Tag Archives: circle

Ring of ancient, massive shafts found near Stonehenge

In archeology, sometimes you can teach an old site new tricks, it seems. New research reports the discovery of at least 20 huge shafts forming a circle at Durrington Walls, the site of a stone-age village about 2 kilometers (1.2 miles) from Stonehenge.

The position of the shafts in relation to Durrington Walls and the village of Durrington, UK.
Image credits Vincent Gaffney et al., (2020), intarch.

The discovery of this major, buried monument could help us better understand how the iconic stone circle in England came to be, or what its purpose was.

Ancient digs

“The size of the shafts and circuit surrounding Durrington Walls is currently unique,” says Vince Gaffney, an archaeologist at the University of Bradford and corresponding author of the paper describing the findings.

“It demonstrates the significance of Durrington Walls Henge, the complexity of the monumental structures within the Stonehenge landscape, and the capacity and desire of Neolithic communities to record their cosmological belief systems in ways, and at a scale, that we had never previously anticipated.”

When the shafts were first found, the team assumed they were natural structures, formed by water flowing through the chalky subsurface. However, remote sensing and sampling quickly showed that this wasn’t the case, and that the shafts were built by human hands.

Researchers say the shafts appear to have been dug around 4,500 years ago. Exactly what their purpose was remains unclear, but the team suspects they served a religious purpose, for example acting as a boundary around a circular monument known as the Durrington Walls henge.

The shafts are, on average, 864 metres from Durrington Walls henge, forming a circle around 2 kilometers in diameter. They are over 10 meters (32 feet) in diameter and 5 meters (16 feet) deep. Although 20 have been discovered so far, there are likely more to be found at the site.

“When these pits were first noted it was thought they might be natural features—solution hollows in the chalk,” says Gaffney. But geophysical surveys carried out at the side showed “there was a pattern on a massive scale.”

Britain is a hotbed for archaeology. Stonehenge, built between 3000 B.C. and 1600 B.C., is iconic across much of the world and one of the country’s top tourist attractions, and a feat of engineering during its day — but it’s by no means the country’s only stone circle. These structures are thousands of years old and the reasons why they were built are still poorly understood It was likely a religious or spiritual place, or a means of keeping track of the seasons.

Among the more exciting implications of this finding is that it betrays a relatively advanced understanding of mathematics, without which the ancient builders couldn’t have produced a neat and organized circle on the scale seen here.

The paper “A Massive, Late Neolithic Pit Structure associated with Durrington Walls Henge” has been published in the journal Internet Archaeology.


What is Pi (π) and what is it good for?

If you have a straight line but want a circle, you’re going to need some Pi.


Image via Max Pixel.

I’m talking about the number, not the delicious baked good. It’s usually represented using the lowercase Greek letter for ‘p’, ‘π’, and probably is the best known mathematical constant today. Here’s why:

The root of the circle

Pi is the ratio of a circle’s diameter to its circumference. No matter the size of a circle, its diameter will always be roughly 3.14 times shorter than its circumference — without fail. This ratio, π, is one of the cornerstones upon which modern geometry was built.

Bear in mind that (uppercase) ∏ is not the same as (lowercase) π in mathematics.

For simplicity’s sake, it’s often boiled down to just two digits, 3.14, or the ratio 22/7. In all its glory, however, pi is impossible to wrap your head around. It’s is an irrational number, meaning a fraction simply can’t convey its exact value. Irrational numbers include a value or a component that cannot be measured against ‘normal’ numbers. For context, there’s an infinite number of irrational numbers between 1.1 and 1.100(…)001. They’re the numbers between the numbers.

There is no unit of measurement small enough in rational numbers that can be used to fully express the value of irrational ones. They’re like apples and oranges — both fruits, but very different.

Real numbers.

Apart from the fact that it implies there are numbers which are neither rational or irrational (there aren’t), this Euler diagram does a good job of showcasing the apples/oranges relationship between the two groups.
Image credits Damien Karras.

Because it can’t properly be conveyed through a fraction, it follows that pi also has an infinite string of decimals. Currently, we’ve calculated pi down to roughly 22.4 trillion digits. Well, I say ‘we’, but it was actually our computers that did it.

Truth be told, we don’t actually need that many digits. They’re very nice to have if you’re NASA and people live or die by how accurate your calculations are — but for us laymen, 3.14 generally does the trick. It’s good enough because it’s just about at the limit of how accurately we can measure things around us. We simply don’t need that much precision in day-to-day activity.

Go around the house, pick up anything round, and run a length of string along its circumference. Unwind it and measure it with a ruler. Measure the circle’s diameter with the same ruler, use this value to divide the circumference, and you’ll get roughly 3.14 each and every time. In other words, if you cut some string in several pieces, each equal to the diameter in length, you’d need 3.14 of those strips to cover the circumference.

