Study math for long enough and you will likely have cursed Pythagoras's name, or said "praise be to Pythagoras" if you're a bit of a fan of triangles.
But while Pythagoras was an important historical figure in the development of mathematics, he did not figure out the equation most associated with him (a2 + b2 = c2). In fact, there is an ancient Babylonian tablet (by the catchy name of IM 67118) that uses the Pythagorean theorem to solve the length of a diagonal inside a rectangle. The tablet, likely used for teaching, dates from 1770 BCE – centuries before Pythagoras was born in around 570 BCE.
Another tablet from around 1800–1600 BCE has a square with labeled triangles inside. Translating the markings from base 60 – the counting system used by ancient Babylonians – showed that these ancient mathematicians were aware of the Pythagorean theorem (not called that, of course) as well as other advanced mathematical concepts.
"The conclusion is inescapable. The Babylonians knew the relation between the length of the diagonal of a square and its side: d=square root of 2," mathematician Bruce Ratner writes in a paper on the topic. "This was probably the first number known to be irrational. However, this in turn means that they were familiar with the Pythagorean Theorem – or, at the very least, with its special case for the diagonal of a square (d2 = a2 + a2 = 2a2) – more than a thousand years before the great sage for whom it was named."
So why did this get attributed to Pythagoras? No original writing from Pythagoras survives. What we know of him was passed on by others, in particular the Pythagoreans – members of a school he set up in what is now modern-day southern Italy. The school, named the Semicircle of Pythagoras, was secretive, but knowledge learned there or discovered was passed on, and often attributed to the man himself.
"One reason for the rarity of Pythagoras original sources was that Pythagorean knowledge was passed on from one generation to the next by word of mouth, as writing material was scarce," Ratner continued. "Moreover, out of respect for their leader, many of the discoveries made by the Pythagoreans were attributed to Pythagoras himself; this would account for the term ‘Pythagoras’ Theorem’."
Though Pythagoras did not come up with the theory, his school certainly popularized it, and it became associated with him for the next few thousand years, at least.
An earlier version of this article was published in October 2023.
Archaeologists discover feline and anthropomorphic geoglyphs in Ica
A team of archaeologists from the San Luis Gonzaga National University of Ica (Unica) have discovered 29 geoglyphs in the Ica region of Southern Peru.
The discovery was made in the districts of El Ingenio and Changuillo, where the team identified 29 geoglyphs that depict feline and anthropomorphic figures.
According to the researchers, the geoglyphs date from between 300 BC to AD 100, corresponding with the late Paracas period and early Nasca period.
The Paracas was an Andean culture that merged around 800 BC. Many geoglyphs in the region have been associated with the Paracas, including the Palpa Geoglyphs in the area around the present-day town of Palpa, and the Paracas Candelabra
It is believed that the Paracas culture was the precursor to the Nasca culture that emerged around 100 BC. While many Nasca geoglyphs represent various living creatures, such as stylised hummingbirds, spiders, monkeys, fish, sharks, orcas, lizards, and plants etched onto the flat desert terrain, the Paracas Geoglyphs are comparatively more enigmatic. They feature motifs depictions reminiscent of Paracas petroglyphs, along with ambiguous human-like figures or warriors.
A recent study using drones in the Ica region has identified 10 geoglyphs in the El Ingenio District that feature feline figures measuring up to 17 metres long by 12 metres tall, while in the Changuillo District, the team found 8 geoglyphs depicting feline figures measuring up to 37 metres long by 13 metres tall.
The remainder of the geoglyphs identified show anthropomorphic figures, 10 of which were found in the El Ingenio District, while 1 anthropomorphic figure was found in the Changuillo District.
According to the researchers, the Paracas regarded felines as a water deity and linked them closely with concepts of fertility.
