Talk:Pythagorean addition

Pythagorean addition has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it. Review: August 24, 2025. (Reviewed version).

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More common term

Latest comment: 3 years ago4 comments3 people in discussion

Good find, David Eppstein. I have encountered the term "addition in quadrature" many times in signal processing but never "Pythagorean addition". They do refer to the same things, so a merge is warranted. Cheers, cmɢʟee⎆τaʟκ 22:03, 3 May 2021 (UTC)Reply

Hypot and Alpha max plus beta min algorithm are also on more or less the same topic. We might consider merging them in as well, or at least using Wikipedia:Summary style to integrate pointers to them into the main article text instead of just listing them under see-also. —David Eppstein (talk) 23:28, 3 May 2021 (UTC)Reply

Note: http://books.google.com/ngrams/graph?content=Pythagorean+addition%2Caddition+in+quadrature%2Cbeta+min%2Chypot&year_start=1820&corpus=26 gives relatives frequencies found in Google Books (year starting 1820 as earlier years have unusually high occurrences of hypot). Hypot takes the lead, though it might be a contraction of hypothesis. Addition in quadrature seems much more common than Pythagorean addition or beta min (the entire phrase was not found). Add in quadrature is even more frequent, but I used addition as a fairer comparison to Pythagorean addition. cmɢʟee⎆τaʟκ 00:56, 7 May 2021 (UTC)Reply

Support merge: Pythagorean addition focusses on the mathematical function, while the Addition in quadrature article primarily discusses the application of this process to signal processing (and error propagation more generally). I think that pattern reflects use too. Perhaps we also have a difference here between mathematical literature and more prevalent engineering/physics literature. On balance, I'd be tempted to merge to Pythagorean addition, giving Addition in quadrature as a synonym in the context of signal analysis and error propagation, the use supported in the references for the latter article. The Noise section can then be included in an Applications section. I think that the ngram for hypot might well be showing contractions for hypothesis and hence has misleading weight. Klbrain (talk) 18:38, 4 October 2021 (UTC)Reply

GA review

Latest comment: 9 days ago10 comments2 people in discussion

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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This review is transcluded from Talk:Pythagorean addition/GA1. The edit link for this section can be used to add comments to the review.

Nominator: David Eppstein (talk · contribs) 08:26, 3 March 2025 (UTC)Reply

Reviewer: Kusma (talk · contribs) 10:23, 23 August 2025 (UTC)Reply

Will review this over the weekend. —Kusma (talk) 10:23, 23 August 2025 (UTC)Reply

Content and prose review

I will comment on anything I notice, but not all of my comments will be strictly related to the GA criteria, so not everything needs to be actioned. Feel free to push back if you think I am asking too much, and please tell me when I am wrong.

• Lead: worth saying that "hypot" comes from "hypotenuse"?
• Properties: "Therefore, if three or more numbers are to be combined with this operation, the order of combination makes no difference to the result: ${\displaystyle x_{1}\oplus x_{2}\oplus \cdots \oplus x_{n}={\sqrt {x_{1}^{2}+x_{2}^{2}+\cdots +x_{n}^{2}}}}$ " this is certainly correct, but I am not certain about the logic. As the operation is associative, we can write the LHS without worrying about brackets. The ordering makes no difference due to the commutativity, but the expression for the RHS does not follow from associativity or commutativity, but is a straightforward computation (that indeed shows the associativity and commutativity).
• You mention "subtraction" later; I assume you mean something like ${\displaystyle a\ominus b={\sqrt {\mathrm {max} (a,b)^{2}-\mathrm {min} (a,b)^{2}}}}$ . Would this make sense to mention/discuss in Properties?
• Applications: Pythagorean addition comes up whenever you compute the ${\displaystyle \ell ^{2}}$  norm of a vector; the Sobel operator is just one of a million examples for that and seems a bit random here. But yes, it is an example.
• Implementation: is it worth saying what the analogous operation on matrices is? (I assume finding a matrix C with ${\displaystyle C^{T}C=A^{T}A+B^{T}B}$  (or the Hermitian version)?)
• History: I haven't had enough coffee. How do you use a slide rule with logarithmic x and x^2 scales to compute Pythagorean sums?

