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Successive application of

**Archimedes**' recurrence formula gives the**Archimedes**algorithm, which can be used to provide successive approximations to pi (pi). The algorithm is ...Draw the perpendicular line from the intersection of the two small semicircles in the arbelos. The two circles C_1 and C_2 tangent to this line, the large semicircle, and ...

**Archimedes**' axiom, also known as the continuity axiom or

**Archimedes**' lemma, survives in the writings of Eudoxus (Boyer and Merzbach 1991), but the term was first coined by ...

**Archimedes**' spiral is an Archimedean spiral with polar equation r=atheta. (1) This spiral was studied by Conon, and later by

**Archimedes**in On Spirals about 225 BC.

**Archimedes**...

Cut a sphere by a plane in such a way that the volumes of the spherical segments have a given ratio.

**Archimedes**' cattle problem, also called the bovinum problema, or

**Archimedes**' reverse, is stated as follows: "The sun god had a herd of cattle consisting of bulls and cows, ...

Let M be the midpoint of the arc AMB. Pick C at random and pick D such that MD_|_AC (where _|_ denotes perpendicular). Then AD=DC+BC.

Taking the origin as the inversion center,

**Archimedes**' spiral r=atheta inverts to the hyperbolic spiral r=a/theta.Let a_n and b_n be the perimeters of the circumscribed and inscribed n-gon and a_(2n) and b_(2n) the perimeters of the circumscribed and inscribed 2n-gon. Then a_(2n) = ...

Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...

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