In geometry, especially, the term **center** appears in several cases; however in all of them it refers to a point of a geometric figure ^{[1]} . And in a careful look, it is concluded that such a point is linked to a certain type of symmetry.

## Summary

[ hide ]

- 1 Various cases
- 2 References
- 3 See also
- 4 Bibliography

## Various cases

Center of symmetry.

Let the points P, P ‘be any and C a given point, the three collinear ones, if the distance from C to P is the same as from C to P’, C is said to be the **center of symmetry** .

- The midpoint of a segment is center of symmetry.
- the intersection of the diagonalsof a rhombus is the center of symmetry of the points of the rhombus
- the intersection of the diagonals of a rectangleis the center of symmetry of the points of the rectangle.
- The intersection of the diagonals of an orthohedron(rectangular rectangular parallelepiped) is the center of symmetry of the points of the faces of said solid.
- The intersection of the three axes of an ellipsoidis the center of symmetry of such a figure.

Of the circumference

Its center is a point on its plane, so the distance from any point is the same. This distance and the segment that unites them is called, interchangeably. *radio* . ^{[2]} . The center is not a point on the circumference.

From the circle

Given a circle, the set of points whose distance is less than or equal to the radius of the circle is called a *circle* . The circle has as its center the same point that is also the center of the circumference.

Of the ellipse

The point where the axes of the ellipse intersect is called the *center* .

Square

It is the intersection of its two diagonals; serves as the center of the inscribed circumference, as circumscribed

Of the regular triangle

The center is the intersection of its perpendicular bisectors

Of the regular polygon

the intersection of the bisectors of the interior angles.

Of the regular tetrahedron

The intersection of the segments that join the center of each face with the opposite vertex

From the bucket

The intersection of the four diagonals

Of the sphere

It is the point from which all points on the surface are equidistant.

Of hyperbola

the intersection of the focl axis and the transversal axis

From an algebraic group

Let G be a group with multiplicative notation, its center is a subset of G, defined thus: Z (G) = {z ε G / zg = gz for all g of G} ^{[}