Stonehenge Builders Used Pythagoras' Theorem 2,000 Years Before He Was Born (techtimes.com) 183
According to a new book entitled "Megalith," which was released on June 21 to coincide with summer solstice, ancient humans who designed Stonehenge followed Pythagoras' theorem 2,000 years before his birth, around 2500 B.C. The theorem states that the square of the hypotenuse is equal to the sum of the other two squares on the triangle. TechTimes reports: [The theorem] was developed by ancient Greek mathematician Pythagoras, who was born in 570 B.C. However, Stonehenge was assembled 2,000 years before his birth, around 2500 B.C. This theory suggests that these ancient humans were smarter than what people give them credit for. In order to use Pythagoras' theorem, they had to be really skilled at geometry.
"We think these people didn't have scientific minds but first and foremost they were astronomers and cosmologists," John Matineau, the editor of the book, told the Telegraph. "They were studying long and difficult to understand cycles and they knew about these when they started planning sites like Stonehenge."
"We think these people didn't have scientific minds but first and foremost they were astronomers and cosmologists," John Matineau, the editor of the book, told the Telegraph. "They were studying long and difficult to understand cycles and they knew about these when they started planning sites like Stonehenge."
Obligatory Spinal Tap (Score:2)
As long as they don't confuse feet & inches... [youtube.com]
Re: (Score:2)
Even more funny: Black Sabbath had this problem the year before "This is Spinal Tap" was released, but in a different direction. Their order was nine times too large.
Big deal. (Score:5, Interesting)
I'm sure that many early cultures were aware of the a^2 +b^2 = c^2 relationship.
What gives Pythagoras the credit is that he proved it.
Re:Big deal. (Score:5, Insightful)
Re: (Score:2)
On the underside of one of the megaliths:
For the LAST time!
Show your WORK Billy!! F-!
Re:Big deal. (Score:5, Insightful)
Prove it!
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
Re: Big deal. (Score:2)
I wouldn't be so sure. While it's only showing an isosceles right triangle, it's a simple thought experiment for someone to explain how it applies to other triangles. The basics are there; it demonstrates that the squared hypotenuse is the sum of the other squared sides. It's easy enough for a maths instructor to walk a student through construting a similar solution to another right triangle. It could simply be that the Sumerian/Akkadian/Babylonian/Assyrians found the diagram more obvious for students if li
Re: (Score:2)
Proof? Article contains no additional info. (Score:4, Interesting)
Re:Proof? Article contains no additional info. (Score:5, Informative)
Plimpton 322 (Score:4, Informative)
Re: (Score:2)
The governing principle here is not the establishment of a mathematical theorem but societies need for that theorem. Without the need there is no need of hypothesis to establish proof and create a theory. So driven by societies need for accurate measurement, that society must have advanced sufficiently in order to make use of the theory to keep it alive, especially prior to the printing press.
Right angled triangle != Pythagoras Theorem. (Score:5, Informative)
I know an ancient Tamil formula that seems to be Pythagoras theorem at the first glance. "Make eight parts of the running length, and discard one part, add to it, half of the altitude. What you get is the hypotenuse". Instantly one notes, there is no quadratic term. It is a linear formula, so it is not a general Pythagoras theorem. It boils down to "when two sides of a right angled triangle is 4 and 3, the hypotenuse is 5".
Nothing unusual. All they needed was an easy way to construct the right angle. That is all. The simplest way is the make a lasso with a rope ten units long, and mark off 3 feet and 4 feet, you can form a right angled triangle. If you make the rope hundreds of feet long, the angle will be accurate enough for the ancient construction techniques.
Egyptians had been using the 3-4-5 right angled triangles to demarcate land holdings after Nile floodings 1500 years before Pythagoras.
For aligning ancient temples, pyramids and other structures with East/West directions, the technique was ridiculously simple. Plant a pole, and mark the tip's shadow location at sunrise on equinox day and again the location at sunset. Line joining these two points is East-West. Use the 3-4-5 triangle from a 10 unit long loop of a rope and mark off North and South. Use plumb bob for vertical. You have a clean three axes Cartesian coordinate axes marked on the ground.
