https://jsxgraph.org/wiki/index.php?title=Triangle_axiom_halving&feed=atom&action=history
Triangle axiom halving - Revision history
2024-03-28T18:16:33Z
Revision history for this page on the wiki
MediaWiki 1.40.1
https://jsxgraph.org/wiki/index.php?title=Triangle_axiom_halving&diff=7219&oldid=prev
A WASSERMANN at 15:41, 12 April 2021
2021-04-12T15:41:20Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:41, 12 April 2021</td>
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<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" 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><del style="font-weight: bold; text-decoration: none;">Axiom (A2) "triangle rule" for affine spaces.</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><ins style="font-weight: bold; text-decoration: none;">Midpoint</ins></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>
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<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>var board = JXG.JSXGraph.initBoard("jxgbox", {boundingbox: [-5,5,5,-5], showCopyright:false, showNavigation:false});</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>var board = JXG.JSXGraph.initBoard("jxgbox", {boundingbox: [-5,5,5,-5], showCopyright:false, showNavigation:false});</div></td></tr>
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<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>var board = JXG.JSXGraph.initBoard("jxgbox", {boundingbox: [-5,5,5,-5], showCopyright:false, showNavigation:false});</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>var board = JXG.JSXGraph.initBoard("jxgbox", {boundingbox: [-5,5,5,-5], showCopyright:false, showNavigation:false});</div></td></tr>
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<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>var p = board.create('point', [-3,-3], {name:'<del style="font-weight: bold; text-decoration: none;">p</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>var p = board.create('point', [-3,-3], {name:'<ins style="font-weight: bold; text-decoration: none;">\\(p_0\\)</ins>'});</div></td></tr>
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<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" 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>var <del style="font-weight: bold; text-decoration: none;">pq </del>= board.create('arrow', [p, <del style="font-weight: bold; text-decoration: none;">q</del>], {withLabel: true, name:'\\(\\vec{<del style="font-weight: bold; text-decoration: none;">pq</del>}\\)', label:{position: 'top', parse: false}, lastArrow: {type: 4, size: 8}});</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>var <ins style="font-weight: bold; text-decoration: none;">pr </ins>= board.create('arrow', [p, <ins style="font-weight: bold; text-decoration: none;">r</ins>], {withLabel: true, name:'\\(\\vec{<ins style="font-weight: bold; text-decoration: none;">v</ins>}\\)', label:{position: 'top', parse: false}, lastArrow: {type: 4, size: 8}});</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>var <del style="font-weight: bold; text-decoration: none;">qr </del>= board.create('arrow', [q<del style="font-weight: bold; text-decoration: none;">, r</del>], {withLabel: true, name:'\\(\\vec{<del style="font-weight: bold; text-decoration: none;">qr</del>}\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});</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>var <ins style="font-weight: bold; text-decoration: none;">pq </ins>= board.create('arrow', [<ins style="font-weight: bold; text-decoration: none;">p, </ins>q], {withLabel: true, name:'\\(\\vec{<ins style="font-weight: bold; text-decoration: none;">u</ins>}\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});</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>var <del style="font-weight: bold; text-decoration: none;">pr </del>= board.create('arrow', [p, <del style="font-weight: bold; text-decoration: none;">r</del>], {withLabel: true, name:'\\(\\vec{<del style="font-weight: bold; text-decoration: none;">pr</del>}\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});</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>var <ins style="font-weight: bold; text-decoration: none;">rq = board.create('arrow', [r, q], {});</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">var ps </ins>= board.create('arrow', [p, <ins style="font-weight: bold; text-decoration: none;">s</ins>], {withLabel: true, name:'\\<ins style="font-weight: bold; text-decoration: none;">(\\frac{1}{2}</ins>(\\vec{<ins style="font-weight: bold; text-decoration: none;">u} + \\vec{v</ins>}<ins style="font-weight: bold; text-decoration: none;">)</ins>\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});</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;"><div></source></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></source></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;"><div>[[Category:Examples]]</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>[[Category:Examples]]</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;"><div>[[Category:Geometry]]</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>[[Category:Geometry]]</div></td></tr>
