# A report on Geometry, Mathematics, Differential geometry and Calculus

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

- GeometryMathematics 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).

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

- Differential 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.

- CalculusSince then, the scope of geometry has been greatly expanded, and the field has been split in many subfields that depend on the underlying methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc.—or on the properties of Euclidean spaces that are disregarded—projective geometry that consider only alignment of points but not distance and parallelism, affine geometry that omits the concept of angle and distance, finite geometry that omits continuity, and others.

- GeometryThe 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.

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

- GeometrySuch curves can be defined as graph of functions (whose study led to differential geometry).

- MathematicsDifferential geometry

- Calculus1 related topic with Alpha

## Area

0 linksQuantity that expresses the extent of a region on the plane or on a curved surface.

Quantity that expresses the extent of a region on the plane or on a curved surface.

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.

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

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.