Geometry all common 2-dimensional shapes. With two dimensions

Geometry is the study of shapes and the space that they inhabitant. One-dimensional geometry is concerned with distance.

Two-dimensional geometry is concerned with area. Three-dimensional geometry is concerned with volume.

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What Is Geometry?

Geometry, along with arithmetic, is one of the oldest branches of mathematics. Geometric concepts have been found within some of the earliest Egyptian and Babylonian civilizations, among others. Individuals such as Euclid, Pythagoras, Archimedes, and Plato did a lot of work to formalize and conceptualize the field of geometry. Although much can be said about geometry, it is basically the study of shapes, the space that they inhabitant, and the rules that govern the relationships between them. This lesson has been divided into sections for each dimension.

No Dimensions

The most basic of all geometric terms is the point. A point is a place in space that has no length or dimension. It is represented using a dot, but this is only so that it is visible for our mathematical purposes. Although it does not have size, it does have position, and that position can be given using an ordered pair such as (x,y).

One Dimension

If we take a step into 1-dimensional geometry, our first concept is a line, the set of all points that fall along a straight path. A line will continue along a straight path in both directions without end. Related to the line are the line segment and the ray.

A line segment is the collection of points that lie between two specific endpoints. A ray has a starting point and then continues into infinity in one direction. These lines, segments, and rays intersect each other to form parallel and perpendicular lines and angles.Measurement is a very common function in geometry. Since we have only one dimension at this point, you can only measure one aspect: length. Length is measured in single units such as miles, feet, inches, centimeters, etc.

If we notice that a train is 300 meters long, we are noting a measure of length.Angles have their own form of measurement. The distance between the line segments that form the angle, a curved measurement, is measured in degrees.

Two Dimensions

When we take into account two dimensions, we are introduce to the plane. A plane is a flat surface, like a piece of paper, that extends forever in all directions. It has length and width but not height. Triangles, rectangles, polygons, and circles are all common 2-dimensional shapes.

With two dimensions you can measure perimeter, which is the distance around a shape. You can also measure area. Area is the amount of space that is on the inside of a 2-dimensional shape and is given in square units. The amount of paint or carpeting it would take to cover your bedroom is a measurement that would require you to find area.When you find the perimeter of a right triangle, The Phythagorean Theorem becomes useful. If you know two of the lengths of a right triangle, you can find the distance of the third using a^2 + b^2 = c^2.

The table provides us with some common shapes and the formulas to find the perimeter and area of each shape:

Perimeter and Area Formulas

Three Dimensions

In 3-dimensional geometry, those 2-dimensional shapes are put together to form 3-dimensional objects such as spheres, prisms, pyramids, cones, and polyhedrons. With 3-dimensional shapes, all three measurements can be taken: length, width, and height. One-dimensional distance can be measured along the edges. Two-dimensional areas come into use as surface area or the area of the base of the solid. The measure of 3-dimensional space is called volume, the amount of space inside of a solid. Volume is measured in cubic units.

The amount of water it takes to fill a swimming pool is a measure of volume. This table gives several solids and the formulas for finding surface area and volume for each solid:

Volume and Surface Area Formulas

Lesson Summary

Geometry is the study of shapes and the space that they inhabitant.

It is concerned with three primary dimensions:

  • One-dimensional distance, which includes the length of line segments and the measurement of angles.
  • Two-dimensional space, which includes perimeter and area of of shapes and planes. Questions such as ‘How many square units does a triangle, trapezoid, or circle take up?’ are common.
  • Three-dimensional space, which includes volume and surface area of 3-dimensional shapes.

    Finding the volume of a sphere, cone, or pyramid is a frequent task.

If you want to describe the size and shape of the world around you, use geometry.


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