# A report onMathematics and Geometry

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

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

- Geometry

## 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.

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

## Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as:

For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations.

## Area

Quantity 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.

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.

## Euclid

Euclid ( Eὐkleídēs; 300 BC), sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.

## Axiom

Statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

Statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms".

The ancient Greeks considered geometry as just one of several sciences, and held the theorems of geometry on par with scientific facts.

## Discrete geometry

Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.

In mathematics, tessellations can be generalized to higher dimensions.

## Measure (mathematics)

In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as mass and probability of events.

## Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas.