keskisymmetrian

Keskisymmetria, also known as point symmetry or central symmetry, is a type of geometric symmetry where an object is symmetric with respect to a fixed point. If an object possesses keskisymmetria, it means that for every point on the object, there is a corresponding point on the opposite side of the center of symmetry, such that the center point is the midpoint of the line segment connecting these two points. In simpler terms, if you rotate an object 180 degrees around its center of symmetry, it will appear unchanged.

A common example of an object with keskisymmetria is a rectangle, where the center point is the intersection of its diagonals. If you rotate a rectangle 180 degrees about this intersection point, it will land exactly on top of its original position. Other shapes like circles, parallelograms, and regular hexagons also exhibit keskisymmetria.

In three-dimensional space, keskisymmetria applies similarly. A sphere, for instance, is symmetric with respect to its center. A cube also has keskisymmetria; its center is the midpoint of any space diagonal. Mathematically, a set $S$ in a vector space has keskisymmetria about a point $c$ if for every point $x$ in $S$, the point $c - (x - c) = 2c - x$ is also in $S$. If the center of symmetry is the origin (0,0), then this condition simplifies to: if $x$ is in $S$, then $-x$ is also in $S$. Keskisymmetria is a fundamental concept in geometry and appears in various branches of mathematics and physics.

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