Students learn geometry at almost every grade level. Elementary students learn the basics of geometry: shapes and counting the number of sides. Middle school student begin learning how to find the volume and area of circles and squares. High school students jump into geometry with Euclidean/Plane Geometry and Symmetry & Tessellations. College students can take their knowledge from high school geometry to the next level and learn about Spherical Geometry, Hyperbolic Geometry, as well as Riemannian Geometry and Fourth Dimensional Geometry. No matter the grade level your student is in, we have expert tutors that will help students understand and conceptualize what they need to know in their geometry class.
What is it?
Euclidean/Plane Geometry is the study of flat space. 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. All of these ideas can be described by drawing on a flat piece of paper. From the laws of Euclidean Geometry, we get the famous Pythagorean Theorem.
Non-Euclidean Geometry is any geometry that is different from Euclidean geometry. It is a consistent system of definitions, assumptions, and proofs that describe such objects as points, lines and planes. The two most common non-Euclidean geometries are spherical geometry and hyperbolic geometry. The essential difference between Euclidean geometry and these two non-Euclidean geometries is the nature of parallel lines: In Euclidean geometry, given a point and a line, there is exactly one line through the point that is in the same plane as the given line and never intersects it. In spherical geometry there are no such lines. In hyperbolic geometry there are at least two distinct lines that pass through the point and are parallel to (in the same plane as and do not intersect) the given line.
Riemannian Geometry is the study of curved surfaces and higher dimensional spaces. For example, you might have a cylinder, or a sphere and your goal is to find the shortest curve between any pair of points on such a curved surface, also known as a minimal geodesic. Or you may look at the universe as a three dimensional space and attempt to find the distance between/around several planets.
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