https://rigidgeometricalgebra.org/wiki/index.php?title=Magnitude&feed=atom&action=historyMagnitude - Revision history2024-03-28T16:08:41ZRevision history for this page on the wikiMediaWiki 1.40.0https://rigidgeometricalgebra.org/wiki/index.php?title=Magnitude&diff=249&oldid=prevEric Lengyel at 08:12, 25 November 20232023-11-25T08:12:17Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:12, 25 November 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>A ''magnitude'' is a quantity that represents a concrete <del style="font-weight: bold; text-decoration: none;">distance </del>of some kind. In rigid geometric algebra, a magnitude $$\mathbf z$$ is composed of two components, a scalar and an antiscalar, as follows:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>A ''magnitude'' is a quantity that represents a concrete <ins style="font-weight: bold; text-decoration: none;">measurement </ins>of some kind. In rigid geometric algebra, a magnitude $$\mathbf z$$ is composed of two components, a scalar and an antiscalar, as follows:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>:$$\mathbf z = x\mathbf 1 + y {\large\unicode{x1d7d9}}$$</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>:$$\mathbf z = x\mathbf 1 + y {\large\unicode{x1d7d9}}$$</div></td></tr>
</table>Eric Lengyelhttps://rigidgeometricalgebra.org/wiki/index.php?title=Magnitude&diff=140&oldid=prevEric Lengyel: /* Examples */2023-08-01T05:07:23Z<p><span dir="auto"><span class="autocomment">Examples</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 05:07, 1 August 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l8">Line 8:</td>
<td colspan="2" class="diff-lineno">Line 8:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>* The [[geometric norm]] produces a magnitude that gives the perpendicular distance between an object and the origin. This is also half the distance that the origin is moved by an object used as an operator.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>* The [[geometric norm]] produces a magnitude that gives the perpendicular distance between an object and the origin. This is also half the distance that the origin is moved by an object used as an operator.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* [[Euclidean distances]] between objects are expressed as magnitudes given by the sum of the [[bulk <del style="font-weight: bold; text-decoration: none;">norms</del>]] and [[weight <del style="font-weight: bold; text-decoration: none;">norms</del>]] of [[<del style="font-weight: bold; text-decoration: none;">commutators</del>]].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>* [[Euclidean distances]] between objects are expressed as magnitudes given by the sum of the [[bulk <ins style="font-weight: bold; text-decoration: none;">norm</ins>]] and [[weight <ins style="font-weight: bold; text-decoration: none;">norm</ins>]] of <ins style="font-weight: bold; text-decoration: none;">expressions involving </ins>[[<ins style="font-weight: bold; text-decoration: none;">attitudes</ins>]].</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Exponentiating the magnitude $$<del style="font-weight: bold; text-decoration: none;">d</del>\mathbf 1 + \phi {\large\unicode{x1d7d9}}$$ produces a [[motor]] for which $$<del style="font-weight: bold; text-decoration: none;">d</del>/\phi$$ is the pitch of the screw transformation.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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>* Exponentiating the magnitude $$<ins style="font-weight: bold; text-decoration: none;">\delta</ins>\mathbf 1 + \phi {\large\unicode{x1d7d9}}$$ produces a [[motor]] for which $$<ins style="font-weight: bold; text-decoration: none;">\delta</ins>/\phi$$ is the pitch of the screw transformation.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>== See Also ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; 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>== See Also ==</div></td></tr>
</table>Eric Lengyelhttps://rigidgeometricalgebra.org/wiki/index.php?title=Magnitude&diff=26&oldid=prevEric Lengyel: Created page with "A ''magnitude'' is a quantity that represents a concrete distance of some kind. In rigid geometric algebra, a magnitude $$\mathbf z$$ is composed of two components, a scalar and an antiscalar, as follows: :$$\mathbf z = x\mathbf 1 + y {\large\unicode{x1d7d9}}$$ Magnitudes are homogeneous just like everything else in a projective geometric algebra. This means it has both a bulk and a weight, and it is unitized by making the magnitude of its weight one. ===..."2023-07-15T05:50:33Z<p>Created page with "A ''magnitude'' is a quantity that represents a concrete distance of some kind. In rigid geometric algebra, a magnitude $$\mathbf z$$ is composed of two components, a scalar and an antiscalar, as follows: :$$\mathbf z = x\mathbf 1 + y {\large\unicode{x1d7d9}}$$ Magnitudes are homogeneous just like everything else in a projective geometric algebra. This means it has both a <a href="/wiki/index.php?title=Bulk" class="mw-redirect" title="Bulk">bulk</a> and a <a href="/wiki/index.php?title=Weight" class="mw-redirect" title="Weight">weight</a>, and it is <a href="/wiki/index.php?title=Unitized" class="mw-redirect" title="Unitized">unitized</a> by making the magnitude of its weight one. ===..."</p>
<p><b>New page</b></p><div>A ''magnitude'' is a quantity that represents a concrete distance of some kind. In rigid geometric algebra, a magnitude $$\mathbf z$$ is composed of two components, a scalar and an antiscalar, as follows:<br />
<br />
:$$\mathbf z = x\mathbf 1 + y {\large\unicode{x1d7d9}}$$<br />
<br />
Magnitudes are homogeneous just like everything else in a projective geometric algebra. This means it has both a [[bulk]] and a [[weight]], and it is [[unitized]] by making the magnitude of its weight one.<br />
<br />
=== Examples ===<br />
<br />
* The [[geometric norm]] produces a magnitude that gives the perpendicular distance between an object and the origin. This is also half the distance that the origin is moved by an object used as an operator.<br />
* [[Euclidean distances]] between objects are expressed as magnitudes given by the sum of the [[bulk norms]] and [[weight norms]] of [[commutators]].<br />
* Exponentiating the magnitude $$d\mathbf 1 + \phi {\large\unicode{x1d7d9}}$$ produces a [[motor]] for which $$d/\phi$$ is the pitch of the screw transformation.<br />
<br />
== See Also ==<br />
<br />
* [[Geometric norm]]<br />
* [[Unitization]]</div>Eric Lengyel