On the Measurement of the Circle

E156207

On the Measurement of the Circle is a mathematical treatise by Archimedes in which he rigorously approximates the value of π and explores properties of circles.

All labels observed (6)

How this entity was disambiguated

Statements (46)

Predicate Object
instanceOf mathematical treatise ⓘ
work on geometry ⓘ
approximateDate 3rd century BCE ⓘ
author Archimedes ⓘ
citedFor classical bounds on pi ⓘ
contains three propositions ⓘ
demonstrates early use of limit-like reasoning ⓘ
rigorous geometric proof techniques ⓘ
field geometry ⓘ
mathematics ⓘ
focusesOn approximation of pi ⓘ
area of a circle ⓘ
circumference of a circle ⓘ
ratio of circumference to diameter ⓘ
genre mathematical text ⓘ
givesLowerBoundForPi 223/71 ⓘ
givesUpperBoundForPi 22/7 ⓘ
historicalPeriod Hellenistic period ⓘ
influenced classical geometry ⓘ
later studies of pi ⓘ
languageOfWork Ancient Greek ⓘ
mainSubject circle ⓘ
geometry ⓘ
pi ⓘ
numberOfPropositions 3 ⓘ
originalTitle Περὶ μέτρου κύκλου ⓘ
partOf Archimedes' works on geometry ⓘ
polygonSidesUsed 96 ⓘ
preservedIn medieval manuscript traditions ⓘ
proposition Proposition 1 ⓘ
Proposition 2 ⓘ
Proposition 3 ⓘ
proposition1States the area of a circle equals that of a right triangle with legs equal to the radius and the circumference ⓘ
proposition2States the area of a circle is proportional to the square of its diameter ⓘ
proposition3States gives upper and lower bounds for pi using inscribed and circumscribed polygons ⓘ
proves inequalities for pi ⓘ
relatedTo Archimedes ⓘ
Method of Exhaustion ⓘ
significance one of the earliest rigorous approximations of pi ⓘ
states 3 1/7 > pi > 3 10/71 ⓘ
studiedIn history of mathematics ⓘ
title On the Measurement of the Circle ⓘ
typeOfResult geometric proof of circle area formula ⓘ
uses circumscribed polygons ⓘ
inscribed polygons ⓘ
usesMethod method of exhaustion ⓘ

How these facts were elicited

Referenced by (12)

Full triples — surface form annotated when it differs from this entity's canonical label.

Archimedes → notableWork → On the Measurement of the Circle ⓘ
On the Measurement of the Circle → title → On the Measurement of the Circle ⓘ
On the Measurement of the Circle → originalTitle → Περὶ μέτρου κύκλου ⓘ
linked to: On the Measurement of the Circle
On Spirals → relatedTo → Measurement of a Circle ⓘ
linked to: On the Measurement of the Circle
Quadrature of the Parabola → relatedTo → On the Measurement of a Circle ⓘ
linked to: On the Measurement of the Circle
Hellenistic mathematics → notableWork → Measurement of a Circle ⓘ
linked to: On the Measurement of the Circle
Method of Exhaustion → appliedBy → Archimedes in Measurement of a Circle ⓘ
linked to: On the Measurement of the Circle
Eutocius of Ascalon → wroteCommentaryOn → On the Measurement of the Circle by Archimedes ⓘ
linked to: On the Measurement of the Circle
Psammitēs → relatedWork → Measurement of a Circle ⓘ
linked to: On the Measurement of the Circle
De spiralibus → relatedTo → On the Measurement of a Circle ⓘ
linked to: On the Measurement of the Circle
Psammites → relatedWork → Measurement of a Circle ⓘ
linked to: On the Measurement of the Circle
corpus of Archimedes → hasWork → On the Measurement of the Circle ⓘ