Dimensional analysis (English Wikipedia)

Roche, John J (1998), The Mathematics of Measurement: A Critical History, Springer, p. 203, ISBN 978-0-387-91581-4, Beginning apparently with Maxwell, mass, length and time began to be interpreted as having a privileged fundamental character and all other quantities as derivative, not merely with respect to measurement, but with respect to their physical status as well.
Rayleigh, Baron John William Strutt (1877), The Theory of Sound, Macmillan
Fourier (1822), p. 156. Fourier, Joseph (1822), Theorie analytique de la chaleur (in French), Paris: Firmin Didot

cam.ac.uk (Global: 670^th place; English: 480^th place)

cl.cam.ac.uk

Kennedy, Andrew J. (April 1996). Programming languages and dimensions (Phd). Vol. 391. University of Cambridge. ISSN 1476-2986. UCAM-CL-TR-391.

camfort.github.io (Global: low place; English: low place)

"CamFort: Specify, verify, and refactor Fortran code". University of Cambridge; University of Kent. 2018.

core.ac.uk (Global: 1,734^th place; English: 1,312^th place)

Berberan-Santos, Mário N.; Pogliani, Lionello (1999). "Two alternative derivations of Bridgman's theorem" (PDF). Journal of Mathematical Chemistry. 26 (1–3): 255–261, See §5 General Results p. 259. doi:10.1023/A:1019102415633. S2CID 14833238.

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

doi.org

Bolster, Diogo; Hershberger, Robert E.; Donnelly, Russell E. (September 2011). "Dynamic similarity, the dimensionless science". Physics Today. 64 (9): 42–47. Bibcode:2011PhT....64i..42B. doi:10.1063/PT.3.1258.
Yalin, M. Selim (1971). "Principles of the Theory of Dimensions". Theory of Hydraulic Models. pp. 1–34. doi:10.1007/978-1-349-00245-0_1. ISBN 978-1-349-00247-4.
Duff, M.J.; Okun, L.B.; Veneziano, G. (September 2002), "Trialogue on the number of fundamental constants", Journal of High Energy Physics, 2002 (3): 023, arXiv:physics/0110060, Bibcode:2002JHEP...03..023D, doi:10.1088/1126-6708/2002/03/023, S2CID 15806354
Macagno, Enzo O. (1971). "Historico-critical review of dimensional analysis". Journal of the Franklin Institute. 292 (6): 391–340. doi:10.1016/0016-0032(71)90160-8.
Martins, Roberto De A. (1981). "The origin of dimensional analysis". Journal of the Franklin Institute. 311 (5): 331–337. doi:10.1016/0016-0032(81)90475-0.
Mitchell, Daniel Jon (2017). "Making sense of absolute measurement: James Clerk Maxwell, William Thomson, Fleeming Jenkin, and the invention of the dimensional formula". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 58: 63–79. Bibcode:2017SHPMP..58...63M. doi:10.1016/j.shpsb.2016.08.004.
Berberan-Santos, Mário N.; Pogliani, Lionello (1999). "Two alternative derivations of Bridgman's theorem" (PDF). Journal of Mathematical Chemistry. 26 (1–3): 255–261, See §5 General Results p. 259. doi:10.1023/A:1019102415633. S2CID 14833238.
Gehani, N. (1977). "Units of measure as a data attribute". Comput. Lang. 2 (3): 93–111. doi:10.1016/0096-0551(77)90010-8.
Gehani, N. (June 1985). "Ada's derived types and units of measure". Software: Practice and Experience. 15 (6): 555–569. doi:10.1002/spe.4380150604. S2CID 40558757.
Cmelik, R. F.; Gehani, N. H. (May 1988). "Dimensional analysis with C++". IEEE Software. 5 (3): 21–27. doi:10.1109/52.2021. S2CID 22450087.
Kennedy, A. (2010). "Types for Units-of-Measure: Theory and Practice". In Horváth, Z.; Plasmeijer, R.; Zsók, V. (eds.). Central European Functional Programming School. CEFP 2009. Lecture Notes in Computer Science. Vol. 6299. Springer. pp. 268–305. CiteSeerX 10.1.1.174.6901. doi:10.1007/978-3-642-17685-2_8. ISBN 978-3-642-17684-5.
Gundry, Adam (December 2015). "A typechecker plugin for units of measure: domain-specific constraint solving in GHC Haskell" (PDF). SIGPLAN Notices. 50 (12): 11–22. doi:10.1145/2887747.2804305. Archived (PDF) from the original on 10 August 2017.
Bennich-Björkman, O.; McKeever, S. (2018). "The next 700 unit of measurement checkers". Proceedings of the 11th ACM SIGPLAN International Conference on Software Language Engineering. pp. 121–132. doi:10.1145/3276604.3276613. ISBN 978-1-4503-6029-6. S2CID 53089559.
McBride, Conor; Nordvall-Forsberg, Fredrik (2022). "Type systems for programs respecting dimensions" (PDF). Advanced Mathematical and Computational Tools in Metrology and Testing XII. Advances in Mathematics for Applied Sciences. World Scientific. pp. 331–345. doi:10.1142/9789811242380_0020. ISBN 9789811242380. S2CID 243831207. Archived (PDF) from the original on 17 May 2022.
Quincey, Paul (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.
Siano (1985-I, 1985-II) Siano, Donald (1985), "Orientational Analysis – A Supplement to Dimensional Analysis – I", Journal of the Franklin Institute, 320 (6): 267–283, doi:10.1016/0016-0032(85)90031-6 Siano, Donald (1985), "Orientational Analysis, Tensor Analysis and The Group Properties of the SI Supplementary Units – II", Journal of the Franklin Institute, 320 (6): 285–302, doi:10.1016/0016-0032(85)90032-8

