Pythagorean addition (English Wikipedia)

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

refsWebsite

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23doi.org

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21books.google.com

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6jstor.org

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5archive.org

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4ams.org

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3arxiv.org

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2psu.edu

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2semanticscholar.org

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1agner.org

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1hal.science

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1zdnet.com

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1dlang.org

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1wg5-fortran.org

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1rust-lang.org

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1cwi.nl

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agner.org

Fog, Agner (April 27, 2020). "Floating point exception tracking and NAN propagation" (PDF). p. 6.

ams.org

mathscinet.ams.org

Falmagne, Jean-Claude (2015). "Deriving meaningful scientific laws from abstract, "gedanken" type, axioms: five examples". Aequationes Mathematicae. 89 (2): 393–435. doi:10.1007/s00010-015-0339-1. MR 3340218. S2CID 121424613.
Ziv, Abraham (1999). "Sharp ULP rounding error bound for the hypotenuse function". Mathematics of Computation. 68 (227): 1143–1148. doi:10.1090/S0025-5718-99-01103-5. JSTOR 2584955. MR 1648423.
Lefèvre, Vincent; Louvet, Nicolas; Muller, Jean-Michel; Picot, Joris; Rideau, Laurence (2023). "Accurate calculation of Euclidean norms using double-word arithmetic" (PDF). ACM Transactions on Mathematical Software. 49 (1) 1: 1–34. doi:10.1145/3568672. MR 4567887.
van Dantzig, D. (1953). "Another form of the weak law of large numbers" (PDF). Nieuw Archief voor Wiskunde. 3rd ser. 1: 129–145. MR 0056872.

archive.org

scholar.archive.org

Moler, Cleve; Morrison, Donald (1983). "Replacing square roots by Pythagorean sums". IBM Journal of Research and Development. 27 (6): 577–581. CiteSeerX 10.1.1.90.5651. doi:10.1147/rd.276.0577.
Dubrulle, Augustin A. (1983). "A class of numerical methods for the computation of Pythagorean sums". IBM Journal of Research and Development. 27 (6): 582–589. CiteSeerX 10.1.1.94.3443. doi:10.1147/rd.276.0582.
Hicks, Charles R. (March 1955). "Two problems illustrating the use of mathematics in modern industry". The Mathematics Teacher. 48 (3). National Council of Teachers of Mathematics: 130–132. doi:10.5951/mt.48.3.0130. JSTOR 27954826.
Weagant, R. A. (June 1919). "Reception thru static and interference". Proceedings of the IRE. 7 (3): 207–244. doi:10.1109/jrproc.1919.217434. See p. 232.

archive.org

"SIN (3M): Trigonometric functions and their inverses". Unix Programmer's Manual: Reference Guide (4.3 Berkeley Software Distribution Virtual VAX-11 Version ed.). Department of Electrical Engineering and Computer Science, University of California, Berkeley. April 1986.

arxiv.org

Barlow, Roger (March 22, 2002). "Systematic errors: facts and fictions". Conference on Advanced Statistical Techniques in Particle Physics. Durham, UK. pp. 134–144. arXiv:hep-ex/0207026.
Muller, Jean-Michel; Salvy, Bruno (2024). "Effective quadratic error bounds for floating-point algorithms computing the hypotenuse function". arXiv:2405.03588 [math.NA].
Borges, Carlos F. (2021). "Algorithm 1014: An Improved Algorithm for hypot(x, y)". ACM Transactions on Mathematical Software. 47 (1): 9:1–9:12. arXiv:1904.09481. doi:10.1145/3428446. S2CID 230588285.

