc.gov

researchgate.net (Global: 96th place; English: 89th place)

semanticscholar.org (Global: 15th place; English: 8th place)

api.semanticscholar.org

st-and.ac.uk (Global: 4,765th place; English: 5,091st place)

www-groups.dcs.st-and.ac.uk

tripod.com (Global: 666th place; English: 543rd place)

jeff560.tripod.com

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

wikibooks.org (Global: 7,048th place; English: low place)

en.wikibooks.org

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

reference.wolfram.com

worldcat.org (Global: 4th place; English: 4th place)

zenodo.org (Global: 737th place; English: 426th place)

adsabs.harvard.edu (Global: 14^th place; English: 9^th place)

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

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

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

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

csiro.au (Global: 3,457^th place; English: 2,432^nd place)

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

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

loc.gov (Global: 63^rd place; English: 47^th place)

researchgate.net (Global: 96^th place; English: 89^th place)

semanticscholar.org (Global: 15^th place; English: 8^th place)

st-and.ac.uk (Global: 4,765^th place; English: 5,091^st place)

tripod.com (Global: 666^th place; English: 543^rd place)

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

wikibooks.org (Global: 7,048^th place; English: low place)

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

worldcat.org (Global: 4^th place; English: 4^th place)

zenodo.org (Global: 737^th place; English: 426^th place)