【Haichuan Teahouse】\"A cup that couldn’t be made even if all the glass materials on Earth were used up,\"
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“\"Even if all the glass materials on Earth were used, it would not be enough to create this cup.\" The Torricelli trumpet is a three-dimensional shape invented by the Italian mathematician Evangelista Torricelli, characterized by an infinite surface area but a finite volume. This shape is also known as the Gabriel’s horn
It simply has an infinite surface area, but a finite volume. Theoretically, one gram of glass can also be used to create a container with an infinite surface area, as long as its thickness approaches zero.
Torricelli’s Trumpet. This shape is also known as Gabriel’s Horn. It is a three-dimensional shape created by the Italian physicist and mathematician Evangelista Torricelli (1608–1647). When we hear his name, we probably think of his other invention: the barometer. Throughout his short life, he achieved outstanding accomplishments in various fields and earned a high reputation. After Galileo’s death in 1642, Torricelli succeeded him as professor of physics and mathematics at the Florence Academy of Sciences, and was appointed as the court’s chief mathematician. Torricelli rotated the part of y=1/x where x≥1 around the x-axis, resulting in the trumpet-shaped figure shown above (note that the diagram shows only a portion of this figure). Note that in Torricelli’s time, calculus had not yet been invented; he arrived at this discovery using Cavalieri’s principle. The principle of Cavalieri states that two solids of the same height have equal volumes if their cross-sectional areas at equal heights are always equal ； If the cross-sectional areas are in direct proportion, then the ratio of volumes is equal to the ratio of the cross-sectional areas. Cavalieri’s principle is the theory most frequently cited by mathematicians when studying infinitesimal problems in geometry; it was hailed by Leibniz as the pinnacle of geometry at that time, and it had a significant impact on the development of calculus. Note: Cavalieri (1598–1647) was an Italian mathematician. Torricelli calculated a truly remarkable property of this small object: its surface area is infinite, yet its volume is π. This clearly goes against human intuition: an object with a finite volume can have an infinite surface area!
Mathematics is used to expand one’s thinking
Isn’t it nice to think of a 90-degree rotation as the silhouette of a skyscraper? The base is open, columns run vertically and horizontally, with fiber optics providing supplementary lighting.
More like an elongated cooling tower: lol