dx.doi.org

Mitchell, Daniel Jon (2017). "Making sense of absolute measurement: James Clerk Maxwell, William Thomson, Fleeming Jenkin, and the invention of the dimensional formula". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 58: 63–79. Bibcode:2017SHPMP..58...63M. doi:10.1016/j.shpsb.2016.08.004.
Quincey, Paul (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.

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

Hart 1995 Hart, George W. (1995), Multidimensional Analysis: Algebras and Systems for Science and Engineering, Springer-Verlag, ISBN 978-0-387-94417-3

gundry.co.uk (Global: low place; English: low place)

adam.gundry.co.uk

Gundry, Adam (December 2015). "A typechecker plugin for units of measure: domain-specific constraint solving in GHC Haskell" (PDF). SIGPLAN Notices. 50 (12): 11–22. doi:10.1145/2887747.2804305. Archived (PDF) from the original on 10 August 2017.

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

hdl.handle.net

Maxwell, James Clerk (1873), A Treatise on Electricity and Magnetism, Clarendon Press series, Oxford, p. 45, hdl:2027/uc1.l0065867749
Griffioen, P. (2019). A unit-aware matrix language and its application in control and auditing (PDF) (Thesis). University of Amsterdam. hdl:11245.1/fd7be191-700f-4468-a329-4c8ecd9007ba. Archived (PDF) from the original on 21 February 2020.

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Bolster, Diogo; Hershberger, Robert E.; Donnelly, Russell E. (September 2011). "Dynamic similarity, the dimensionless science". Physics Today. 64 (9): 42–47. Bibcode:2011PhT....64i..42B. doi:10.1063/PT.3.1258.
Duff, M.J.; Okun, L.B.; Veneziano, G. (September 2002), "Trialogue on the number of fundamental constants", Journal of High Energy Physics, 2002 (3): 023, arXiv:physics/0110060, Bibcode:2002JHEP...03..023D, doi:10.1088/1126-6708/2002/03/023, S2CID 15806354
Mitchell, Daniel Jon (2017). "Making sense of absolute measurement: James Clerk Maxwell, William Thomson, Fleeming Jenkin, and the invention of the dimensional formula". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 58: 63–79. Bibcode:2017SHPMP..58...63M. doi:10.1016/j.shpsb.2016.08.004.
Quincey, Paul (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.

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

"ISO 80000-1:2009(en) Quantities and units — Part 1: General". International Organization for Standardization. Retrieved 12 May 2023.

