Talk:Integral: Difference between revisions
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imported>Catherine Woodgold (→Totality vs size: Possible first sentence) |
imported>Robert Tito m (Intuitively) |
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:The first sentence could be ''"An integral generalizes the idea of a sum to cover quantities which may be continuously varying, allowing for example the area or volume of curved objects to be calculated."'' --[[User:Catherine Woodgold|Catherine Woodgold]] 18:51, 30 April 2007 (CDT) | :The first sentence could be ''"An integral generalizes the idea of a sum to cover quantities which may be continuously varying, allowing for example the area or volume of curved objects to be calculated."'' --[[User:Catherine Woodgold|Catherine Woodgold]] 18:51, 30 April 2007 (CDT) | ||
== Intuitively == | |||
Please can somebody explain to me why I would '''Intuitively''' see integral as the way described in the first line ot the article? In my (and yes I am playing advocate of the devil) notion integral means total/aggregated. Can we put it into simpler lingo? [[User:Robert Tito|Robert Tito]] | <span style="background:grey"> <font color="yellow"><b>[[User talk:Robert Tito|Talk]]</b></font> </span> 19:34, 30 April 2007 (CDT) | |||
Revision as of 18:34, 30 April 2007
Totality vs size
"Totality" might be better because integrals also describe such concepts as mass. But it's really hard to come up with a formulation that is both easy to grasp and accurate. Fredrik Johansson 13:54, 29 April 2007 (CDT)
- I agree. "size" is not necessarily the best. Change it back to "totality" if you like. There may be something better. "Extent in space" doesn't cover all cases, either: one might want to integrate prices or interest rates or temperatures or something else, but since it says "intuitively" I think "extent in space" is good enough for that part -- it helps the reader get an image in their mind. I'll try to think of other words. --Catherine Woodgold 14:03, 29 April 2007 (CDT)
- "Intuitively, we can think of an integral as a measure of the totality of an object with an extent in space. "
- "... as a measure of the totality of some aspect, such as area or volume, of an object with an extent in space."
- "... as a measure of some additive quality of an object."
- "... as a measure of qualities such as area or volume, of the type whose values add when two objects are joined into a larger object."
- "... as a measure of such qualities as area and volume."
- "... as a way of extending the definition and measurement of area and volume to curved objects."
- OK, I give up: leave it as "totality". I changed it back to the original. --Catherine Woodgold 18:35, 29 April 2007 (CDT)
Maybe you should just note that integrals generalize sums to (possibly) continuously varying quantities. Greg Woodhouse 13:47, 30 April 2007 (CDT)
- The first sentence could be "An integral generalizes the idea of a sum to cover quantities which may be continuously varying, allowing for example the area or volume of curved objects to be calculated." --Catherine Woodgold 18:51, 30 April 2007 (CDT)
Intuitively
Please can somebody explain to me why I would Intuitively see integral as the way described in the first line ot the article? In my (and yes I am playing advocate of the devil) notion integral means total/aggregated. Can we put it into simpler lingo? Robert Tito | Talk 19:34, 30 April 2007 (CDT)