Calculus

Steinmetz solid created from the intersection of two cylinders.

This illustration showcases the intersection of two cylinders, forming a unique three-dimensional solid known as a Steinmetz solid or bicylinder. The diagram demonstrates how two cylindrical surfaces intersect at right angles, with the overlapping region highlighted in green.

In the upper part of the image, the shaded area S represents the shared interior of the two cylinders, capturing the intersected volume. Below, the blue transparent cylinders visually convey the cross-sections and spatial arrangement, emphasizing the symmetry and geometry of their intersection.

This geometric construction is widely used in mathematics, engineering, and architectural design to explore complex volumetric calculations and spatial relations. The intersection of surfaces such as this is crucial in integral calculus for determining volumes and areas of intricate shapes.

This illustration is ideal for multivariable calculus and geometry textbooks, academic journals, and interactive educational materials.

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