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highered.mcgraw-hill.com

Cimbala, John; Çengel, Yunus (2006). "§7-2 Dimensional homogeneity". Essential of Fluid Mechanics: Fundamentals and Applications. McGraw-Hill. p. 203–. ISBN 9780073138350.

nagoya-u.ac.jp (Global: 5,551^st place; English: low place)

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Garrigue, J.; Ly, D. (2017). "Des unités dans le typeur" (PDF). 28ièmes Journées Francophones des Langaeges Applicatifs, Jan 2017, Gourette, France (in French). hal-01503084. Archived (PDF) from the original on 10 November 2020.

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

physics.nist.gov

Thompson, Ambler (November 2009). Guide for the Use of the International System of Units (SI): The Metric System (PDF). DIANE Publishing. ISBN 9781437915594.

openlibrary.org (Global: 325^th place; English: 255^th place)

(Huntley 1967) Huntley, H. E. (1967), Dimensional Analysis, Dover, OCLC 682090763, OL 6128830M, LOC 67-17978

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Grecco, Hernan E. (2022). "Pint: makes units easy".

psu.edu (Global: 207^th place; English: 136^th place)

citeseerx.ist.psu.edu

Kennedy, A. (2010). "Types for Units-of-Measure: Theory and Practice". In Horváth, Z.; Plasmeijer, R.; Zsók, V. (eds.). Central European Functional Programming School. CEFP 2009. Lecture Notes in Computer Science. Vol. 6299. Springer. pp. 268–305. CiteSeerX 10.1.1.174.6901. doi:10.1007/978-3-642-17685-2_8. ISBN 978-3-642-17684-5.

ramsay-maunder.co.uk (Global: low place; English: low place)

Ramsay, Angus. "Dimensional Analysis and Numerical Experiments for a Rotating Disc". Ramsay Maunder Associates. Retrieved 15 April 2017.

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Duff, M.J.; Okun, L.B.; Veneziano, G. (September 2002), "Trialogue on the number of fundamental constants", Journal of High Energy Physics, 2002 (3): 023, arXiv:physics/0110060, Bibcode:2002JHEP...03..023D, doi:10.1088/1126-6708/2002/03/023, S2CID 15806354
Berberan-Santos, Mário N.; Pogliani, Lionello (1999). "Two alternative derivations of Bridgman's theorem" (PDF). Journal of Mathematical Chemistry. 26 (1–3): 255–261, See §5 General Results p. 259. doi:10.1023/A:1019102415633. S2CID 14833238.
Gehani, N. (June 1985). "Ada's derived types and units of measure". Software: Practice and Experience. 15 (6): 555–569. doi:10.1002/spe.4380150604. S2CID 40558757.
Cmelik, R. F.; Gehani, N. H. (May 1988). "Dimensional analysis with C++". IEEE Software. 5 (3): 21–27. doi:10.1109/52.2021. S2CID 22450087.
Bennich-Björkman, O.; McKeever, S. (2018). "The next 700 unit of measurement checkers". Proceedings of the 11th ACM SIGPLAN International Conference on Software Language Engineering. pp. 121–132. doi:10.1145/3276604.3276613. ISBN 978-1-4503-6029-6. S2CID 53089559.
McBride, Conor; Nordvall-Forsberg, Fredrik (2022). "Type systems for programs respecting dimensions" (PDF). Advanced Mathematical and Computational Tools in Metrology and Testing XII. Advances in Mathematics for Applied Sciences. World Scientific. pp. 331–345. doi:10.1142/9789811242380_0020. ISBN 9789811242380. S2CID 243831207. Archived (PDF) from the original on 17 May 2022.

springer.com (Global: 274^th place; English: 309^th place)

link.springer.com

Yalin, M. Selim (1971). "Principles of the Theory of Dimensions". Theory of Hydraulic Models. pp. 1–34. doi:10.1007/978-1-349-00245-0_1. ISBN 978-1-349-00247-4.

stackexchange.com (Global: 1,983^rd place; English: 1,330^th place)

physics.stackexchange.com

For a review of the different conventions in use see: Pisanty, E (17 September 2013). "Square bracket notation for dimensions and units: usage and conventions". Physics Stack Exchange. Retrieved 15 July 2014.

strath.ac.uk (Global: low place; English: 7,329^th place)

strathprints.strath.ac.uk

McBride, Conor; Nordvall-Forsberg, Fredrik (2022). "Type systems for programs respecting dimensions" (PDF). Advanced Mathematical and Computational Tools in Metrology and Testing XII. Advances in Mathematics for Applied Sciences. World Scientific. pp. 331–345. doi:10.1142/9789811242380_0020. ISBN 9789811242380. S2CID 243831207. Archived (PDF) from the original on 17 May 2022.

