What Is Geometry?

Measuring Lines, Shapes, Angles, and Circles

High Angle View Of Multi Colored Paper Pyramids
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Simply put, geometry is a branch of mathematics that studies the size, shape, and position of 2-dimensional shapes and 3-dimensional figures. Although ancient Greek mathematician Euclid is typically considered the "Father of Geometry," the study of geometry arose independently in a number of early cultures.

Geometry is a word derived from Greek. In Greek, "geo" means "earth" and "metria" means measure.

Geometry is in every part of a student's curriculum from kindergarten through 12th grade and continues through college and postgraduate study. Since most schools use a spiraling curriculum, introductory concepts are re-visited throughout the grades and advances in the level of difficulty as time goes on.

How Is Geometry Used?

Even without ever cracking open a geometry book, geometry is used daily by almost everyone. Your brain makes geometric spatial calculations as you step your foot out of bed in the morning or parallel park a car. In geometry, you are exploring spatial sense and geometric reasoning. 

You can find geometry in art, architecture, engineering, robotics, astronomy, sculptures, space, nature, sports, machines, cars, and much more.

Some of the tools often used in geometry include a compass, protractor, square, graphing calculators, Geometer's Sketchpad, and rulers.

Euclid

A major contributor to the field of geometry was Euclid (365-300 B.C.) who is famous for his works called "The Elements." We continue to use his rules for geometry today. As you progress through primary and secondary education, Euclidean geometry and the study of plane geometry, are studied throughout. However, non-Euclidean geometry will become a focus in the later grades and college math.

Geometry in Early Schooling

When you take geometry in school, you are developing spatial reasoning and problem-solving skills. Geometry is linked to many other topics in math, specifically measurement.

In early schooling, the geometric focus tends to be on shapes and solids. From there, you move to learning the properties and relationships of shapes and solids. You will begin to use problem-solving skills, deductive reasoning, understand transformations, symmetry, and spatial reasoning. 

Geometry in Later Schooling

As abstract thinking progresses, geometry becomes much more about analysis and reasoning. Throughout high school there is a focus on analyzing properties of two- and three-dimensional shapes, reasoning about geometric relationships, and using the coordinate system. Studying geometry provides many foundational skills and helps to build the thinking skills of logic, deductive reasoning, analytical reasoning, and problem-solving.

Major Concepts in Geometry

The main concepts in geometry are lines and segments, shapes and solids (including polygons), triangles and angles, and the circumference of a circle. In Euclidean geometry, angles are used to study polygons and triangles.

As a simple description, the fundamental structure in geometry—a line—was introduced by ancient mathematicians to represent straight objects with negligible width and depth. Plane geometry studies flat shapes like lines, circles, and triangles, pretty much any shape that can be drawn on a piece of paper. Meanwhile, solid geometry studies three-dimensional objects like cubes, prisms, cylinders, and spheres.

More advanced concepts in geometry include platonic solidscoordinate gridsradians, conic sections, and trigonometry. The study of the angles of a triangle or of angles in a unit circle forms the basis of trigonometry.