c. mid-3rd century BCE / Europe
Archimedes bounds a circle with polygons
Inscribed and circumscribed polygons let Archimedes place the circumference-to-diameter ratio between demonstrable upper and lower bounds.
The story
Measurement of the Circle establishes that the ratio is greater than 223/71 and less than 22/7. The achievement combines approximation with a proof controlling its error. The work's exact year is unknown. Its geometric procedures belong to the history of integration, but are not identical to later calculus.
Connections and context
Liu Hui later developed polygon-based circle calculations. Their methods invite comparison without assuming a documented direct transmission.
Dates and precision
c. mid-3rd century BCE Approximate year
An estimated date from the surviving evidence, not a claim about one exact year.
Representative map location
Syracuse
Archimedes' principal city of activity, not an exact location for composing Measurement of the Circle.
Representative coordinates · 37.07°, 15.29°
A marker identifies one representative place, such as a manuscript collection, laboratory or observing site. It does not mean the work happened only there, or assign a shared discovery to one country.
Bibliography
- University of St Andrews, MacTutor | Archimedes' numerical methods
- University of St Andrews, MacTutor | Archimedes of Syracuse
References are listed as plain bibliography titles. They support particular facts or context; a reference does not certify every interpretation in a story.