Explanation
In this lesson, we learn how to understand 3D, 4D, and higher dimensions in real life from a mathematical point of view.
In mathematics, a dimension can be thought of as one independent piece of information.
So, the number of dimensions depends on how many independent inputs we use.
For example:
3D usually means we use three coordinates:
(x, y, z)
These tell us the position of a point in space.
But we can add more information, such as time, temperature, color intensity, wind speed, or pressure.
Each extra independent input can create a new dimension.
3D
A 3D point has three pieces of information:
(x, y, z)
For example, a point on a face or a building can be described by its position:
right / left
forward / backward
up / down
So, 3D means:
location in space
4D
To make a 3D point into 4D, we can add time.
For example:
(x, y, z, time)
This tells us where the point is and when we are looking at it.
So, 4D can mean:
3D space + time
5D
To make it 5D, we can add another input, such as temperature.
For example:
(x, y, z, temperature, time)
Now we know the location, the temperature at that location, and the time.
6D
To make it 6D, we can add another input, such as color intensity.
For example:
(x, y, z, temperature, color intensity, time)
Now the point has six pieces of information.
The key idea is:
In mathematics, the number of dimensions equals the number of independent inputs.
Formula / Rule
A simple rule is:
Number of dimensions = number of independent inputs
Examples:
3D → (x, y, z)
4D → (x, y, z, time)
5D → (x, y, z, temperature, time)
6D → (x, y, z, temperature, color intensity, time)
We usually put time at the end, so it is easier to read the location first and the time last.
Example
Suppose we choose a point on a face.
First, we describe its 3D location:
(0, 4, 2)
This means:
x = 0 → no movement right or left
y = 4 → moved forward
z = 2 → moved up
So, this is a 3D point.
Now add time:
(0, 4, 2, 1)
This is 4D because we added time.
Now add temperature:
(0, 4, 2, 37, 1)
This is 5D because we added temperature.
Now add color intensity:
(0, 4, 2, 37, 0.5, 1)
This is 6D because we added color intensity.
So, each time we add one independent input, the number of dimensions increases by one.
Video Explanation
Practice
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