Math and Mystery of the Inca

The Inca first emerged near Cusco, Peru, around the 12th or early 13th century. For many generations, they lived in a relatively small region. Then, during the 15th century, Inca rulers rapidly expanded their territory through conquest and diplomacy. By the time the Spanish arrived in the 1530s, the Inca Empire stretched across South America from present-day Chile to Colombia.

Knot for Everyone

The Inca kept records using a system of knotted cords called a quipu. Using a base-10 system, they tied knots to represent place values, similar to the numbers we use today. The colors and arrangement of the cords probably helped organize different types of information. Trained experts created, read, and cared for these important records.

In addition to the quipu, the Inca used a counting board, similar to an abacus, called a yupana. Some were small enough to carry, while others may have been carved into stone or built into floors. Unfortunately, there is not enough information to know exactly how this tool was used.

Amazing Architecture

The Inca were expert architects and engineers even without the use of wheels, draft animals, or iron tools. In a short period of time, they created a sophisticated network of roads and structures. Many of them are still standing today.

Ancient Inca masonry was so precise that some structures were assembled without the use of mortar. It is said that their stones fit together so perfectly that a knife blade could not fit between them. The interlocking pieces, sloping walls, and trapezoid-shaped openings also helped many buildings withstand earthquakes. During some powerful tremors, newer sites were badly damaged while nearby Inca walls remained intact.

Perhaps the most impressive structures can be found at the renowned Machu Picchu. This mountaintop settlement was built during the 15th century, most likely as a royal estate for the emperor and his household. Stone stairways wind through it, connecting its many levels and buildings. Rather than serving as a military fortress, it appears to have been a place for living and working.

Machu Picchu was abandoned around the time of the Spanish conquest. Disease, warfare, and the collapse of the Inca government may all have contributed, but nobody knows for certain. Archaeologists have found little evidence that conquistadors ever reached the site.

From Every Angle

If you visit this site, you’ll see many geometric features. For example, parallel terraces built into the side of the mountain were used for farming and provided support for the slopes. Many windows and doorways are shaped like trapezoids, which may have made the buildings more stable. The Temple of the Sun has a curved, semicircular wall, and one of its windows lines up with the rising sun around the June solstice.

Geometric features are also found in many other Inca sites, such as Ollantaytambo and Sacsayhuamán. Although the Inca Empire lasted for only a short time, it left a lasting legacy that still intrigues and amazes people today!

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