Not a lot to complain in the prose :) The content is rather focused on computational aspects, but these are probably the most interesting anyway. I will look at sources within the next couple hours. —Kusma (talk) 14:04, 23 August 2025 (UTC)Reply

Thanks for taking this on. Some replies:

• Lead, properties: done.
• Subtraction: I added this formula as an explanation, but I don't know a good source for properties.
• Applications: it wasn't clear whether you were asking for any specific change here.
• Implementation: if we can find a source saying what the operation is and that it is analogous, but I don't know of one.
• History: My guess is that if you have a slide rule whose scale is sqrt (not logarithmic) then you just use it in the same way that you would use a log-scale slide rule to multiply or a linear-scale slide rule to add: line up the zero on stick A with the position of ${\displaystyle x}$  on the stick B, then the position of ${\displaystyle y}$  on stick A lines up with the position of ${\displaystyle x\oplus y}$  on stick B. But I don't think we should go into detail on this in the article.

—David Eppstein (talk) 00:42, 24 August 2025 (UTC)Reply

Source spotchecks

Numbering from Special:PermanentLink/1295675891.

• 1: ok
• 6: ok
• 7b: ok (and there are different versions depending on matrix properties; I understand why you do not go into detail)
• 23a/b: sure. the central point is the orthogonality to allow for Pythagorean addition.
• 34: ok
• 43: ok
• 51: Ah, it is a non-logarithmic slide rule. Now I understand.
• 52: ok

Spot checks passed. —Kusma (talk) 16:16, 23 August 2025 (UTC)Reply

General comments and GA criteria

• Prose generally fine, minor comments above.
• MoS: should any of the History content be in the lead?
• References are fine.
• The article mentions extensions; probably enough to be broad without going too far beyond. (I could imagine ${\displaystyle \ell ^{p}}$  versions but I'm not sure there is much of a point). But perhaps "subtraction" could be explained.
• No evidence of edit warring.
• Images are fine. Thank you for the calculator, it is nice. The "energy-momentum" picture could do with slightly more explanation in the caption what the terms mean (kinetic energy versus rest energy). But triangles in the energy plane are a bit weird anyway.

A nice and elementary article, I am surprised it took so long to get reviewed. —Kusma (talk) 16:27, 23 August 2025 (UTC)Reply

Thanks! I added a sentence about history to the lead and expanded the caption of the energy-momentum figure. —David Eppstein (talk) 00:56, 24 August 2025 (UTC)Reply

That is fine then. I agree on not adding further detail to the article. —Kusma (talk) 09:47, 24 August 2025 (UTC)Reply

Good Article review progress box Criteria: 1a. prose ( ) 1b. MoS ( ) 2a. ref layout ( ) 2b. cites WP:RS ( ) 2c. no WP:OR ( ) 2d. no WP:CV ( ) 3a. broadness ( ) 3b. focus ( ) 4. neutral ( ) 5. stable ( ) 6a. free or tagged images ( ) 6b. pics relevant ( ) Note: this represents where the article stands relative to the Good Article criteria. Criteria marked   are unassessed

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Did you know nomination

Latest comment: 8 days ago1 comment1 person in discussion

(

• Comment or view
• Article history

)

• ... that Pythagorean addition, available in many programming libraries as hypot, can compute distances, polar coordinates, and the relativistic energy of moving objects?

• Source:
  • available in many languages as hypot: van der Leun, Vincent (2017). "Java Class Library". Introduction to JVM Languages: Java, Scala, Clojure, Kotlin, and Groovy. Packt Publishing Ltd. pp. 10–11.
  • distances: Manglik, Rohit (2024). "Section 14.22: Math.hypot". Java Script Notes for Professionals. EduGorilla. p. 144.
  • polar coordinates: "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.
  • relativistic energy: 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.

• Reviewed: Template:Did you know nominations/Ethan Mollick

Improved to Good Article status by David Eppstein (talk). Number of QPQs required: 1. Nominator has 190 past nominations.

—David Eppstein (talk) 20:12, 24 August 2025 (UTC).Reply