Main concepts

The following are some of the most important concepts in geometry.

• Axioms

Euclid introduced certain axioms, or postulates, expressing primary or self-evident properties of points, lines, and planes. He proceeded to rigorously deduce other properties by mathematical reasoning. The characteristic feature of Euclid’s approach to geometry was its rigor, and it has come to be known as axiomatic or synthetic geometry.

• Points

Points are generally considered fundamental objects for building geometry. They may be defined by the properties that thay must have, as in Euclid’s definition as “that which has no part”, or in synthetic geometry. In modern mathematics, they are generally defined as elements of a set called space, which is itself axiomatically defined.

• Lines

Euclid described a line as “breadthless length” which “lies equally with respect to the points on itself”. In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic geometry, a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation, but in a more abstract setting, such as incidence geometry, a line may be an independent object, distinct from the set of points which lie on it. In differential geometry, a geodesic is a generalization of the notion of a line to curved spaces.

• Planes

In Euclidean geometry a plane is a flat, two-dimensional surface that extends infinitely; the definitions for other types of geometries are generalizations of that. Planes are used in many areas of geometry. For instance, planes can be studied as a topological surface without reference to distances or angles; it can be studied as an affine space, where collinearity and ratios can be studied but not distances; it can be studied as the complex plane using techniques of complex analysis; and so on.

• Angles

Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. In modern terms, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

• Curves

A curve is a 1-dimensional object that may be straight (like a line) or not; curves in 2-dimensional space are called plane curves and those in 3-dimensional space are called space curves.

• Surfaces

A surface is a two-dimensional object, such as a sphere or paraboloid. In differential geometry and topology, surfaces are described by two-dimensional ‘patches’ (or neighborhoods) that are assembled by diffeomorphisms or homeomorphisms, respectively. In algebraic geometry, surfaces are described by polynomial equations.

• Length, area, and volume

Area and volume can be defined as fundamental quantities separate from length, or they can be described and calculated in terms of lengths in a plane or 3-dimensional space.Mathematicians have found many explicit formulas for area and formulas for volume of various geometric objects. In calculus, area and volume can be defined in terms of integrals, such as the Riemann integral or the Lebesgue integral.

For more such videos : https://www.youtube.com/c/ExperiHub?sub_confirmation=1

For more Science related blogs and videos : https://experihub.com/did-you-know/

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …
The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths.

For more such videos : https://www.youtube.com/c/ExperiHub?sub_confirmation=1

For more Science related blogs and videos : https://experihub.com/did-you-know/

For more such videos : https://www.youtube.com/c/ExperiHub?sub_confirmation=1

For more Science related blogs and videos : https://experihub.com/did-you-know/

For more such videos : https://www.youtube.com/c/ExperiHub?sub_confirmation=1

For more Science related blogs and videos : https://experihub.com/did-you-know/

According to Merriam-Webster dictionary, statistics is defined as “classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement”.

According to statistician Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts in any department of inquiry placed in relation to each other”.

For more such videos : https://www.youtube.com/c/ExperiHub?sub_confirmation=1

For more Science related blogs and videos : https://experihub.com/did-you-know/

A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.

For more such videos : https://www.youtube.com/c/ExperiHub?sub_confirmation=1

For more Science related blogs and videos : https://experihub.com/did-you-know/

They are natural and whole numbers, odd and even numbers, rational and irrational numbers, etc. We will discuss all the types here in this article.

For more such videos : https://www.youtube.com/c/ExperiHub?sub_confirmation=1

For more Science related blogs and videos : https://experihub.com/did-you-know/

For more such videos : https://www.youtube.com/c/ExperiHub?sub_confirmation=1

For more Science related blogs and videos : https://experihub.com/did-you-know/

For more such videos : https://www.youtube.com/c/ExperiHub?sub_confirmation=1

For more Science related blogs and videos : https://experihub.com/did-you-know/