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I use the term “figure” and teach it to my students (high school). I like the terms “construct” and “construction” because all mathematics is made in our minds. A “figment” of our imaginations … But “construction” is reserved for straight edge + compass drawings. And for me it also conjures up images of building sites.

Personal preferences aside, is there a formal (by convention) general term for bits of mathematical drawings? For example, from simple angles to teach things like acute angle and three point notation, to complex geometric figures or graphs represented on a plane (inc. projections of 3D curves and surfaces).

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    $\begingroup$ Diagram/figure? $\endgroup$ Commented Feb 6, 2018 at 6:32
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    $\begingroup$ There is no standard term. Diagram, picture, graph, figure. illustration, etc. $\endgroup$
    – copper.hat
    Commented Feb 6, 2018 at 6:52
  • $\begingroup$ Why do you say “construction” is reserved for straight edge + compass drawings? $\endgroup$ Commented Feb 7, 2018 at 18:24
  • $\begingroup$ @TheoreticalEconomist It’s a convention I was taught. See also: en.wikipedia.org/wiki/Compass_and_straightedge_constructions $\endgroup$ Commented Feb 7, 2018 at 23:50

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I don't think there is any general term, but there is a default term, which is "figure". Indeed, this is the default caption chosen for $\LaTeX$ . That is, if you type

\caption{This is a figure.}

then by default the caption appears as

Figure 1: This is a figure.

Of course, there are options to change this behaviour, but this is a reasonable default choice, which seems to have the agreement of most mathematicians.

That being said, you can introduce your own term with a sentence like

The picture [commutative diagram, graph, etc.] summarising these properties is represented in Figure 1.

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  • $\begingroup$ If LaTeX uses “figure” as a general term, that’s a pretty significant usage. I hadn’t noticed that yet (I’m a light LaTeX user). I’ll mark this answer as correct, not for the LaTeX part but for writing an answer consistent with the other comments. I really wanted there to be a formal general word but I guess not all mathematical language is so rigorously formalised. $\endgroup$ Commented Feb 7, 2018 at 23:57

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