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Time translation symmetry is a concept in physics, particularly in the context of classical mechanics and field theory, that indicates that the laws of physics do not change over time. This means that the physical laws that govern a system remain invariant regardless of when the system is observed.

Transformation geometry is a branch of mathematics that focuses on the study of geometric figures and their properties under various transformations. These transformations can change the position, size, or orientation of the figures, while often preserving some of their fundamental properties. Some of the primary types of transformations in geometry include: 1. **Translation**: Moving a figure from one place to another without changing its shape, size, or orientation. This is done by shifting every point of the figure a certain distance in a specified direction.

Translational symmetry is a property of a system or object that remains unchanged when it is shifted or translated in space by a certain distance in a specific direction. In other words, if you can move the entire system a certain distance and it still looks the same, then it has translational symmetry. This concept is commonly observed in various fields such as physics, mathematics, and art.

A triptych is a work of art that is divided into three sections or panels. These panels are usually hinged together and can be displayed either open or closed. Triptychs have been used in various forms of art throughout history, particularly in painting, but they can also be found in sculpture and photography. Traditionally, triptychs were common in medieval Christian art and often depicted religious scenes, such as altarpieces in churches.

A triskelion, also known as a triskeles or triplex, is an ancient symbol consisting of three interlocked spirals or three bent human legs. The design is typically arranged in a rotating pattern, which can symbolize motion and progress.

Yang–Mills theory is a fundamental framework in theoretical physics that describes the behavior of gauge fields. Named after physicists Chen-Ning Yang and Robert Mills, who proposed it in 1954, the theory is a cornerstone of the Standard Model of particle physics, which describes the electromagnetic, weak, and strong forces.

Zimmer's conjecture is a significant hypothesis in the field of mathematics, particularly in the areas of differential geometry, group theory, and dynamical systems. Proposed by Robert Zimmer in the 1980s, the conjecture suggests that any smooth action of a higher-rank Lie group on a compact manifold admits some form of rigidity.