Filling the Gap between Dimensions

Episode 18 of Mind-Bending Math: Riddles and Paradoxes

Enter another dimension - a fractional dimension! First, hone your understanding of dimensionality by solving the riddle of Gabriel's horn, which has finite volume but infinite surface area. Then venture into the fractal world of Sierpinski's triangle, which has 1.58 dimensions, and the Menger sponge, which has 2.73 dimensions.