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Gabriel’s Horn, also known as Torricelli’s trumpet, is a three-dimensional solid that arises when the curve y=1/x for x>=1 is rotated around the -axis. Although it extends indefinitely, it encloses a limited volume of cubic units, but has an unlimited surface area, which poses a mathematical paradox. This figure, studied since the 17th century, challenges the intuitive understanding of infinity. The analysis focuses on the theoretical formulation of the solid, addressing its structure using calculus tools, particularly integrals over infinite domains. In addition, the study is extended to functions of the form 1/x^p, revealing how small variations in the exponent modify the geometric behavior. Finally, it reflects on the philosophical implications of the model, highlighting the gap between what mathematical logic allows and what physical experience can conceive.
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