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Tao 2012, "With a bit of additional effort (and taking full advantage of the one-dimensionality of the vector spaces), one can also define spaces with fractional exponents ...". Tao, Terence (2012). "A mathematical formalisation of dimensional analysis".
Tao 2012, "However, when working with vector-valued quantities in two and higher dimensions, there are representation-theoretic obstructions to taking arbitrary fractional powers of units ...". Tao, Terence (2012). "A mathematical formalisation of dimensional analysis".
Tao 2012 "Similarly, one can define $V T -1$ as the dual space to $V T$ ..." Tao, Terence (2012). "A mathematical formalisation of dimensional analysis".

uva.nl (Global: 3,518^th place; English: 2,652^nd place)

pure.uva.nl

Griffioen, P. (2019). A unit-aware matrix language and its application in control and auditing (PDF) (Thesis). University of Amsterdam. hdl:11245.1/fd7be191-700f-4468-a329-4c8ecd9007ba. Archived (PDF) from the original on 21 February 2020.

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

JCGM (2012), JCGM 200:2012 – International vocabulary of metrology – Basic and general concepts and associated terms (VIM) (PDF) (3rd ed.), archived from the original (PDF) on 23 September 2015, retrieved 2 June 2015
Gundry, Adam (December 2015). "A typechecker plugin for units of measure: domain-specific constraint solving in GHC Haskell" (PDF). SIGPLAN Notices. 50 (12): 11–22. doi:10.1145/2887747.2804305. Archived (PDF) from the original on 10 August 2017.
Garrigue, J.; Ly, D. (2017). "Des unités dans le typeur" (PDF). 28ièmes Journées Francophones des Langaeges Applicatifs, Jan 2017, Gourette, France (in French). hal-01503084. Archived (PDF) from the original on 10 November 2020.
Griffioen, P. (2019). A unit-aware matrix language and its application in control and auditing (PDF) (Thesis). University of Amsterdam. hdl:11245.1/fd7be191-700f-4468-a329-4c8ecd9007ba. Archived (PDF) from the original on 21 February 2020.
McBride, Conor; Nordvall-Forsberg, Fredrik (2022). "Type systems for programs respecting dimensions" (PDF). Advanced Mathematical and Computational Tools in Metrology and Testing XII. Advances in Mathematics for Applied Sciences. World Scientific. pp. 331–345. doi:10.1142/9789811242380_0020. ISBN 9789811242380. S2CID 243831207. Archived (PDF) from the original on 17 May 2022.

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reference.wolfram.com

Wolfram Research (2018). "NondimensionalizationTransform". Wolfram Language & System Documentation Center. Retrieved 30 June 2025.
Wolfram Research (2022) [2012]. "UnitDimensions". Wolfram Language & System Documentation Center. Retrieved 30 June 2025.
Wolfram Research (2018) [2014]. "DimensionalCombinations". Wolfram Language & System Documentation Center. Retrieved 30 June 2025.
Wolfram Research (2014). "UnityDimensions". Wolfram Language & System Documentation Center. Retrieved 30 June 2025.
Wolfram Research (2018) [2014]. "QuantityVariableDimensions". Wolfram Language & System Documentation Center. Retrieved 30 June 2025.

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Kennedy, Andrew J. (April 1996). Programming languages and dimensions (Phd). Vol. 391. University of Cambridge. ISSN 1476-2986. UCAM-CL-TR-391.
(Huntley 1967) Huntley, H. E. (1967), Dimensional Analysis, Dover, OCLC 682090763, OL 6128830M, LOC 67-17978

yoric.github.io (Global: low place; English: low place)

Teller, David (January 2020). "Units of Measure in Rust with Refinement Types".

Dimensional analysis (English Wikipedia)

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