Dont get me wrong. I am amazed they can identify the equinox and solstice days, that they can predict eclipses, form calendars, They were as intelligent and smart as any modern human being. 5000 years is, but a blink of an eye, in evolutionary time scale. But let us also note that what we mean by Pythogoras theorem today is vastly different what they were using back then.
Re: (Score:2, Informative)
The link sheds no light. But lots of ancient cultures knew right angled triangles. That does not mean they knew Pythagoras theorem as we know it today.
I know an ancient Tamil formula that seems to be Pythagoras theorem at the first glance. "Make eight parts of the running length, and discard one part, add to it, half of the altitude. What you get is the hypotenuse". Instantly one notes, there is no quadratic term. It is a linear formula, so it is not a general Pythagoras theorem. It boils down to "when two sides of a right angled triangle is 4 and 3, the hypotenuse is 5".
Nothing unusual. All they needed was an easy way to construct the right angle. That is all. The simplest way is the make a lasso with a rope ten units long, and mark off 3 feet and 4 feet, you can form a right angled triangle. If you make the rope hundreds of feet long, the angle will be accurate enough for the ancient construction techniques.
Egyptians had been using the 3-4-5 right angled triangles to demarcate land holdings after Nile floodings 1500 years before Pythagoras.
For aligning ancient temples, pyramids and other structures with East/West directions, the technique was ridiculously simple. Plant a pole, and mark the tip's shadow location at sunrise on equinox day and again the location at sunset. Line joining these two points is East-West. Use the 3-4-5 triangle from a 10 unit long loop of a rope and mark off North and South. Use plumb bob for vertical. You have a clean three axes Cartesian coordinate axes marked on the ground.
Dont get me wrong. I am amazed they can identify the equinox and solstice days, that they can predict eclipses, form calendars, They were as intelligent and smart as any modern human being. 5000 years is, but a blink of an eye, in evolutionary time scale. But let us also note that what we mean by Pythogoras theorem today is vastly different what they were using back then.
Then there is the table of Pythagorean Triples in Plimpton 322 from 1800 BC. And also Babylonian math exercises on other tablets that give hypotenuse and side of a right triangle and ask for the third side, and solve using the Pythagorean Theorem. There are few who doubt that the Babylonians knew the Pythagorean Theorem.
https://en.wikipedia.org/wiki/Plimpton_322
Re: (Score:2)
Re: (Score:2)
But the only difference is: from Babylonians and Egypts we have written relicts, from stonehenge people not.
Bottom line: contrarily to popular believe, math, especially geometry, is simple everyone who is not polluted by "math is hard" brainwashing easily can figure such things.
If Neanderthals had come to the idea to build a pyramid, they most likely had succeeded. They were as smart as we are, just lacked knowledge about metallurgy e.g.
Re: (Score:2)
Yes indeed, and a number of other geometrical and numerical tricks as well. However, I don't think that it ever occurred to them to find out why they worked, or to generalize from them. They only cared about getting the job done and never worried about why their various tricks worked.
Re: (Score:2)
You choose a fixed place and mark the point on the horizon the sun appears each morning (and maybe the point it goes down). The most northward point is the point the sun goes up on summer solstice, the most southward point is the one it goes up on winter solstice. Half the distance between the two points are the equinoxes. The people around Goseck
Re: (Score:3)
For aligning ancient temples, pyramids and other structures with East/West directions, the technique was ridiculously simple. Plant a pole, and mark the tip's shadow location at sunrise on equinox day and again the location at sunset.
No, just no.
The pyramids are aligned to within 1 degree of true north. Modern civilisation is only just approaching that level of accuracy with GPS *today*.
Aside for that the great pyramid is a *eight* sided pyramid and keeping enough tension on rope to line that up is pretty much impossible. It is packed with information.
To give you some idea, pi is represented *1, *10, *100 and *1000 in this structure. It contains phi, the euler constant and more. The diagonal long edge is the length of seconds i
Re: (Score:2)
Re: (Score:2)
None of this is on Wikipedia.
