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Serenus of Antinoöpolis

Geometer and Specialist in Conic Sections

Serenus of Antinoöpolis (c. 300–c. 360 CE) was a Greek mathematician known for his work on geometry, particularly conic sections and the properties of cylinders and cones. His writings are largely preserved through references by later commentators, and he is recognized for continuing the Hellenistic tradition of rigorous geometric analysis.

Serenus focused on the detailed study of volumes, sections, and ratios of solids. He explored problems such as slicing a cylinder or cone along planes at various angles and deriving the areas and volumes of the resulting figures. For example, in a right circular cone of height \(h\) and base radius \(r\), he analyzed the volume of sections cut parallel to the base: \[ V = \frac{1}{3} \pi r^2 h \] and examined how slicing at different heights produces similar cross-sections, laying the groundwork for proportional reasoning in solid geometry.

He also addressed relationships between spheres, cylinders, and cones, expanding on Archimedes’ earlier work and providing alternative proofs of classical theorems. His contributions demonstrate a systematic method for decomposing complex solids into simpler, computable shapes, anticipating concepts used in integral geometry centuries later.

Although Serenus did not develop new branches of mathematics, his careful analysis and exposition strengthened the understanding of three-dimensional geometry in the Late Antique period. His work influenced later Byzantine mathematicians, including Eutocius, who preserved and commented on Hellenistic geometric knowledge.

Serenus’ legacy lies in his precision, methodical approach, and dedication to transmitting geometric knowledge, ensuring that the study of conic sections and solid geometry remained robust through centuries of mathematical scholarship.