I chose this topic because I find the idea of embracing different visuals of dimensions very interesting. Dimensional space is what makes up everything around you, and it is what is used to locate anything in any given place from the tip of your nose to the North Pole. The number of dimensions present tells you how many numbers are used to locate something in any given place. A number line is an example of a one dimensional space because you only use one number to locate a point on the number line.
A plane is an example of a two dimensional space because it adds length to the dimension and thus requires two numbers to locate any given point on the plane.
Finally there is the third dimension, the one we live in. A third number is added because there are three dimensions, we get height added in this dimension and thus three numbers are used to locate any given point.
When you make a graph on a graphing calculator, it's showing you the coordinates of a two dimensional space because you use two numbers, x and y, to find that point on the graph.
Let's add a third dimension to our graphing calculator and call the variable for this dimension z. If we were to put a formula on this graph, the way we would locate a point on it is by finding x, which is width, y, which is length and z which would be height. You should be able to look at this graph the same exact way you look at the world around you.
If we go a step further and talk about the fourth dimension, it starts to get very complicated and hard to understand. The fourth dimension is considered in science to be the dimension of time, it's not something we as humans can physically see, but it exists and we are a part of it. There aren't many examples of four dimensional graphs, let alone graphing in four dimensions. In fact the only clear example of a four dimensional space is a hyper cube or a tesseract.
There are several examples of fourth dimensional space physically manifesting in pop culture, such as in the movie interstellar. When the main character enters the fourth dimension he is in a hyper cube like the one above, and is able to see moments in time as a physical chain connecting from the moment of birth to the moment of death. The reason the fourth dimension is hard to understand is because we as human beings cannot physically comprehend the idea of seeing time as something you can physically touch.