Angle (English Wikipedia)

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

refsWebsite

Global rank English rank

16doi.org

2^nd place

15harvard.edu

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10arxiv.org

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9semanticscholar.org

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9books.google.com

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7web.archive.org

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7archive.org

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2researchgate.net

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2csiro.au

4,114^th place

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2mathsisfun.com

6,108^th place

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2wolfram.com

513^th place

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1encyclopediaofmath.org

3,863^rd place

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1utexas.edu

916^th place

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1bipm.org

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1sanu.ac.rs

9,183^rd place

low place

1thefreedictionary.com

614^th place

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1oopic.com

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1wikipedia.org

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1msdn.com

3,029^th place

2,272^nd place

1hpmuseum.org

low place

1boost.org

low place

1mathwords.com

low place

archive.org

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
Willis, Clarence Addison (1922). Plane Geometry. Blakiston's Son. p. 8.
Jeans, James Hopwood (1947). The Growth of Physical Science. CUP Archive. p. 7.
Bridgman, Percy Williams (1922). Dimensional analysis. New Haven : Yale University Press. Angular amplitude of swing [...] No dimensions.
Robert Baldwin Hayward (1892) The Algebra of Coplanar Vectors and Trigonometry, chapter six

arxiv.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.
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.

bipm.org

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 from the original on 18 October 2021

books.google.com

Evgrafov, M. A. (2019-09-18). Analytic Functions. Courier Dover Publications. 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 (2023-08-19). A Guide to Penrose Tilings. Springer Nature. ISBN 978-3-031-28428-1.
Bulboacǎ, Teodor; Joshi, Santosh B.; Goswami, Pranay (2019-07-08). Complex Analysis: Theory and Applications. Walter de Gruyter GmbH & Co KG. ISBN 978-3-11-065803-3.
Redei, L. (2014-07-15). Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein. Elsevier. ISBN 978-1-4832-8270-1.
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.
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
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.

boost.org

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

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

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.

encyclopediaofmath.org

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

harvard.edu

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.

hpmuseum.org

Bonin, Walter (2016-01-11). "RE: WP-32S in 2016?". HP Museum. Archived from the original on 2019-08-06. Retrieved 2019-08-05.

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Hargreaves, Shawn [in Polish]. "Angles, integers, and modulo arithmetic". blogs.msdn.com. Archived from the original on 2019-06-30. Retrieved 2019-08-05.

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"ooPIC Programmer's Guide - Chapter 15: URCP". ooPIC Manual & Technical Specifications - ooPIC Compiler Ver 6.0. Savage Innovations, LLC. 2007 [1997]. Archived from the original on 2008-06-28. Retrieved 2019-08-05.

researchgate.net

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.

sanu.ac.rs

elib.mi.sanu.ac.rs

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.

semanticscholar.org

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.

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