Geometry and Trigonometry
Basics of Geometry
How do we interpret dimensions in everyday life?
We are all familiar with dimensions around us, although we may not be aware of them. Most people are familiar with the ideas of two- (such as a drawing on paper) and three-dimensional objects (ordinary objects, including an apple or a car, exist in three-dimensional space), but there are others as well.
Zero dimension can be thought of as a point in space. One dimension can be visualized by a line or a curve in space. Another way of understanding one dimension is with time, something we think of as consisting of only “now,” “before,” and “after.” Because the “before” and “after”—regardless of whether they are long or short—are actually extensions, time becomes similar to a line (as in “timeline”)—or a one-dimensional object.
Two dimensions are defined by two coordinates in space, such as a rectangle. One of the most obvious two-dimensional objects we see all around us are paintings and photographs—although they represent a three-dimensional object. Even this page you are reading can be considered a two-dimensional object, though strictly speaking, the thickness of the paper gives it a third dimension. Three dimensions are considered the space we occupy, as three dimensions give everything around us depth. Our binocular vision allows us to see depth (things in three dimensions), which is why everything becomes “flat” or two-dimensional when we view the world through just one eye.
One can also conceive of four or more dimensions, but there are few common examples. Most hyper-dimensional aspects are used by mathematicians, various scientists, and even economists. They need such dimensional analysis for their complex mathematics, such as for modeling weather patterns or the ups and downs of the stock market.