The grand pillars on ancient Greek temples, modern soda bottles, and the metric system all testify to the importance of geometry in our world. For millennia, human beings have been engaged in the study of geometry, which is a subset of mathematics that addresses issues such as position, space, size, volume, shape, and so forth. Today, it is a required course in most secondary education programs.Euclidean geometry is the most famous branch of geometry, but there are several other branches such as differential geometry, projective geometry, and others. This resource guide to geometry deals mainly with Euclidean geometry and features links to several resource pages with lessons, games, and other activities to help you master the subject. Use it to enhance your understanding of this important branch of mathematics and to have fun with shapes, lines, points, and more.
The point is one of the basic elements in most every geometrical system. Essentially, it is a location on a plane surface or in the space that a person is studying. The primary thing that a point indicates is location, as points do not have measurements such as area, perimeter, volume, length, or any other. Excuse the pun, but a point is the starting point for geometry.
Another fundamental concept in geometry is the line, which is a straight arrangement of points, or points all on the same level that extends infinitely in both directions. A line segment represents that portion of a line found between two specific points and all the points in between them. Lines have no thickness, and they have no curves.
Angles are likewise basic and important in the study of geometry. An angle is created when two lines intersect but they do not lie on a straight line relative to one another. The angles that we often think of consist of two rays that have the same endpoint and extend out in different directions without lying on a straight line. However, angles exist wherever two lines cross one another. Two true lines that intersect, for example, will create four angles with the lines’ intersection point at their center.
Plane shapes are objects in two dimensions that are made up of line segments or curved segments or both that are all connected at corners or vertices. Plane shapes are very familiar to us, and include such things as triangles, circles, rectangles, squares, and other polygons. They can be drawn on a flat surface, known as a plane.
The study of geometry is often the study of the measurements of plane shapes and solids. Perimeter measures the distance of an object’s sides; area measures the coverage of a flat surface; and volume is the measurement of how much a solid can contain. Being able to accurately measure shapes and solids has dozens of practical applications, including the calculation of the area of a room, determining how much liquid will fit in a particular bottle, and much more.
Symmetry is related to measurement, and occurs in several different forms. In mirror symmetry, the two halves of an object mirror one another exactly so that they can fold over and line up precisely. Rotational symmetry occurs when an object can be rotated and maintain the same appearance as one continues to view it from the same angle.
Solids are essentially three-dimensional forms of plane shapes. They have properties such as volume and surface area. Familiar solids include pyramids, cylinders, spheres, cones, cubes, and many others. We see solids all the time, with everything from construction materials to toy building blocks being examples of such solids.
Lines are important for geometry, and there are many ways in which lines can be related to one another in the same plane. Parallel lines are two lines that do not intersect and have the same distance between every single point on both lines. For example, two lines are parallel if all the points on line A are equally distant from their corresponding points on line B.
A transformation occurs when you change the position of a shape within a plane of coordinates. Basically, transformations occur whenever shapes move from one place to another. Change the location points of the vertices of a shape in an x-y coordinate system, for example, and you will have a transformation.
Coordinates are used to determine a specific point or other element of geometry in a specific space. The most common coordinate system uses an x axis and a y axis to locate various shapes and points. The z axis is added to create three-dimensional objects and graphs.