[Tex/LaTex] Which dot character to use in which context

best practicespunctuationsymbolsunicodeunicode-math

Wikipedia lists several dot characters in Unicode. These are the ones that are ambiguous to me:

  • interpunct, middle dot (·) · · U+00B7 "midpoint (in typography)"
  • dot operator (⋅) ⋅ ⋅ U+22C5
  • bullet operator (∙) ∙ U+2219 "(mathematics)"
  • bullet (•) • • U+2022 "black small circle" "often used to mark list items"

I'm mostly interested in the Unicode characters, but Math.SE told me to try here, and LaTeX likewise has:

  • \cdot
  • \cdotp
  • \bullet
  • \textbullet

For example:

  • Wikipedia shows multiplication as both "x ⋅ y" ("dot operator") and "x ∙ y" ("bullet operator") in the same paragraph.
  • WP List of mathematical symbols uses "middle dot" for multiplication.
  • WP Multiplication article uses \cdot for scalar multiplication.
  • WP says the matrix dot product should be written using the "bullet operator" character, like "ab".
  • The WP Dot product article uses the LaTeX \cdot character for dot products.
  • Wikipedia shows a raised decimal point example "£21·48", which uses the "middle dot" character.
  • Wikipedia notates chemistry hydrates like "CuSO4 · 5H2O", which uses the "middle dot" character.
  • Combined units can also be written with a dot, like "N·m". Wikipedia uses a "middle dot" for this, not the "dot operator".
  • Characters in SI notations has a paragraph on combined units, seeming to say that dot operator is preferred for this, like "N⋅m".
  • Wolfram Alpha considers \cdot and · to be equivalent, as well as \bullet and •. Valid?

Of course it's pedantic, they all look the same, and the meaning can always be assumed from context, but I'd like to know, once and for all, which Unicode/HTML and LaTeX characters are semantically correct in each application?

(If there are other examples I left out, feel free to edit the question and add them.)

Best Answer

The following is my personal view on this matter. I have not seen hard rules anywhere.

  • Normal mathematics

The \cdot is a multiplication symbol. The following are all equivalent

xy = x⋅y = x×y

It is useful in thermo-fluid dynamics formulas where there are a lot of multi character values such as Reynolds number, Prandtl number, etc.

s = Pr⋅Re⋅v

Compound SI units (see siunitx package) is also multiplication

1 N = 1 kg⋅m/s^2

For vector-tensors it is element wise multiplication

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  • Chemical formula

I don't know much about chemical notation (ask Joseph Wright)

  • Decimal marker

The center dot as decimal marker is only found in very old books or non-scientific literature. Because it can be confused with a multiplication sign is is not used in scientific literature any more.