托里拆利小號

這個形狀是由${\displaystyle y=1/x}$（x的域為${\displaystyle x\geq 1}$）的曲線沿${\displaystyle x}$軸旋轉而成。這個發現是在微積分發明前用祖暅原理得出的。

使用旋轉體的體積(V)和旋轉曲面的面積(A)公式，可得：

${\displaystyle V=\int _{1}^{\infty }\pi y^{2}\mathrm {d} x=\pi \int _{1}^{\infty }{\frac {1}{x^{2}}}\mathrm {d} x=\pi }$

${\displaystyle A=\int _{1}^{\infty }2\pi y{\sqrt {1+({\frac {\mathrm {d} y}{\mathrm {d} x}})^{2}}}\mathrm {d} x=2\pi \int _{1}^{\infty }{\frac {\sqrt {1+{\frac {1}{x^{4}}}}}{x}}\mathrm {d} x>2\pi \int _{1}^{\infty }{\frac {1}{x}}\mathrm {d} x={\infty }}$

• 双曲线
• 科赫曲線
• 宇宙的形状
• 旋轉曲面
• 芝诺悖论

• Information and diagrams about Gabriel's horn
• Torricelli's trumpet at PlanetMath
• 埃里克·韦斯坦因. . MathWorld.
• "Gabriel's Horn" by John Snyder, the Wolfram Demonstrations Project, 2007.
• Gabriel's Horn: An Understanding of a Solid with Finite Volume and Infinite Surface Area by Jean S. Joseph.