Symmetrical in the context of Rotation (mathematics)

Romanesque architecture is an architectural style of medieval Europe that was predominant in the 11th and 12th centuries. The style eventually developed into the Gothic style with the shape of the arches providing a simple distinction: the Romanesque is characterized by semicircular arches, while the Gothic is marked by the pointed arches. The Romanesque emerged nearly simultaneously in multiple countries of Western Europe; its examples can be found across the continent, making it the first pan-European architectural style since Imperial Roman architecture. Similarly to Gothic, the name of the style was transferred onto the contemporary Romanesque art.

Combining features of ancient Roman and Byzantine buildings and other local traditions, Romanesque architecture is known by its massive quality, thick walls, round arches, sturdy pillars, barrel vaults, large towers and decorative arcading. Each building has clearly defined forms, frequently of very regular, symmetrical plan. The overall appearance is one of simplicity when compared with the Gothic buildings that were to follow. The style can be identified right across Europe, despite regional characteristics and different materials.

In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape.

Peitgen et al. explain the concept as such:

A gambrel or gambrel roof is a usually symmetrical two-sided roof with two slopes on each side. The upper slope is positioned at a shallow angle, while the lower slope is steep. This design provides the advantages of a sloped roof while maximizing headroom inside the building's upper level and shortening what would otherwise be a tall roof, as well as reducing the span of each set of rafters. The name comes from the Medieval Latin word gamba, meaning horse's hock or leg. The term gambrel is of American origin, the older, European name being a curb (kerb, kirb) roof.

Europeans historically did not distinguish between a gambrel roof and a mansard roof but called both types a mansard. In the United States, various shapes of gambrel roofs are sometimes called Dutch gambrel or Dutch Colonial gambrel with bell-cast eaves, Swedish, German, English, French, or New England gambrel.

A bow tie or dicky bow /boʊ/ is a type of neckwear, distinguishable from a necktie because it does not drape down the shirt placket, but is tied just underneath a winged collar. A modern bow tie is tied using a common shoelace knot, which is also called the bow knot for that reason. It consists of a ribbon of fabric tied around the collar of a shirt in a symmetrical manner so that the two opposite ends form loops.

There are generally three types of bow ties: the pre-tied, the clip-on, and the self-tie. Pre-tied bow ties are ties in which the distinctive bow is sewn onto a band that goes around the neck and clips to secure. Some "clip-ons" dispense with the band altogether, instead clipping straight to the collar. The traditional bow tie, consisting of a strip of cloth that the wearer has to tie by hand, is also known as a "self-tie", "tie-it-yourself", or "freestyle" bow tie.

An imperial staircase (sometimes erroneously known as a "double staircase") is the name given to a staircase with divided flights. Usually the first flight rises to a half-landing and then divides into two symmetrical flights both rising with an equal number of steps and turns to the next floor. The feature is reputed to have first been used at El Escorial. One of the grandest examples, the Escalier des Ambassadeurs at the Palace of Versailles, was built by 1680 but demolished in 1752 as the palace was rearranged. The Jordan Staircase of the Winter Palace is a notable example, while other such staircases can be found at Buckingham Palace, Windsor Castle, Palazzo Reale di Caserta, Palacio Real de Madrid and Mentmore Towers.

The advantages of an imperial staircase became apparent during the 18th century, when Matthew Brettingham revolutionised the design of the piano nobile of the London town house. Guests would proceed through a series of reception rooms arranged as a circuit. At large gatherings the two branches could ease the flow of guests arriving and departing, or moving between a ballroom and a supper room on the floor below. An imperial staircase is often used today for similar reasons where two streams of people are moving in opposite directions in buildings as diverse as an opera house to a railway station. This use explains why the first single flight is often wider than the following two divided flights, although narrowing flights are also an architectural trick to lengthen perspective in order to increase the impression of size.