https://spherical-harmonics.hateblo.jp/entry/Kyodai/1931/Rigaku

2025.01.22記

[1] Find the number of combinations of $n$ things $r$ at a time. Prove by the mathematical induction.

[2] $a$ , $b$ are such that $2x+3y=5$ always touches the curve $\dfrac{y^2}{a^2}-\dfrac{x^2}{b^2}=1$ . Represent graphically the condition between $a$ and $b$ .

[3] The curve $\dfrac{x^2}{\alpha^2}+\dfrac{y^2}{\beta^2}=1$ revolves around one of its tangents whose distance from the centre of the figure is $p$ . Prove that the volume of revolution is $\pi\alpha\beta\cdot 2\pi p$ .

[4] In the preceding probrem, find the maximum of minimum of the volume of revolution when the tangent varies.

1931年(昭和6年)京都帝國大學理學部-數學[1] - [別館]球面倶楽部零八式markIISR
1931年(昭和6年)京都帝國大學理學部-數學[2] - [別館]球面倶楽部零八式markIISR
1931年(昭和6年)京都帝國大學理學部-數學[3] - [別館]球面倶楽部零八式markIISR
1931年(昭和6年)京都帝國大學理學部-數學[4] - [別館]球面倶楽部零八式markIISR