A sphere is a degenerate case of an ellipsoid just as a circle is a degenerate case of an ellipse.Leo Authersh said:Is Sphere a more generalized form of Cone i.e. formed by 2 dimensional rotation to 360° of a cone?
Or is Cone a more generalized form of Sphere since sphere can be formed by rotating about Z axis a zero eccentric planar intersection of a cone?
@fresh_42 @FactChecker @WWGD
This representation is excellent. I remember the term Hyperboloid.fresh_42 said:
Why do you think this?Leo Authersh said:But what confuses me is that, if the hyperboloid is rotated to 90°, we get a cube.
This isn't right, either. Let's look at two dimensions first. The unit square in the first quadrant does not have a single equation. Instead, it has four equations, one for each side, along with inequalities that indicate the minimum and maximum values of the variable on each side. For example, the upper horizontal side would be represented by the equation y = 1, and the inequality ##0 \le x \le 1##. There would be an equation/inequality pair for each side.Leo Authersh said:How is a cube which is a linear geometric form that has one variable be formed by a Hyperboloid that has three variables?
The conical representation of a sphere is a geometric shape that is formed by projecting the surface of a sphere onto a cone. This allows for a visual representation of a spherical object on a flat surface.
The purpose of using a conical representation of a sphere is to accurately depict the surface of a spherical object in a two-dimensional form. This can be useful in various fields such as cartography, astronomy, and engineering.
A conical representation of a sphere is created by placing a cone over a sphere and projecting the points on the sphere's surface onto the cone. The cone is then unrolled onto a flat surface, resulting in a conical representation of the sphere.
One of the main advantages of using a conical representation of a sphere is that it preserves the relative distances and angles between points on the surface of the sphere. This allows for more accurate representations compared to other methods.
A conical representation of a sphere has various real-world applications. It is commonly used in map projections, where the curved surface of the Earth is represented on a flat map. It is also used in the design and construction of spherical objects such as domes and arches.