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Physics
A particle's rest energy in special relativity
In Einstein's special relativity, the rest energy of a mass \(m\) is \(E = mc^2\), where \(c\) is the speed of light in a vacuum.
Physics
Einstein's field equations in general relativity
In Einstein's general relativity, the field equation \(\mathcal{G} = - \frac{8\pi G}{c^4} \mathcal{T}\) relates spacetime curvature (\(\mathcal{G}\)) to its mass-energy content (\(\mathcal{T}\)).
Mathematics
Euler's product formula
Prime numbers are key to Euler's product formula, \(\sum_{k=1}^{\infty}\frac{1}{k^s}=\prod_{p \;\; \mathrm{prime}}\frac{1}{1-p^{-s}}\), which establishes equality between an infinite sum and product for fixed \(s>1\).