books.google.com

Johnson, David L. (2017). "12.2.3 Addition in Quadrature". Statistical Tools for the Comprehensive Practice of Industrial Hygiene and Environmental Health Sciences. John Wiley & Sons. p. 289. ISBN 9781119143017.
Penner, R. C. (1999). Discrete Mathematics: Proof Techniques and Mathematical Structures. World Scientific. pp. 417–418. ISBN 9789810240882.
Manglik, Rohit (2024). "Section 14.22: Math.hypot". Java Script Notes for Professionals. EduGorilla. p. 144. ISBN 9789367840320.
Meyer, J. G. A. (1902). "225. – To find the diagonal of a rectangle when its length and breadth are given". Easy Lessons in Mechanical Drawing & Machine Design: Arranged for Self-instruction, Vol. I. Industrial Publication Company. p. 133.
Grieser, Daniel (2018). "6.2 The diagonal of a cuboid". Exploring Mathematics: Problem-Solving and Proof. Springer Undergraduate Mathematics Series. Springer International Publishing. pp. 143–145. doi:10.1007/978-3-319-90321-7. ISBN 9783319903217.
Beebe, Nelson H. F. (2017). The Mathematical-Function Computation Handbook: Programming Using the MathCW Portable Software Library. Springer. p. 70. ISBN 9783319641102.
Weisberg, Herbert F. (1992). Central Tendency and Variability. Quantitative Applications in the Social Sciences. Vol. 83. Sage. pp. 45, 52–53. ISBN 9780803940079.
D. B. Schneider, Error Analysis in Measuring Systems, Proceedings of the 1962 Standards Laboratory Conference, page 94
Smith, Walter F. (2020). Experimental Physics: Principles and Practice for the Laboratory. CRC Press. pp. 40–41. ISBN 9781498778688.
Kuehn, Kerry (2015). A Student's Guide Through the Great Physics Texts: Volume II: Space, Time and Motion. Undergraduate Lecture Notes in Physics. Springer New York. p. 372. doi:10.1007/978-1-4939-1366-4. ISBN 9781493913664.
Lyons, Richard G. (2010). "13.2 High-speed vector magnitude approximation". Understanding Digital Signal Processing (3rd ed.). Pearson. pp. 13-6 – 13-8.
Summerfield, Mark (2012). Programming in Go: Creating Applications for the 21st Century. Pearson Education. p. 66. ISBN 9780321774637.
Nagar, Sandeep (2017). Beginning Julia Programming: For Engineers and Scientists. Apress. p. 105. ISBN 9781484231715.
Higham, Desmond J.; Higham, Nicholas J. (2016). "26.9 Pythagorean sum". MATLAB Guide (3rd ed.). Society for Industrial and Applied Mathematics. pp. 430–432. ISBN 9781611974669.
Atkinson, Leon; Suraski, Zeev (2004). "Listing 13.17: hypot". Core PHP Programming. Prentice Hall. p. 504. ISBN 9780130463463.
Hill, Christian (2020). Learning Scientific Programming with Python (2nd ed.). Cambridge University Press. p. 14. ISBN 9781108787468.
Hanson, Daniel (2024). Learning Modern C++ for Finance. O'Reilly. p. 25. ISBN 9781098100773.
Horton, Ivor (2005). Ivor Horton's Beginning Java 2. John Wiley & Sons. p. 57. ISBN 9780764568749.
van der Leun, Vincent (2017). "Java Class Library". Introduction to JVM Languages: Java, Scala, Clojure, Kotlin, and Groovy. Packt Publishing Ltd. pp. 10–11. ISBN 9781787126589.
Taylor, Mischa; Vargo, Seth (2014). "Mathematical operations". Learning Chef: A Guide to Configuration Management and Automation. O'Reilly Media. p. 40. ISBN 9781491945117.
Maor, Eli (2007). The Pythagorean Theorem: A 4,000-Year History. Princeton, New Jersey: Princeton University Press. pp. 4–15. ISBN 978-0-691-12526-8.

cwi.nl

ir.cwi.nl

van Dantzig, D. (1953). "Another form of the weak law of large numbers" (PDF). Nieuw Archief voor Wiskunde. 3rd ser. 1: 129–145. MR 0056872.

dlang.org

"std.math.algebraic". Phobos Runtime Library Reference, version 2.109.1. D Language Foundation. Retrieved 2025-02-21.

