https://www.rasmusen.org/rasmapedia/index.php?action=history&feed=atom&title=DefinitionsDefinitions - Revision history2026-04-13T01:10:12ZRevision history for this page on the wikiMediaWiki 1.32.0https://www.rasmusen.org/rasmapedia/index.php?title=Definitions&diff=5148&oldid=prevRasmusen p1vaim: /* Introduction */2022-02-28T00:20:57Z<p><span dir="auto"><span class="autocomment">Introduction</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Introduction==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Introduction==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>A good example of the issue of whether the most useful definition is general or narrow is Trapezoid, which is a quadrilateral with two sides parallel. Should that be the definition, or should it be ONLY two sides parallel, not four, so excluding parallelograms such as squares?</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>A good example of the issue of whether the most useful definition is general or narrow is Trapezoid, which is a quadrilateral with two sides parallel. Should that be the definition, or should it be ONLY two sides parallel, not four, so excluding parallelograms such as squares?</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The Wikipedia discussion of this is good: https://en.wikipedia.org/wiki/Trapezoid#Inclusive_vs_exclusive_definition. The text I'm teaching 7th graders from uses the narrow definition, but I think W. is right that mathematicians do not. Texts do, to simplify teaching. Is that OK? Maybe.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Actually, we could define parallelograms to exclude rectangles, and rectangles to exclude squares, on the same principle of ordinary language simplification. When I think of a rectangle, I don't think of a square.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Ultimately, what definition is good comes to what clarifies thinking. I'm undecided as to which definition does that here.</ins></div></td></tr>
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</table>Rasmusen p1vaimhttps://www.rasmusen.org/rasmapedia/index.php?title=Definitions&diff=5144&oldid=prevRasmusen p1vaim: Created page with "==Introduction== A good example of the issue of whether the most useful definition is general or narrow is Trapezoid, which is a quadrilateral with two sides parallel. Should..."2022-02-27T23:59:46Z<p>Created page with "==Introduction== A good example of the issue of whether the most useful definition is general or narrow is Trapezoid, which is a quadrilateral with two sides parallel. Should..."</p>
<p><b>New page</b></p><div>==Introduction==<br />
A good example of the issue of whether the most useful definition is general or narrow is Trapezoid, which is a quadrilateral with two sides parallel. Should that be the definition, or should it be ONLY two sides parallel, not four, so excluding parallelograms such as squares?<br />
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