Infinite Acres

Series: Calculus Series

Duration: 10

Year Published: 1967

Creator: Mathematical Association of America

Format: 16mm

Color: Color

Description: Illustrates through animation the paradox of a solid having a finite volume and an infinite surface area. Derives a "solution" to the following problem: how much paint would be necessary to paint the surface of an apartment house constructed from the curve y = 10/x, where X goes from one to infinity. Proves that although the amount of paint required to fill up the inside of the apartment house can be calculated, it is impossible to determine the amount of paint required to cover the surface area. Presumes knowledge of improper integrals and solids of revolution., Using animation the film represents the paradoxical situation of a solid with a finite volume and an infinite surface area. Some knowledge of the surface area and volume of a solid and of improper integrals is assumed. (Calculus Films series)

Complete Record: Illustrates through animation the paradox of a solid having a finite volume and an infinite surface area. Derives a "solution" to the following problem: how much paint would be necessary to paint the surface of an apartment house constructed from the curve y = 10/x, where X goes from one to infinity. Proves that although the amount of paint required to fill up the inside of the apartment house can be calculated, it is impossible to determine the amount of paint required to cover the surface area. Presumes knowledge of improper integrals and solids of revolution., NOTE: Two (or more) records have been merged together to create this data.