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Dimension
Dimension is one of the most important concepts in our daily lives because we live in a multi-dimensional world, but surprisingly, throughout our studies, we have never defined it explicitly. The concept of the dimension of a given object can be explained by a number of independent motion orientations of any point belonging to that object. For example, a point cannot move in any direction, and therefore, a point is 0. On any line or curve, the point can move forward or backward, and therefore, the dimension of a curve (or line) is 1-this is like a train on the tracks). The distance can move in two independent directions, and therefore, from dimension 2 (this is similar to the movement of a car on a plane - it can move in the direction of the x-axis or in the direction of the y-axis, but it cannot detach from the ground). When we look at the space, we get 3 possible motion directions for each point, and therefore, the dimension of space is 3 (it is similar to the movement of an airplane - it can move in 3 independent directions - in the direction of the x-axis or the y- z - meaning both up and down).
During the course, "When Mathematics Meets Art", we not only clarified the definition of dimension, but also learned a formula for calculating dimension. We also expanded the geometric knowledge by presenting shapes that do not belong to Euclidean geometry and whose dimension is not an integer. These shapes are called fractals and have unique mathematical properties as well as great visual beauty. Here are some sample forms:
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