The Romans first used arches around 273 B.C. Arches served as entrances for large, outdoor public spaces. Today, arches are for porches, doorways and windows. The wedge shape of the arch allows for more weight to be placed on top of it, thus it enables larger openings to the outside. The interconnected wedges that form an arch relieve it of vertical pressure and give it lateral pressure, allowing it to be one of the sturdiest shapes in architecture. Different styles of arches include Gothic, Tudor and Moorish arches.
Circles in architecture are mostly found in domes. Domes are important structures in architecture because they support themselves -- they don't require pillars to stand them up. The advantages of a dome include improved ventilation because of the heightened ceiling and a lack of hindering structures within it, allowing for cool and warm air to flow much more easily than in other kinds of buildings. Domes are considered environmentally friendly. Most sports arenas are domes.
Because of a triangle's relationship between intersecting angles and length, triangles may be the most reliable shape in architecture. When you change the angle of a triangle, you change its length as well. The triangle is a stable shape that is a great weight bearer because it's widest at its base. Triangles are often used as internal support pieces.
Rectangles and parallelograms are the most used shapes in architecture, although squares, rhombuses and trapezoids are in rare creative designs. While rectangles are weak and need structural support, such shapes are generally more economical to construct. A golden rectangle is one that has a proportional ratio of phi, which in mathematics means that the long side can be divided by the smaller side and be equal to the whole length divided by the longer side. Golden rectangles are prevalent in architecture, both in the interior structure and exterior, like windows, doors and entrances.