obliqkartio

Obliqkartio is a geometric solid defined as a cone whose apex is displaced laterally relative to the base plane, producing an oblique cone based on a circular base. The term blends oblique with kartio, the Finnish word for cone, and appears in some geometrical descriptions and CAD tutorials to denote this orientation of a cone.

Construction and shape: The base is a circle of radius R in the plane z = 0. The apex is at (d, 0, h) with h > 0 and d ≠ 0. The surface consists of all straight line generators joining the apex to points of the base circle. Because the apex is not above the base center, the axis is slanted and the cross-sections parallel to the base are ellipses. A plane that passes through the apex intersects the solid in a triangle.

Properties: The lateral surface is a ruled surface generated by lines from the apex to the base. Like other cones, the obliqkartio is a developable surface and can be unfolded into a planar region, though it is not a cone of revolution.

Applications: Obliqkartio appears in computer graphics, geometric modeling, and architectural visualization to illustrate oblique conical shapes, tapering structures, and conic-section behavior. It also serves as an instructional example of how shifting the apex affects cross-sections and surface properties.

See also: Cone, Oblique cone, Conic sections, Developable surface.

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