# What is geometry?

jovona | Student

Geometry is a branch of mathematics that deals with the properties, measurement, and relationships between points, lines, surfaces, and solids. The word, geometry, comes from the Greek word geometria. The literal translation of geometria is "to measure the earth." The ancient Greeks developed geometry from their efforts to measure distances and calculate areas.

The two main areas of geometry are plane geometry and solid geometry. Plane geometry deals with two dimensional (flat or planar) shapes like circles, lines, and triangles. Three dimensional shapes like cubes, spheres, and cones are studied in solid geometry.

hari12 | Student

The branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs is Geometry.

Euclidean Geometry

An example is the study of flat space, or Euclidean geometry. Between every pair of points there is a unique line segment, which is the shortest curve between those two points. These line segments can be extended to lines. Lines are infinitely long in both directions and, for every pair of points on the line, the segment of the line between them is the shortest curve that can be drawn between them. Furthermore, if you have a line and a point which isn't on the line, there is a second line running through the point, which is parallel to the first line (i.e. never hits it). All of these ideas can be described by a drawing on a flat piece of paper. From the laws of Euclidean Geometry, we get the famous theorem of Pythagoras, and all the formulas you learn in trigonometry.

Riemannian Geometry

Now suppose we are on the surface of a sphere, which is no longer flat, but curved. A shortest curve between any pair of points on a surface is called a minimal geodesic. You can find a minimal geodesic between two points by stretching a rubber band between them. The first thing that you will notice is that sometimes there is more than one minimal geodesic between two points. For example, there are many minimal geodesics between the north and south poles of a globe. As in Euclidean space, we can look for lines with the property that the segment between every pair of points on the line is a minimal geodesic. Curved surfaces are harder to study than flat surfaces, but there are still theorems that can be used to estimate the length of the hypotenuse of a triangle, the circumference of a circle, and the area inside the circle. These estimates depend on the amount that the surface is curved or bent.

Gravitational Lensing

Riemannian Geometers also study higher dimensional spaces. The universe can be described as a three dimensional space. Near the earth, the universe looks roughly like three dimensional Euclidean space. However, near very heavy stars and black holes, the space is curved and bent. The Hubble Telescope has discovered points in space that have more than one minimal geodesic to the telescope. This is called gravitational lensing. The amount that space is curved can be estimated by using theorems from Riemannian Geometry and measurements taken by astronomers. Physicists believe that the curvature of space is related to the gravitational field of a star, according to a partial differential equation called Einstein's Equation. So using the results from the theorems in Riemannian Geometry, they can estimate the mass of the star or black hole which causes the gravitational lensing.

Other Types of Geometry

In general, any mathematical construction which has a notion of curvature falls under the study of geometry. Examples include:

• Differential geometry
• Algebraic geometry
• Semi-Riemannian geometry
• Symplectic geometry

clayton188 | Student

Geometry is the study of planes, lines, points, and things that can be created of these. Angles, shapes, 3d models, and measurements are all examples of geometry.

tosyed | Student

Geometry is the study of angles and shapes and their properties .

user4666037 | Student

It is math. you have to learn it in high school.

princessita-2-day | Student

the branch of math concerned with the properties and relationships of points, lines, surface, solids and higher dimensional analogs.

or a part of math that describes properties like the Non-Euclidean geometry.

kimmmyjoy | Student

Well, Geometry is the learning of shapes, their properties, and formulas to calculate distances, missing angles/side-lengths, or just about anything you can find out about the shape/object.

devanil | Student

Part of Mathematics which addresses areas through means of drawings of various shapes to convey and evaluate distances, laws of science,etc,

This study helps in forecasting specific measurments,in the field of aeronautical and space programs also.

pixiegal | Student

Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metria "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.[1] Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. A mathematician who works in the field of geometry is called a geometer.

cutiepie92298 | Student

it depends because theres diffrent kind of geometry like shapes or word problems...........