What type of column is characterized as a half-round column attached to a wall?

The half-round column that is attached to a wall is known as an engaged column. Engaged columns serve both decorative and structural purposes, projecting from the wall to which they are attached, while often retaining the classical features associated with full columns. This design allows for the visual aesthetics of a column without the need for it to stand freely, making it a popular choice in various architectural styles throughout history.

Engaged columns can enhance the perception of depth and add to the grandeur of a building's facade. They are commonly found in structures influenced by classical architecture, where they mimic the appearance of full columns while providing support to the wall and contributing to the overall compositional elements of the design.

In contrast, the other options like composite, pillar, and Corinthian columns refer to different styles or types of columns. The composite column blends features of the Ionic and Corinthian orders, a pillar generally refers to a more generic vertical support structure, and the Corinthian column is characterized by its ornate capital. Understanding these distinctions helps illustrate why the engaged column stands out as a unique architectural element.