Because this simplification is so widely-used, we celebrate Pi day on March 14 (3/14) every year.

If you do happen to need a more-detailed value for Pi, here it is up to 100 million decimal places.

What’s it for?

Pi is used in all manner of formulas. For example, it can be used to calculate a circle’s circumference (π times diameter), or its area: A=πr2 — how I keep this formula lodged in my neurons is using the “all pies are square” trick. It’s also used in calculating various elements of the sphere, such as its volume (3/4πr3) or surface area (4πr²).

But it also shows up in a lot of engineering and computational problems. Weirdly enough, pi can be used to obtain the finite sum of an infinite series. For example, if you add up the inverse of all natural squares — 1/12+1/22+1/32+….+1/n2 — you get π2/6.

Most branches of science stumble into pi in their calculations at one point or another. Computer scientists use it to gauge how fast or powerful a computer is, and how reliable its software, by having the device crunch numbers and calculate pi. It’s very useful for determining both circular velocities (how fast something is spinning) as well as voltage across coils and capacitors. Pi can be used to describe the motion of waves on a beach, the way light moves through space, the motion of planets, or to track population dynamics if you’re into statistics.

Another place pi pops up (that you wouldn’t suspect) is in the value of the gravitational constant. This shows how fast an object will accelerate towards the ground as it’s falling. Its most widely-accepted value is 9.8 m/s2. The square root of that value is 3.1305-ish, which is close to the value of pi. That’s actually because the original definition of a meter involved a pendulum that took 1 second to swing either way. Wired has a more comprehensive explanation here.

Pi also underpins modern global positioning systems (GPS) since the Earth is a sphere. So give a little mental thanks to mathematics the next time you’re drunkenly thumbing your phone to hail an Uber.

Who discovered pi?

Domenico Fetti Archimedes.

“Archimedes Thoughtful” by Domenico Fetti, currently at the Gemäldegalerie Alte Meister in Dresden, Germany. Archimedes calculated one of the most accurate values for Pi during the Antiquity.

Pi is not a newcomer to the mathematical stage by any means. We refer to it using the letter ‘π’ from the ancient Greek word ‘περίμετρος’ — perimetros — which means ‘periphery’ or ‘circumference’. It was introduced by William Jones in 1706 and further popularized by Leonhard Euler. The notation was likely adopted in recognition of the efforts of one great ancient mathematician: Archimedes.

Archimedes put a lot of effort into refining the value of pi. He was also the first to use it to calculate the sum of an infinite number of elements over 2,200 years ago, and it’s still in use today.

But he wasn’t the first to realize the importance of pi(e). In his book A History of Pi, professor Petr Beckmann writes that “the Babylonians and the Egyptians (at least) were aware of the existence and significance of the constant π” as far back as 4,000 years ago. They likely only had rough estimations of its exact value (maths was still a new ‘tech’ back then) but they were in the right ballpark.

“The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. One Babylonian tablet (ca. 1900–1680 BC) indicates a value of 3.125 for pi, which is a closer approximation,” writes Exploratorium in a look at the history of pi.

They add that ancient Egyptian mathematicians also settled on a quite-ok-for-the-time value of 3.1605, as revealed by the Rhind Papyrus. Chinese and Indian mathematicians also approximated the value of pi down to seven or five digits, respectively, by the 5th century AD.

Further work, most notably that of Archimedes, helped refine this value. He used the Pythagorean Theorem to measure the area of a circle via the areas of inscribed and circumscribed regular polygons. If you slept during math class, that’s the polygon inside the circle and the one that contains the circle, respectively. It was an elegant method, but it did have its limits — since the areas of those two polygons aren’t exactly the same as the surface area of the circle, what Archimedes got was an interval that contained pi. He was aware of this limitation. His calculations revealed that pi must fall between 3 1/7 and 3 10/71 — which is between 3.14285 and 3.14085. Today we know that the five-digit value of pi is 3.14159, so that result isn’t at all bad for a guy without a proper pen to write it down with.

The first method to calculate the exact value of pi came up during the 14th century, with the development of the Madhava-Leibniz series. By the time the 20th-century swang by, pi was known down to about 500 digits.

10 Amazing Sights Discovered Over Google Earth

I’ve really loved the Google Earth/Maps technology ever since it’s first rolled out of the Silicon Valley giant many years back. The prospect of having my own digital satellite at my fingertips has been simply mind-blowing, keeping me constantly fascinated by how easy it is for me to reach far away places. Thanks to Google Earth I can now physically see where I need to go, what routes to take or even my cousin’s car in front of her flat in The Village. The possibilities are incredibly wide, as well as the privacy issues…but that’s a story for another time.

