Surfaces | Calculus | Paradoxes of infinity | Mathematical paradoxes
Gabriel's horn (also called Torricelli's trumpet) is a particular geometric figure that has infinite surface area but finite volume. The name refers to the Christian tradition that (albeit not strictly supported by the Bible itself) identifies the archangel Gabriel as the angel who blows the horn to announce Judgment Day. The properties of this figure were first studied by Italian physicist and mathematician Evangelista Torricelli in the 17th century. These colourful informal names and the allusion to religion came along later.Torricelli's own name for it is to be found in the Latin title of his paper De solido hyperbolico acuto, written in 1643, a truncated acute hyperbolic solid, cut by a plane.Volume 1, part 1 of his Opera geometrica published the following year included that paper and a second more orthodox (for the time) Archimedean proof of its theorem about the volume of a truncated acute hyperbolic solid.This name was used in mathematical dictionaries of the 18th century (including "Hyperbolicum Acutum" in Harris' 1704 dictionary and in Stone's 1726 one, and the French translation Solide Hyperbolique Aigu in d'Alembert's 1751 one. Although credited with primacy by his contemporaries, Torricelli was not the first to describe an infinitely long shape with a finite volume/area.The work of Nicole Oresme in the 14th century had either been forgotten by, or was unknown to them.Oresme had posited such things as an infinitely long shape constructed by subdividing two squares of finite total area 2 using a geometric series and rearranging the parts into a figure, infinitely long in one dimension, comprising a series of rectangles. (Wikipedia).
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Gabriel's Horn Paradox has a very interesting *spin* to it. The Gabriel's Horn volume is finite while Gabriel's Horn surface area is infinite! What can be done about this? This is sometimes known as the Gabriel's Horn painter's paradox It's time to have Gabriel's Horn explained. Let's do
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Gabriel's Horn Paradox - Numberphile
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Gabriel's Trumpet / Horn Paradox
This video shows that Gabriel's horn has finite volume and infinite surface area. http://mathispower4u.com
From playlist Mathematics General Interest
In this video, we talk about the painter's paradox, that describes an object that can't be covered with paint but can be filled with paint. How is it possible to have an object with an infinite surface area but a finite volume? Doesn't it make sense that the outside of an object always tak
From playlist Analysis
Infinite Surface Area but Finite Volume!?!? *Gabriel's Horn*
Gabriels' Horn - aka Torricelli's Horn - is one of my favorite examples in Calculus. This is a region of revolution where the surface area is infinite but the volume is finite. How cool is that! In this video we recall the formulas for surface area and volume of regions of revolution and c
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Virtual Panoramic Exploration of Gabriel's Horn in GeoGebra Augmented Reality!
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This Object has Infinite Surface Area, but Finite Volume
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Gabriel's Horn, Painters paradox
Start learning today, click https://brilliant.org/blackpenredpen/ to check out Brillant.org. First 200 people to sign up will get 20% off your annual premium subscription! Review disc method, https://youtu.be/BeVQKkUJCVg Review surface area, https://youtu.be/A_vSMlXH3sg Integral of 1/x f
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