Gabriel's Horn is the surface generated when the graph of the function f.x/ D x~(-1), defined for x ≥ 1, is revolved around the x-axis as in FIGURE 1. The Horn was discovered in 1641 by Evangelista Torricelli, who established its celebrated properties, infinite surface area and finite volume-which we will refer to together as the Horn Property. The proper name Gabriel refers to the Archangel Gabriel, who in some religious traditions is viewed as the messenger of God, heralding the End of Days with a trumpet blast. Coupling the divine with the infinite completes the metaphor for the Horn, which is elsewhere called Torricelli's trumpet or the infinite paint can. The latter description gives rise to the "painter's paradox":How can a paint can full of paint contain insufficient liquid to coat its interior?
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机译：加百列的号角是当定义为x≥1的函数fx / D x〜（-1）的图围绕x轴旋转时生成的表面，如图1所示。号角由Evangelista Torricelli在1641年发现，建立了著名的特性，无限的表面积和有限的体积，我们将它们统称为“霍恩特性”。加百列（Gabriel）的专有名称是大天使加百列（Arcangel Gabriel），在某些宗教传统中，他被视为上帝的使者，用小号炮弹宣告了“天涯”。将神圣与无限耦合在一起，就完成了号角的隐喻，在其他地方也称为Torricelli的喇叭或无限的油漆罐。后面的描述引起了“画家的悖论”：充满油漆的油漆怎么能容纳不足的液体来覆盖其内部？
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