Quadrics example sentences

"Quadrics" Example Sentences

1. Quadrics are mathematical expressions used to describe the three-dimensional shape of an object.
2. A hyperboloid is an example of a quadric that curves outward like a saddle.
3. The paraboloid is a quadric that curves upward in a bowl shape.
4. Quadrics can be used to model the shapes of planets and asteroids.
5. The quadric surface known as an ellipsoid can be used to model the shape of Earth.
6. Quadrics are often used in computer graphics to create realistic 3D models of objects.
7. The quadric surface known as a torus can be used to model the shape of a donut.
8. Quadrics can be classified as elliptic, hyperbolic, or parabolic based on their mathematical properties.
9. The quadric surface known as a hyperboloid of two sheets has two separate branches.
10. The intersection of two quadrics is called a quadric section.
11. A cone is a type of quadric with a circular base and a pointed apex.
12. Some quadrics can be expressed as the sum or difference of squares of linear expressions.
13. The ellipsoid is a quadric surface that is symmetric in all three dimensions.
14. The quadric surface known as a hyperboloid of one sheet has a single branch that curves outward.
15. Quadrics can be used to model the shape of lenses, mirrors, and other optical components.
16. The quadric surface known as a hyperbolic paraboloid is saddle-shaped and has negative curvature.
17. Some quadrics can be expressed in terms of conic sections, such as circles, ellipses, and hyperbolas.
18. The quadric surface known as an elliptic paraboloid curves upward in two directions and downward in one.
19. Quadrics can also be used to model the shapes of molecules in chemistry.
20. The quadric surface known as a sphere is a special case of an ellipsoid.
21. The quadric surface known as a hypercone has a conical shape with an opening angle greater than 90 degrees.
22. The quadric surface known as a hyperbolic cylinder is shaped like a tube that curves outward.
23. Quadrics can be described using matrices and linear algebra.
24. The quadric surface known as a parabolic cylinder curves upward in one direction and is straight in the other.
25. Some quadrics can be expressed as the product or quotient of linear expressions.
26. The quadric surface known as a hyperbolic ellipsoid is curved like a saddle in all three dimensions.
27. Quadrics can also be used to model the shapes of clouds and weather patterns.
28. The quadric surface known as a hyperbolic cone has a conical shape with an opening angle less than 90 degrees.
29. The quadric surface known as an elliptic hyperboloid is shaped like a saddle in two directions and like a cup in the other.
30. Some quadrics can be described as degenerate, meaning they have lost some of their defining properties.

Common Phrases

1. Quadrics are second-degree algebraic curves;
2. Quadrics in 3D space can be represented as ellipsoids, paraboloids or hyperboloids;
3. The surface of a quadric can be defined by a quadratic equation with variables x, y, and z;
4. In computer graphics, quadrics are used to create 3D objects such as spheres, cones, and cylinders;
5. Quadrics are useful in optimization problems involving nonlinear equations;
6. The study of quadrics is fundamental in algebraic geometry and differential geometry.