In architecture, geometry is everywhere you look! Buildings are designed to have an appealing shape that elicits reactions such as wonder at their scale or desire to touch them.

Landscape architects design gardens to use natural curves and shapes of land to create tranquil spaces. City planners determine how much space each building has by figuring out how many feet high it is and then dividing this number into what is already known as the “footprint” of the lot it sits on.

Architects also apply mathematics in designing structures. They measure distances between things and figure out which triangles they form using various rules. These rules help ensure that the structure functions properly and that it does not break down due to stress caused by internal forces.

Mathematics plays a significant role in shaping our surroundings for good or bad depending on who uses it and why. This article will go more in depth about some examples of how geometry is used in architectural fields and concepts.

Construction lines

Another fundamental concept in architecture is construction lines or axis. These are boundaries that separate one part of your building from another. For example, if your house has an attached garage, then there would be a construction line between the garage and the house.

The architect designs the space within this boundary with care. For instance, you may want to have the garage as an extension of your home so it feels like it’s a part of yours. Or maybe you wanted to create an outdoor feel by having less interior walls, etc.

These design decisions are influenced by what materials you use in the structure and how they relate to each other. For instance, using wooden doors instead of glass will help give the feeling of nature. A brick exterior gives some weight and stability.

Architecture is more than just designing pretty buildings, it is also about understanding basic concepts such as these.

Plan shapes

Another fundamental shape used in architecture is called a plan shape. These are two-dimensional figures that have an interior and exterior, as well as lower and upper boundaries. Some examples of plan shapes are squares, rectangles, ovals, triangles, and circles.

Triangle shapes are one example — think about how most buildings have a triangular roof. A triangle is formed by three lines intersecting at a common point. The word “triangular” comes from this intersection pattern.

Circle shapes are another example –think of the circle windows in many skyscrapers. A circle is defined by a center and radius, where the radius is length of line segment connecting center to circumference.

Other famous architectural shapes include the octagon (eight sided figure) and the hexagon (six sided figure). Both these shapes contain eight or six sides respectively.

These similarities between different geometric forms make it easy to apply geometry to study them. For instance, you can find the area of a circle using π times the diameter, which both are invariant properties. This means once you know one, you know the other!

The area of a square box = half base x height

The area of a rectangle = width × height

The area of an oval = major axis * minor axis / 2

Area is also found via distance formula.

Design elements

Another integral part of architecture is designing specific shapes and patterns. These are called design elements or motifs. A common example of this is the use of triangles as an element to be re-used throughout different designs.

Triangles play a significant role in geometry, most notably right triangle concepts like angles, areas, and perimeters. They also form half of a square which makes them important for creating squares and rectangles.

A circle is the purest shape built out of three lines that have a constant radius. This creates very symmetrical looking shapes that relate back to nature. Plants and flowers are great examples of this.

Architectural styles often feature geometric forms such as circles, squares, or triangles. These proportions are studied and learned to make waves in the field of art and decoration. It is not uncommon to see these forms in home decorations and furniture.

The way they are organized and balanced is what makes some more appealing than others. When used effectively, there are many ways they can be applied.