In geometry, we have concepts such as length (of a 1-dimensional line), area (of a 2-dimensional square) and volume (of a 3-dimensional cube).

What is the general term for these concepts, such that we could say something like: the (general term) of a 2-dimensional object is area; or, the (general term) of a 3-dimensional object is volume?

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    $\begingroup$ Volume $\phantom{I don't want to make short comments}$ $\endgroup$ – Thomas Rot Jan 11 '16 at 16:22
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    $\begingroup$ I have seen the word "content" to refer to this concept. $\endgroup$ – Tim Raczkowski Jan 11 '16 at 16:24
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    $\begingroup$ Measure?${}{}{}$ $\endgroup$ – TonyK Jan 11 '16 at 16:25

Here's a list of terms that would work

  • Content
  • Area
  • n-Area
  • n-Dimensional Area
  • Generalized Area
  • Volume
  • n-Volume
  • n-Dimensional Volume
  • Generalized Volume
  • Measure
  • Lebesgue Measure
  • $\begingroup$ I made this a CW so if you want to add more just edit them in. $\endgroup$ – user137731 Jan 11 '16 at 16:35
  • $\begingroup$ So can I say something like "the 3-dimensional Lebesque measure of a sphere is its volume, and its 2-dimensional Lebesque measure is its surface area?" $\endgroup$ – Somatic Jan 11 '16 at 16:38
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    $\begingroup$ I would say the "Lebesgue measure of the region bounded by a sphere is its volume and the Lesbesgue measure of a sphere is its surface area". Though if it's clear from context (which in this case it is) I wouldn't even write the word Lebesgue. $\endgroup$ – user137731 Jan 11 '16 at 16:39
  • $\begingroup$ Some ancient stock. on Mensuration , (to define and measure basic units of length, area and volume.) Text-book on Practical, Solid Or Descriptive Geometry, David Allan Low, Vol 2 $\endgroup$ – Narasimham Jan 11 '16 at 16:45

'Mensuration' is the term for measurement of length, area, and volume etc.


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