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ART-Skript Eq: math.1110.20

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TeX (original user input):

\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}

TeX (checked):

{\begin{aligned}&\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{aligned}}

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MathML (4.502 KB / 467 B) :

\begin{aligned} Δ r = c Δ t \to {(Δ r)}^{2} = c^{2} {(Δ t)}^{2} \\ \to {(Δ x^{1})}^{2} + {(Δ x^{2})}^{2} + {(Δ x^{3})}^{2} = c^{2} Δ t^{2} \\ \to Δ s^{2} : = c^{2} Δ t^{2} - {(Δ x^{1})}^{2} - {(Δ x^{2})}^{2} - {(Δ x^{3})}^{2} \\ \to d s^{2} = c^{2} d t^{2} - {(d x^{1})}^{2} - {(d x^{2})}^{2} - {(d x^{3})}^{2} = 0 \end{aligned}

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