Explanation
In this page, we practice understanding higher dimensions using simple real-life examples.
Remember:
A dimension is one independent input.
So, if we describe something using three inputs, it is \(3D\).
If we describe it using four inputs, it is \(4D\).
If we describe it using five inputs, it is \(5D\).
The more independent information we add, the higher the dimension becomes.
Formula / Rule
Number of dimensions = number of independent inputs
Examples:
\begin{align}2D &\longrightarrow (x, y)\\
3D &\longrightarrow (x, y, z)\\
4D &\longrightarrow (x, y, z, \text{time})\\
5D &\longrightarrow (x, y, z, \text{temperature}, \text{time})\\
6D &\longrightarrow (x, y, z, \text{temperature}, \text{wind speed}, \text{time})\end{align}
Example 1
A point in \(3D\) space is:
$$(2, 3, 4)$$
This has three inputs:
$$x = 2$$
$$y = 3$$
$$z = 4$$
So, this point is:
$$3D$$
Example 2
A point in \(3D\) space with time is:
$$(2, 3, 4, 7)$$
This has four inputs:
\begin{align}x &= 2\\
y &= 3\\
z &= 4\\
\text{time} &= 7\end{align}
So, this point is:
$$4D$$
Example 3
A point in \(3D\) space with temperature and time is:
$$(2, 3, 4, 25, 7)$$
This has five inputs:
\begin{align}x &= 2\\
y &= 3\\
z &= 4\\
\text{temperature} &= 25^\circ \text{ C}\\
\text{time} &= 7\end{align}
So, this point is:
$$5D$$
Example 4
A point in \(3D\) space with temperature, wind speed, and time is:
$$(2, 3, 4, 25, 15, 7)$$
This has six inputs:
\begin{align}x &= 2\\
y &= 3\\
z &= 4\\
\text{temperature} &= 25^\circ \text{C}\\
\text{wind speed} &= 15 \text{ km/h}\\
\text{time} &= 7\end{align}
So, this point is:
$$6D$$
Example 5
A point on a flat map is:
$$(2, 3)$$
This has two inputs:
$$x = 2$$
$$y = 3$$
So, this is:
$$2D$$
Now suppose the point represents a building with \(4\) floors.
Then we can write:
$$(2, 3, 4)$$
This is now:
$$3D$$
because we added the number of floors as another input.
Example 6
A point on a map is:
$$(2, 3)$$
Now we add:
• floor number
• temperature
• wind speed
• time
So the point becomes:
$$(2, 3, 4, 25, 15, 7)$$
This has six inputs.
So, this point is:
$$6D$$
Practice
- More Examples (Current page)
- Take the Quiz
Continue Learning
- Length, Area, and Volume: What’s the Difference?
- Difference between \(1D, 2D,\) and \(3D\)
- \(3D, 4D,\) and Beyond in Real Life