A spherical shell is a three-dimensional hollow structure that is shaped like a sphere. It is typically defined as the space between two concentric spherical surfaces — an outer surface and an inner surface. The shell has a certain thickness, which is the difference between the radii of the outer and inner surfaces. Key characteristics of a spherical shell include: 1. **Outer Radius (R_outer)**: The radius of the outer surface of the shell.
Tarski's axioms refer to a set of formal axioms proposed by the Polish logician and mathematician Alfred Tarski, particularly in his work on the semantics of formal languages and the theory of truth. Tarski is best known for his semantic definition of truth, which he formalized in the early 20th century.
In geometry, translation refers to a type of transformation that moves every point of a figure or object a constant distance in a specified direction. This motion is uniform, meaning that all points move the same distance and in the same direction, resulting in a shape that is congruent to the original. Key characteristics of translation include: 1. **Vector Representation**: A translation can be represented using a vector, which indicates the direction and distance of the movement.
In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal crosses two lines, it creates several pairs of angles that have specific relationships. For instance: 1. **Corresponding Angles**: Angles in the same relative position at each intersection. If the lines are parallel, corresponding angles are equal. 2. **Alternate Interior Angles**: Angles that are on opposite sides of the transversal and inside the two intersected lines.