Axial symmetry in the context of "Paraboloid of revolution"

⭐ In the context of a paraboloid of revolution, axial symmetry is considered…

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⭐ Core Definition: Axial symmetry

Axial symmetry is symmetry around an axis or line (geometry). An object is said to be axially symmetric if its appearance is unchanged if transformed around an axis. The main types of axial symmetry are reflection symmetry and rotational symmetry (including circular symmetry for plane figures and cylindrical symmetry for surfaces of revolution). For example, a baseball bat (without trademark or other design), or a plain white tea saucer, looks the same if it is rotated by any angle about the line passing lengthwise through its center, so it is axially symmetric.

Axial symmetry can also be discrete with a fixed angle of rotation, 360°/n for n-fold symmetry.

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👉 Axial symmetry in the context of Paraboloid of revolution

In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry.

Every plane section of a paraboloid made by a plane parallel to the axis of symmetry is a parabola. The paraboloid is hyperbolic if every other plane section is either a hyperbola, or two crossing lines (in the case of a section by a tangent plane). The paraboloid is elliptic if every other nonempty plane section is either an ellipse, or a single point (in the case of a section by a tangent plane). A paraboloid is either elliptic or hyperbolic.

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Axial symmetry in the context of Rolling

Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are in contact with each other without sliding.

Rolling where there is no sliding is referred to as pure rolling. By definition, there is no sliding when there is a frame of reference in which all points of contact on the rolling object have the same velocity as their counterparts on the surface on which the object rolls; in particular, for a frame of reference in which the rolling plane is at rest (see animation), the instantaneous velocity of all the points of contact (for instance, a generating line segment of a cylinder) of the rolling object is zero.

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Axial symmetry in the context of Metal spinning

Metal spinning, also known as spin forming or spinning or metal turning most commonly, is a metalworking process by which a disc or tube of metal is rotated at high speed and formed into an axially symmetric part. Spinning can be performed by hand or by a CNC lathe.

The metal spinning trade is one that dates back to antiquity and was a skill used in the Ancient Egyptian era. This is when metal spinning was limited to soft metals spun by human power on primitive lathes. The technique gave significant advances to hydro and steam power in Europe and North America in the 19th century and by the early 20th century the electric motor provided the necessary power and high-speed turning capability. With this advancement, metal spinning craftsmen were now able to spin higher quality pieces made out of brass, copper, aluminum and even stainless and cold-rolled steel.

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Axial symmetry in the context of Concentric objects

In geometry, two or more objects are said to be concentric when they share the same center. Any pair of (possibly unalike) objects with well-defined centers can be concentric, including circles, spheres, regular polygons, regular polyhedra, parallelograms, cones, conic sections, and quadrics.

Geometric objects are coaxial if they share the same axis (line of symmetry). Geometric objects with a well-defined axis include circles (any line through the center), spheres, cylinders, conic sections, and surfaces of revolution.

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LINKED FROM (PARENTS)
← Paraboloid of revolution ← Rolling ← Metal spinning ← Concentric objects ← Paraboloid ← Hyperbolic paraboloid ← Concentric
LINKS TO (CHILDREN)
Surface of revolution → Symmetry → Line (geometry) → Geometric transformation → Reflection symmetry → Rotational symmetry → Circular symmetry → Cylindrical symmetry → Baseball bat → Saucer → Discrete symmetry →