Mathematics Club

For this 4PM Thursday 28.September 2023 meeting of Maths Club of Science Circle, we will take a deep dive into “The Painter’s Dilemma”, based on Gabriel’s Horn (La Trompette de Gabriel) which has FINITE VOLUME but INFINITE SURFACE AREA, as studied by Evangelista Torricelli in 1641. The relationship of this unbounded structure to the harmonic series and the concept of volume of rotation underlying Gabriel’s Horn will be discussed. Finally, we will consider the existence of 3-dimensional structures that are finite and bounded in volume, yet of infinite surface area. One of these can be constructed using fractal geometry, and the other I developed while on holiday.