doi.org

Moler, Cleve; Morrison, Donald (1983). "Replacing square roots by Pythagorean sums". IBM Journal of Research and Development. 27 (6): 577–581. CiteSeerX 10.1.1.90.5651. doi:10.1147/rd.276.0577.
Ellis, Mark W.; Pagni, David (May 2008). "Exploring segment lengths on the Geoboard". Mathematics Teaching in the Middle School. 13 (9). National Council of Teachers of Mathematics: 520–525. doi:10.5951/mtms.13.9.0520. JSTOR 41182606.
Falmagne, Jean-Claude (2015). "Deriving meaningful scientific laws from abstract, "gedanken" type, axioms: five examples". Aequationes Mathematicae. 89 (2): 393–435. doi:10.1007/s00010-015-0339-1. MR 3340218. S2CID 121424613.
Incertis, F. (March 1985). "A faster method of computing matrix pythagorean sums". IEEE Transactions on Automatic Control. 30 (3): 273–275. doi:10.1109/tac.1985.1103937.
Dubrulle, Augustin A. (1983). "A class of numerical methods for the computation of Pythagorean sums". IBM Journal of Research and Development. 27 (6): 582–589. CiteSeerX 10.1.1.94.3443. doi:10.1147/rd.276.0582.
Deza, Michel Marie; Deza, Elena (2014). Encyclopedia of Distances. Springer. p. 100. doi:10.1007/978-3-662-44342-2. ISBN 9783662443422.
Grieser, Daniel (2018). "6.2 The diagonal of a cuboid". Exploring Mathematics: Problem-Solving and Proof. Springer Undergraduate Mathematics Series. Springer International Publishing. pp. 143–145. doi:10.1007/978-3-319-90321-7. ISBN 9783319903217.
Hicks, Charles R. (March 1955). "Two problems illustrating the use of mathematics in modern industry". The Mathematics Teacher. 48 (3). National Council of Teachers of Mathematics: 130–132. doi:10.5951/mt.48.3.0130. JSTOR 27954826.
Drosg, Manfred (2009). "Dealing with Internal Uncertainties". Dealing with Uncertainties. Springer Berlin Heidelberg. pp. 151–172. doi:10.1007/978-3-642-01384-3_8. ISBN 9783642013843.
Kuehn, Kerry (2015). A Student's Guide Through the Great Physics Texts: Volume II: Space, Time and Motion. Undergraduate Lecture Notes in Physics. Springer New York. p. 372. doi:10.1007/978-1-4939-1366-4. ISBN 9781493913664.
Weagant, R. A. (June 1919). "Reception thru static and interference". Proceedings of the IRE. 7 (3): 207–244. doi:10.1109/jrproc.1919.217434. See p. 232.
Eimerl, D. (August 1987). "Quadrature frequency conversion". IEEE Journal of Quantum Electronics. 23 (8): 1361–1371. doi:10.1109/jqe.1987.1073521.
Powers, J. E.; Phillips, D. J.; Brandestini, M.; Ferraro, R.; Baker, D. W. (1980). "Quadrature sampling for phased array application". In Wang, Keith Y. (ed.). Acoustical Imaging: Visualization and Characterization. Vol. 9. Springer. pp. 263–273. doi:10.1007/978-1-4684-3755-3_18. ISBN 9781468437553.
Yoo, Yongjae; Hwang, Inwook; Choi, Seungmoon (April 2022). "Perceived intensity model of dual-frequency superimposed vibration: Pythagorean sum". IEEE Transactions on Haptics. 15 (2): 405–415. doi:10.1109/toh.2022.3144290.
Kanopoulos, N.; Vasanthavada, N.; Baker, R.L. (April 1988). "Design of an image edge detection filter using the Sobel operator". IEEE Journal of Solid-State Circuits. 23 (2): 358–367. doi:10.1109/4.996.
Jeannerod, Claude-Pierre; Muller, Jean-Michel; Plet, Antoine (2017). "The classical relative error bounds for computing ${\sqrt {a^{2}+b^{2}}}$ and $c/{\sqrt {a^{2}+b^{2}}}$ in binary floating-point arithmetic are asymptotically optimal". In Burgess, Neil; Bruguera, Javier D.; de Dinechin, Florent (eds.). 24th IEEE Symposium on Computer Arithmetic, ARITH 2017, London, United Kingdom, July 24–26, 2017. IEEE Computer Society. pp. 66–73. doi:10.1109/ARITH.2017.40.
Ziv, Abraham (1999). "Sharp ULP rounding error bound for the hypotenuse function". Mathematics of Computation. 68 (227): 1143–1148. doi:10.1090/S0025-5718-99-01103-5. JSTOR 2584955. MR 1648423.
Borges, Carlos F. (2021). "Algorithm 1014: An Improved Algorithm for hypot(x, y)". ACM Transactions on Mathematical Software. 47 (1): 9:1–9:12. arXiv:1904.09481. doi:10.1145/3428446. S2CID 230588285.
Lefèvre, Vincent; Louvet, Nicolas; Muller, Jean-Michel; Picot, Joris; Rideau, Laurence (2023). "Accurate calculation of Euclidean norms using double-word arithmetic" (PDF). ACM Transactions on Mathematical Software. 49 (1) 1: 1–34. doi:10.1145/3568672. MR 4567887.
Morrell, William E. (January 1946). "A slide rule for the addition of squares". Science. 103 (2665): 113–114. doi:10.1126/science.103.2665.113. JSTOR 1673946.
Dempster, J. R. (April 1946). "A circular slide rule". Science. 103 (2677): 488. doi:10.1126/science.103.2677.488.b. JSTOR 1671874.
Dawson, Bernhard H. (July 1946). "An improved slide rule for the addition of squares". Science. 104 (2688): 18. doi:10.1126/science.104.2688.18.c. JSTOR 1675936.
Stern, T. E.; Lerner, R. M. (April 1963). "A circuit for the square root of the sum of the squares". Proceedings of the IEEE. 51 (4): 593–596. doi:10.1109/proc.1963.2206.

