By Jonny Lupsha, News Writer

The architects of the world’s oldest-known temple knew complicated geometry, Science Alert reported. The design and structure of the Turkish place of worship both surpass what was believed to have been known about mathematics at the time. Ancient geometry dates back several millennia.

According to Science Alert, an 11,000-year-old temple in Turkey called Göbekli Tepe was discovered in the 1990s and has been studied ever since. Recent looks at its architecture have revealed some surprising information.

“[Göbekli Tepe] was designed with an understanding of geometric principles somewhat unusual for the hunter-gatherer cultures thought to have built it,” the article said. “According to researchers, who used a spatial algorithm to measure and analyze the architectural form of Göbekli Tepe’s layout, the complex is not made up of separate, unrelated structures, but by linked enclosures and pillars that were designed together according to a single design plan—and which might have even been constructed at the same time, in contrast with previous thinking.”

Geometry as it’s known today dates back several thousand years, though its study looked much different.

Origins of Geometry

Most people don’t often think of where fields of mathematical study originated. We know our numbers are Arabic; we know the mathematical tools that are used in algebra, calculus, and so on, but where does something like geometry come from?

“The word ‘geometry’ comes from the Greek word ‘ge,’ meaning ‘earth,’ and ‘metria,’ meaning ‘measure,’” said Dr. James Tanton, Mathematician in Residence at the Mathematical Association of America. “Geometry—earth measure. As the name suggests, the study of geometry evolved from very practical concerns with regard to accurately measuring tracts of land, with issues of navigation, of architecture, and engineering and the like.”

One of the earliest examples of practical geometry dates back to 1950 BCE in ancient Egypt. Dr. Tanton said that workers in the fields would often need to measure perfect right angles, which are 90 degrees. To do this, many scholars believe they would make a length of rope with 13 evenly spaced knots, resulting in 12 even spaces between the knots. They would then measure off four spaces vertically and place a heavy stone at the end of the fourth space. One person would hold up this first section of rope, while other people would continue measuring.

Then, they would measure three more spaces sticking out along the floor and place a second stone at the end of the third space. Lastly, they would hold the remaining five measured spaces of rope and move it at an angle until the end of the rope touched the first end of the rope that one of the workers held.

This gave them a triangle that measured four units vertically, three units horizontally along the bottom, and five units diagonally, also called a 3-4-5 triangle. The angle at the point weighed down by the first stone—where the vertical length meets the horizontal length—was a right angle.

Thales, Father of Geometry

“The Greek mathematician Thales of Ionia of the year 600 BCE, roughly, is dubbed ‘the Father of Geometry’ because he’s the first person in recorded history to have written down a geometric result and a line of reasoning to explain why it’s true,” Dr. Tanton said. “Thales said [to] draw a circle, and then draw a diameter [through] that circle. And what Thales proved was if you draw any angle from that diameter to a point on that circle, then that angle is sure to be a perfect 90-degree angle, just like those angles in the 3-4-5 triangles, apparently.”

This became known as Thales’ Theorem, and Thales proved that the reverse of the theorem is also true—that if you ever draw an angle from a point on a circle and that angle is a perfect 90 degrees, then it must have come from the diameter.

It may not seem very practical at first, but thanks to Thales’ Theorem, farmers can find the center of a circular plot of land for their crops—very handy for positioning sprinklers for central pivot irrigation—and archaeologists can determine the size of broken circular artifacts so they know what to look for and how to reconstruct them.

Right angles made with ancient ropes and at the edges of circles are some of our earliest documented uses of geometry, but Göbekli Tepe seems to show far more geometric knowledge than that and it predates Egypt’s knotted ropes by some 7,000 years. There’s no telling what archaeologists will find out as they continue to research it.

Dr. James Tanton contributed to this article. Dr. Tanton is the Mathematician in Residence at the Mathematical Association of America (MAA). He earned a Ph.D. in Mathematics from Princeton University.