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A WASSERMANN
https://jsxgraph.org/wiki/index.php?title=Triangle_axiom_halving&diff=7218&oldid=prev
A WASSERMANN at 15:40, 12 April 2021
2021-04-12T15:40:34Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:40, 12 April 2021</td>
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<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>var pr = board.create('arrow', [p, r], {withLabel: true, name:'\\(\\vec{v}\\)', label:{position: 'top', parse: false}, lastArrow: {type: 4, size: 8}});</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>var pr = board.create('arrow', [p, r], {withLabel: true, name:'\\(\\vec{v}\\)', label:{position: 'top', parse: false}, lastArrow: {type: 4, size: 8}});</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;"><div>var pq = board.create('arrow', [p, q], {withLabel: true, name:'\\(\\vec{u}\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});</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>var pq = board.create('arrow', [p, q], {withLabel: true, name:'\\(\\vec{u}\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});</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>var rq = board.create('arrow', [q<del style="font-weight: bold; text-decoration: none;">, r</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>var rq = board.create('arrow', [<ins style="font-weight: bold; text-decoration: none;">r, </ins>q], {});</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>var ps = board.create('arrow', [p, s], {withLabel: true, name:'\\(\\frac{1}{2}(\\vec{u} + \\vec{v}\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});</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>var ps = board.create('arrow', [p, s], {withLabel: true, name:'\\(\\frac{1}{2}(\\vec{u} + \\vec{v}<ins style="font-weight: bold; text-decoration: none;">)</ins>\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});</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;"><div></jsxgraph></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></jsxgraph></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>
</table>
A WASSERMANN
https://jsxgraph.org/wiki/index.php?title=Triangle_axiom_halving&diff=7217&oldid=prev
A WASSERMANN: Created page with "<html> <script type="text/javascript" src="/distrib/MathJax/MathJax.js"></script> </html> Axiom (A2) "triangle rule" for affine spaces. <jsxgraph width="500" height="500">..."
2021-04-12T15:39:56Z
<p>Created page with "<html> <script type="text/javascript" src="/distrib/MathJax/MathJax.js"></script> </html> Axiom (A2) "triangle rule" for affine spaces. <jsxgraph width="500" height="500">..."</p>
<p><b>New page</b></p><div><html><br />
<script type="text/javascript" src="/distrib/MathJax/MathJax.js"></script><br />
</html><br />
<br />
Axiom (A2) "triangle rule" for affine spaces.<br />
<br />
<jsxgraph width="500" height="500"><br />
JXG.Options.label.autoPosition = true;<br />
JXG.Options.text.useMathJax = true;<br />
JXG.Options.text.fontSize = 20;<br />
<br />
var board = JXG.JSXGraph.initBoard("jxgbox", {boundingbox: [-5,5,5,-5], showCopyright:false, showNavigation:false});<br />
<br />
var p = board.create('point', [-3,-3], {name:'\\(p_0\\)'});<br />
var q = board.create('point', [3, -3], {name:'\\(q\\)'});<br />
var r = board.create('point', [2, 2], {name:'\\(r\\)'});<br />
var s = board.create('midpoint', [q, r], {name:'\\(s\\)'});<br />
<br />
var pr = board.create('arrow', [p, r], {withLabel: true, name:'\\(\\vec{v}\\)', label:{position: 'top', parse: false}, lastArrow: {type: 4, size: 8}});<br />
var pq = board.create('arrow', [p, q], {withLabel: true, name:'\\(\\vec{u}\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});<br />
var rq = board.create('arrow', [q, r], {});<br />
var ps = board.create('arrow', [p, s], {withLabel: true, name:'\\(\\frac{1}{2}(\\vec{u} + \\vec{v}\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});<br />
</jsxgraph><br />
<br />
<br />
=== The underlying JavaScript code ===<br />
<br />
<source lang="javascript"><br />
JXG.Options.label.autoPosition = true;<br />
JXG.Options.text.useMathJax = true;<br />
JXG.Options.text.fontSize = 20;<br />
<br />
var board = JXG.JSXGraph.initBoard("jxgbox", {boundingbox: [-5,5,5,-5], showCopyright:false, showNavigation:false});<br />
<br />
var p = board.create('point', [-3,-3], {name:'p'});<br />
var q = board.create('point', [0, 2], {name:'q'});<br />
var r = board.create('point', [3, -3], {name:'r'});<br />
<br />
var pq = board.create('arrow', [p, q], {withLabel: true, name:'\\(\\vec{pq}\\)', label:{position: 'top', parse: false}, lastArrow: {type: 4, size: 8}});<br />
var qr = board.create('arrow', [q, r], {withLabel: true, name:'\\(\\vec{qr}\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});<br />
var pr = board.create('arrow', [p, r], {withLabel: true, name:'\\(\\vec{pr}\\)', label:{position: 'top'}, lastArrow: {type: 4, size: 8}});<br />
</source><br />
[[Category:Examples]]<br />
[[Category:Geometry]]</div>
A WASSERMANN