# A report on Geometry, Area, Calculus and Mathematics

Geometry is, with arithmetic, one of the oldest branches of mathematics.

- GeometryCalculus, 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.

- CalculusMathematics 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).

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

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

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

- CalculusIn 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.

- Area287–212 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.

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

- GeometryHe 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.

- Mathematics2 related topics with Alpha

## Integral

0 linksIn 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

0 linksDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.

The first systematic or rigorous treatment of geometry using the theory of infinitesimals and notions from calculus began around the 1600s when calculus was first developed by Gottfried Leibniz and Isaac Newton.

Various concepts based on length, such as the arc length of curves, area of plane regions, and volume of solids all possess natural analogues in Riemannian geometry.