# A report onGeometry, Area, Calculus and Mathematics                                                    Geometry is, with arithmetic, one of the oldest branches of mathematics.

- Geometry

Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.

- Calculus

Mathematics is an area of knowledge that includes such topics as numbers (arithmetic, number theory), formulas and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis).

- Mathematics

In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

- Area

For shapes with curved boundary, calculus is usually required to compute the area.

- Area

Calculations of volume and area, one goal of integral calculus, can be found in the Egyptian Moscow papyrus (c.

- Calculus

In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry.

- Area

287–212 BC) of Syracuse used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave remarkably accurate approximations of pi.

- Geometry

This was a necessary precursor to the development of calculus and a precise quantitative science of physics.

- Geometry

He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.

- Mathematics ## 2 related topics with Alpha ## Integral    In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Along with differentiation, integration is a fundamental, essential operation of calculus, and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others.

Area can sometimes be found via geometrical compass-and-straightedge constructions of an equivalent square. ## Differential geometry  