Geometry is the study of shapes and figures in various spaces including their properties and behaviour. Certain elements of geometry were discovered in 6th century BC. It wasn't until the 3rd century BC that geometry was put into axiom form by Euclid, whose work, Euclidian geometry, set a standard for future generations of study. Descartes was the first to apply algebra to geometry and give us a coordinate system as well as representing geometric figures and planes in terms of functions and equations. In the 19th century, geometry took a new turn with the discovery of non-Euclidian geometry which transformed the concept of space. Now, past the 20th century, one has to differentiate between physical, geometrical, and abstract spaces.
The geometry that is studied in today's school system is composed of many different subjects infused with algebra. Along with the new Common Core requirements, one must now learn each topic a bit more in depth and be able to apply his or her knowledge to complex situations. Students must learn to calculate the slope given information in the form of a graph, points, or another equation of a line as reference. They'll also need to recognize the different properties of triangles, parallelograms, angles, parallel and perpendicular lines, and together with the use of vocabulary and certain definitions, compose geometric proofs. One of the most hands-on topics learned is constructions with the aid of a compass and straightedge. At a later time, students are also exposed to 3-D geometry which focuses on developing spacial thinking and recognition of boundaries, the challenge of which is to manipulate 3-D figures while only being able to handle them on the 2-D surface of the paper.