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The circumference of a unit circle is \( 2\pi \). The surface of a unit sphere is \( 4\pi \).

Consider now the generalization of a unit sphere in \( N \) dimensions: find ...

Find the largest six-digit natural number \(\overline{abcdef}\) \((a,d\neq 0\)) that satisfies: \[(\overline{abc}\times \overline{def}) \mid \overline{abcdef}\]

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In some countries this problem ...

in quantum mechanics, the spin of an electron in different direction is written as a linear combination of the two orthonormal spin basis. it is known ...

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Evaluate \(\displaystyle{\int_{0}^{1}\tan^{-1}(x)\ln(x)\,\mathrm{d}x}\). If the answer can be expressed as ...

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