Love making paper airplanes, tangram puzzles, and origami? Geometry is the math behind them all. Students begin learning about geometry when they are taught different shapes and angles and how to create new objects from them. They are still interested even when it is time to learn how to determine how much water it will take to fill the bucket or paint they will need to paint the house, but when students get into theorems and postulates, the fun with geometry starts to fade. Terms like hyperbolic, conical, and elliptical send many student straight to panic mode and they struggle in their classes. Getting the help of a geometry tutor can provide the student with an understanding they may miss in the classroom.
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.
Practice. Practice. Practice. For most students success in any math course comes from regular studying and practicing habits. However, we find that geometry is the one math class can be a foreign language for many students. No matter the level of the geometry class that the student is taking, we have expert tutors available and ready to help. All of our geometry tutors have a degree in mathematics, science, or a related field like engineering. Our goal is to provide a geometry tutor that can make understanding the concepts simple and straightforward and to help the student achieve success in the classroom.
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