hal.science

Lefèvre, Vincent; Louvet, Nicolas; Muller, Jean-Michel; Picot, Joris; Rideau, Laurence (2023). "Accurate calculation of Euclidean norms using double-word arithmetic" (PDF). ACM Transactions on Mathematical Software. 49 (1) 1: 1–34. doi:10.1145/3568672. MR 4567887.

jstor.org

Ellis, Mark W.; Pagni, David (May 2008). "Exploring segment lengths on the Geoboard". Mathematics Teaching in the Middle School. 13 (9). National Council of Teachers of Mathematics: 520–525. doi:10.5951/mtms.13.9.0520. JSTOR 41182606.
Hicks, Charles R. (March 1955). "Two problems illustrating the use of mathematics in modern industry". The Mathematics Teacher. 48 (3). National Council of Teachers of Mathematics: 130–132. doi:10.5951/mt.48.3.0130. JSTOR 27954826.
Ziv, Abraham (1999). "Sharp ULP rounding error bound for the hypotenuse function". Mathematics of Computation. 68 (227): 1143–1148. doi:10.1090/S0025-5718-99-01103-5. JSTOR 2584955. MR 1648423.
Morrell, William E. (January 1946). "A slide rule for the addition of squares". Science. 103 (2665): 113–114. doi:10.1126/science.103.2665.113. JSTOR 1673946.
Dempster, J. R. (April 1946). "A circular slide rule". Science. 103 (2677): 488. doi:10.1126/science.103.2677.488.b. JSTOR 1671874.
Dawson, Bernhard H. (July 1946). "An improved slide rule for the addition of squares". Science. 104 (2688): 18. doi:10.1126/science.104.2688.18.c. JSTOR 1675936.

psu.edu

citeseerx.ist.psu.edu

Moler, Cleve; Morrison, Donald (1983). "Replacing square roots by Pythagorean sums". IBM Journal of Research and Development. 27 (6): 577–581. CiteSeerX 10.1.1.90.5651. doi:10.1147/rd.276.0577.
Dubrulle, Augustin A. (1983). "A class of numerical methods for the computation of Pythagorean sums". IBM Journal of Research and Development. 27 (6): 582–589. CiteSeerX 10.1.1.94.3443. doi:10.1147/rd.276.0582.

rust-lang.org

doc.rust-lang.org

"Primitive Type f64". The Rust Standard Library. February 17, 2025. Retrieved 2025-02-22.

semanticscholar.org

api.semanticscholar.org

Falmagne, Jean-Claude (2015). "Deriving meaningful scientific laws from abstract, "gedanken" type, axioms: five examples". Aequationes Mathematicae. 89 (2): 393–435. doi:10.1007/s00010-015-0339-1. MR 3340218. S2CID 121424613.
Borges, Carlos F. (2021). "Algorithm 1014: An Improved Algorithm for hypot(x, y)". ACM Transactions on Mathematical Software. 47 (1): 9:1–9:12. arXiv:1904.09481. doi:10.1145/3428446. S2CID 230588285.

wg5-fortran.org

Reid, John (March 13, 2014). "9.6 Error and gamma functions". The new features of Fortran 2008 (PDF) (Report N1891). ISO/IEC JTC 1/SC 22, WG5 international Fortran standards committee. p. 20.

zdnet.com

Cimpanu, Catalin (March 10, 2019). "CSS to get support for trigonometry functions". ZDNet. Retrieved 2019-11-01.