Along the years Google Earth hasn’t just been a source of geographical information, but also a valuable tool in spotting remote places and making surprising findings. It helped find a forest packed with undiscovered species, early mammal fossils or even a huge cannabis plantation (sure beats finding crop circles), and much, much more. Bellow, I’ve listed a few truly amazing sights captured with Google Earth, that are either fun, odd or simply mind blowing captured by people with waaay too much time on their hands.

1. Arizona <3 Oprah

Oprah Crop Circle

Throughout this list you’ll see a lot of crop circle ‘art,’ but this one can be considered by far one of the weirdest, not because it foretells of the arrival of an alien master race to enslave us all, but rather because it’s a really clear example of how far obsession and cult-like personality can go. Above captioned is the portrait of famous talk-show host Oprah Winfrey carved in a 10-acre crop by an Arizona farmer. Now that’s a fan! [see it on Google Maps | Coordinates: +33° 13′ 33.18″, -111° 35′ 48.32″]

2. The Jet Plane Inside a Parking Lot


Talk about a smooth ride! We’re used to using jet planes either on air stripes or in the sky, where they belong, not in a residential parking lot in a Parisian suburb as is the case in the above photo. Weird as heck! [see it on Google Maps | Coordinates: 48.825183,2.1985795]

3. A Farmer Who Hates Internet Explorer


Back in 2006, the Oregon State University Linux Users made this huge Mozilla Firefox logo in a corn field to celebrate the world’s most favorite web browser’s 50 millionth downloads. I can really say I get the man… as can anyone who’s used Internet Explorer lately. (See on Google Maps | Coordinates: +45° 7′ 25.39″, -123° 6′ 49.08″ ).

4. The Huge Bunny In The Woods


Built by a group of artists from Vienna, this huge 200 feet bunny rabbit thingy was built in Prata Nevoso, Italy a few years back. Quite cute. (See on Google Maps | Coordinates: +44° 14′ 39.38″, +7° 46′ 11.05″)

5. The Bloody Iraqi Lake


This lake’s colour, located outside of Baghdad, Iraq, has been puzzling people for a lot of time now. Most likely, the reddish colour is a product of pollution or a water treatment facility (which might explain the corrosive colour). Then again, this might as well had been the dumping pool for Saddam’s enemies. (See on Google Maps | Coordinates: 33.39845000,44.48416800 )

6. Building A Brand, Can By Can


What’s quite possibly the largest logo on Earth (if not, it’s definitely the biggest Coke logo), this is what advertising enthusiasts drool about. This huge Coke ad, 50m tall and 120m wide, was built using 70,000 empty coke bottles in northern Chile near Arica desert. This veritable Coke monument was meant to mark the anniversary of 100 years since the brand’s inception, as one can see in the photo (“100 años” – 100 years). Don’t worry, tree huggers, the Aniro desert is one of the most barren places on Earth. (See on Google Maps | Coordinates: -18° 31′ 45.21″, -70° 15′ 0.07″)

7. The Noble Clay Indian


This is one of the most famous Google Earth photos to have circulated on the web. Dubbed the Badlands Guardian, this eroded valley very much resembles the face of a man, and if you take a closer look at the tip of the head, you might notice something like the feather head-piece decoration native Americans used to wear. NOW, if you take an even closer look, you might notice what may seem like a pair of iPod headsets. Pretty funky, right? Unfortunately, it’s just a road with an oil rig at its end. (See on Google Maps | Coordinates: +50° 0′ 37.76″, -110° 7′ 0.86″ )

8. African Zoom


Google Earth is great, but it’s hard to tell a lot of things apart at low res, this wonderful piece of African life, however, depicting a herd of elephants on the move, is one sweet exception. You can even see details in the grass! Simply wonderful. (See on Google Maps – be sure to zoom… a lot! | Coordinates: +50° 0′ 37.76″, -110° 7′ 0.86″)

9. The Highest Place … In Your Living Room


Peeking at 8,848 meters  or 29,029 ft, Mount Everest is the highest place on Earth. Let’s face it, neither of us will ever get to climb it, but thanks to Google Earth, we now have an incredible view of the mountain from the high-up. When I first found it, I was simply stunned by its beauty. Be sure to scroll around it when viewing it – the perspective of it all will undoubtedly send a few shivers up your spine. So serene, yet to deadly! (See on Google Maps | Coordinates: +27° 59′ 9.12″, +86° 55′ 42.38″)

10. Stunning Victoria Falls


One of the tallest and, at the same time, most spectacular waterfall in the world, Victoria Falls never ceases to amaze people. This true spectacle of nature should be on everybody’s must-see/go-to list, but until you book a flight to Zimbabwe, Google Earth should do the trick. (See on Google Maps | Coordinates: -17° 55′ 31.84″, +25° 51′ 29.60″)

Note: Use the coordinates for inputting into Google Earth. If you’d have the software installed, you can use Google Maps as an alternative. It’s not even half as fun, but still pretty incredible.