# Architecture and Construction Through Mathematics

## Math forges the foundations of buildings

Every building you spend time in––schools, libraries, houses, apartment complexes, movie theaters, and even your favorite ice cream shop––is the product of mathematical principles applied to design and construction. Have you ever wondered how building professionals incorporate math to create the common structures you walk in and out of every day?

Before construction workers can build a habitable structure, an architect has to design it. Geometry, algebra, and trigonometry all play a crucial role in architectural design. Architects apply these math forms to plan their blueprints or initial sketch designs. They also calculate the probability of issues the construction team could run into as they bring the design vision to life in three dimensions.

Since ancient times, architects have used geometric principles to plan the shapes and spatial forms of buildings. In 300 B.C., the Greek mathematician Euclid defined a mathematical law of nature called the Golden Ratio. For more than two thousand years, architects have used this formula to design proportions in buildings that look pleasing to the human eye and feel balanced. It is also known as the Golden Constant because it manifests literally everywhere.

The Golden Ratio still serves as a basic geometric principle in architecture. You could even call it a timeless archetype, as it evokes in human beings a universal sense of harmony when they see or stand in a building designed with this principle. And perhaps not surprisingly, we see the Golden Ratio demonstrated throughout “architectures” of the natural world. Read here to learn more!

Calculating ratio is essential, as well, when it’s time to construct a building from the architectural blueprints. For example, it’s important to get the proportions right between the height and length of a roof. To do that, building professionals divide the length by the height to get the correct ratio.

The Pythagorean theorem, formulated in the 6th century B.C., has also come into play for centuries to calculate the size and shape of a structure. This theorem enables builders to accurately measure right angles. It states that in a triangle the square of the hypotenuse (the long side opposite the right angle) is equal to the sum of the squares of the other two sides. Read here to find out more about how builders use the Pythagorean theorem to make roofs!

The most remarkable ancient architecture of all may be the pyramids of Egypt, constructed between 2700 B.C. and 1700 B.C. Most of them were built and scaled at about a 51-degree angle. The Egyptians clearly and mysteriously possessed knowledge of geometry, as evidenced by the accuracy of pyramid construction. Just in case you’re curious about the geometry and triangle mathematics that ancient Egyptians applied to build their pyramids, read here.

In the modern world, builders use math every day to do their work. Construction workers add, subtract, divide, multiply, and work with fractions. They measure the area, volume, length, and width. How much steel do they need for an office building? How much weight in books and furniture will the library floors need to bear? Even building a small single-family home calls for careful calculations of square footage, wall angles, roofs, and room sizes. How many square yards of carpet? How much water do you need to fill up a swimming pool?

Chances are you’re in a building right now. Look around at the walls and windows. Math is everyplace you walk into––work, school, home, or pet store. Imagine that you are an architect. How would you apply math to build a small dwelling?

### Ali Cunlisk

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