The word "symmetry" comes from Greek συμμετρία and is translated as "harmony". Frequent an element concerning which it is possible to call a figure symmetric is a certain imagined line. Such piece is called an axis of symmetry of a figure.
Some figures, for example, have no versatile triangles or parallelograms of an axis of symmetry, other than a rectangle. Others them can have 1, 2, 4 or even an infinite set.
Whether the cylinder has a symmetry axis
Basic elements of a cylinder are two circles and all pieces connecting them circles. Circles at cylinders are called the bases, and pieces — forming.
The axis of symmetry divides a figure into two specularly identical parts. That is in symmetric figures each point has a point, symmetric concerning this axis, belonging to the same figure.
The cylinder is a rotation body. That is it is formed at rotation of a rectangle around one of the parties. The axis of symmetry of a cylinder which is only available for this figure one also coincides with this party.
At a direct cylinder the axis of symmetry passes through the centers of the bases. At the same time its length is equal to height of the figure. Section of a cylinder parallel to a symmetry axis represents a rectangle, perpendicular — a circle.
Order of an axis of symmetry of a cylinder
At geometrical figures there can be axes of symmetry of any orders — from the first and to infinite. Figures with an axis of the second order at turn around it, for example, are combined with themselves twice, including a starting position. Regular pyramids and prisms with even number of sides and also rectangular parallelepipeds differ in such properties.
The cylinder will coincide with itself at turn on any corner. Therefore it is considered that such figure has an axis of rotation of an infinite order.
Symmetry planes
Besides an axis, the cylinder has also the symmetry planes. Such planes specularly reflect the second half of a figure, completing it as whole. One of the symmetry planes at cylinders passes through the center perpendicular to a rotation axis.
Also the planes of symmetry of such figures are all planes containing an axis of their symmetry. The bases at cylinders represent circles. Osei of symmetry is available for circles a set. Respectively, and the cylinder will have an infinite set of the planes of symmetry coinciding with an axis of its rotation.