# How do shapes affect structure?

From the Roman arches to the triangular Great pyramids to religious domes and the variety of quadrilaterals found on steel-frame buildings of the 20th century, architecture is largely predicated on shapes. The mathematical attributes of shapes are necessary to the design of any standing structure.

Arch

The Romans first used arches around 273 B.C. Arches served as entrances for large, outdoor public spaces. Today, arches are found on porches, doorways and windows. The shape of the arch allows more weight to be placed on top of it, thus creating larger openings to the outside. The connected wedges that form an arch takes away the vertical pressure and gives it lateral pressure, allowing it to be one of the sturdiest shapes in architecture. Circle

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. This allows for cool and warm air to flow easily. Domes are considered environmentally friendly. Triangle

A triangle's relationship between intersecting angles and length make it 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. Quadrilateral

Rectangles and parallelograms are the most used shapes in architecture. 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 π. In mathematics, this means that the long side can be divided by the smaller side and equal to the whole length divided by the longer side. Golden rectangles are prevalent in architecture,...

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