One-dimensional
One-dimensional
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Mental exercise
Two-dimensional
Creatures living in Flatland (two-dimensional world) see triangles and other two-dimensional objects as lines.
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One-dimensional and
Two-dimensional world

In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 1, the set of all such locations is called a one-dimensional space.
In physics and mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space. When n = 2, the set of all such locations is called two-dimensional space or bi-dimensional space, and usually is thought of as a Euclidean space.
(Wikipedia)


One-dimensional.


One-dimensional
The animation above shows the observer as a grey line, who is trying to percieve a reality (a 2D circle in this case) in his 1D limited mind. The animated blue line is what he perceives. Note that the reality, the circle, is not changing in time, its radius, colour and all other properties are a part of the reality. The observed thing is very different from this, it is a blue line varying in length WITH TIME. For the observer, it remains a mystery as to what happened to the original full length of line, why and how it changes length and 'pops in and out' of his 'observed reality'.


Two-dimensional.


Two-dimensional
Let's now start analysing a 2D case, that of the classic Flatland example, in which a person lives in a 2D universe and is only aware of two dimensions (shown as the blue grid), or plane, say in the x and y direction. Such a person can never conceive the meaning of height in the z direction, he cannot look up or down, and can see other 2D persons as shapes on the flat surface he lives in.
So, what does a 3D reality sphere look like into a 2D plane? The answer is again graphically shown in the animation, which shows a circle expanding and contracting depending on which slice of the sphere intersects the 2D observation plane.