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Display information for equation id:math.1110.20 on revision:1110
* Page found: ART-Skript (eq math.1110.20)
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\begin{align}
& \Delta r=c\Delta t\to {{\left( \Delta r \right)}^{2}}={{c}^{2}}{{\left( \Delta t \right)}^{2}} \\
& \to {{\left( \Delta {{x}^{1}} \right)}^{2}}+{{\left( \Delta {{x}^{2}} \right)}^{2}}+{{\left( \Delta {{x}^{3}} \right)}^{2}}={{c}^{2}}\Delta {{t}^{2}} \\
& \to \Delta {{s}^{2}}:={{c}^{2}}\Delta {{t}^{2}}-{{\left( \Delta {{x}^{1}} \right)}^{2}}-{{\left( \Delta {{x}^{2}} \right)}^{2}}-{{\left( \Delta {{x}^{3}} \right)}^{2}} \\
& \to d{{s}^{2}}={{c}^{2}}d{{t}^{2}}-{{\left( d{{x}^{1}} \right)}^{2}}-{{\left( d{{x}^{2}} \right)}^{2}}-{{\left( d{{x}^{3}} \right)}^{2}}=0 \\
\end{align}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi mathvariant="normal">Δ</mi><mi>r</mi><mo>=</mo><mi>c</mi><mi mathvariant="normal">Δ</mi><mi>t</mi><mo accent="false">→</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Δ</mi><mi>r</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Δ</mi><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo accent="false">→</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Δ</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Δ</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Δ</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi mathvariant="normal">Δ</mi><msup><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo accent="false">→</mo><mi mathvariant="normal">Δ</mi><msup><mi>s</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>:</mi><mo>=</mo><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi mathvariant="normal">Δ</mi><msup><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Δ</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Δ</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Δ</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo accent="false">→</mo><mi>d</mi><msup><mi>s</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>d</mi><msup><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>d</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>d</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>d</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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