Yep. I recommend you consider it from one of the corners as a three dimensional structure. You can't consider it in two dimensions.
J H Cole.
Re: (Score:2)
he pyramids are aligned to within 1 degree of true north. Modern civilisation is only just approaching that level of accuracy with GPS *today*.
That is nonsense.
You seem not to grasp the parents explanation. With a simple stick everyone can figure true north with 1/10th accuracy super easy. Just make the stick long enough and measure a couple of days. E.g. use a small hill and put the stick on top of it.
The rest of your post seems rather nuts to me, starting with an 8 sided pyramid when you clearly see: it i
Re: (Score:2)
he pyramids are aligned to within 1 degree of true north. Modern civilisation is only just approaching that level of accuracy with GPS *today*. That is nonsense.
You seem not to grasp the parents explanation. With a simple stick everyone can figure true north with 1/10th accuracy super easy.
Yep.
Just make the stick long enough and measure a couple of days. E.g. use a small hill and put the stick on top of it.
Not without introducing error. Richard Feynman suggested that there are simple, beautiful elegant explanations that are also wrong.
The rest of your post seems rather nuts to me, starting with an 8 sided pyramid when you clearly see: it is a standard 4 sided one.
Then, my friend, you are as uninformed about these matters as we have found some people to be about Nuclear Power. There is nothing nuts about the information contained in the pyramids. What's nuts is that the actual truth of these structures is being dictated by archaeologist with arts degrees making assumptions instead of geologist, engineers and mathematicians who
Re: (Score:2)
The numbers are irrelevant.
With enough points on a pice of paper you can construct any kind of number ...
Re: (Score:2)
However it isn't paper - it's stone. And there aren't just points, there are derived constants. Circle the flats and the corners of the base of the great pyramid and subtract the smaller circumference from the large and tell me the number you get. It will blow you away. No way that is irrelevant.
And consider that you didn't even realize it was an eight sided structure until I pointed it out to you, I have little doubt that you have confirmed it by now. I don't care what you think about this howev
Re: (Score:2)
It wont blow me away.
It is known since 40 years that there many natural constants you can "derive" by picking measurements from the pyramids.
And it is scientific consensus: this is coincidence.
Just take a picture from a random part of the stars, then use your idea about the pyramids ... you get the same surprising results.
Re: (Score:2)
And it is scientific consensus: this is coincidence.
It's a coincidence that Pythagoras, one of the founders of mathematics [wikipedia.org] studied the Pyramids not the great wall of china which probably didn't exist then, can you show me an older man made structure that coincidentally has all of those mathematical constants in them?
It's a coincidence that all of these constants are in the Pyramids a structure that comes before all other megalythic and modern structures built, with no evidence that it's a tomb, yet here it exists like a textbook in stone with most of the i
Re: (Score:2)
From a web search: Each of the pyramid's four side are evenly split from base to tip by very subtle concave indentations.
Call me nitpicking: but this is still 4 sided. A 8 sided pyramid has an octagon and not a square as base.
Re: (Score:2)
Well, ... or has a good design reason. At least it is pretty clear that the Pyramid at the time when it was build was covered in limestone, and the 4 sides where completely flat.
you would be correct.
I was neer there, but I assume it is a square and the concave "cut" is probably caused by the people who abused the Pyramid as a quarry
Re: (Score:2)
Wait, so the ancient Egyptians used the modern (and arbitrary) British unit of a foot? As in 12 inches? 30.48 cm? At most it's a coincidence. Or an alien conspiracy.
I'm sure there are constants such as Pi, phi, euler's constant, the golden ratio, and more that can be found in the pyramids' construction, as a consequence of geometry. That in no way is proof they understood the constants in abstract. In fact there's little evidence they did.
Great Pyramid Constants (Score:2)
Wait, so the ancient Egyptians used the modern (and arbitrary) British unit of a foot? As in 12 inches? 30.48 cm?
More like the British used the foot which is a universal constant of measure. The foot to the cubit represents the euler constant, if you care to take a look at it. Also, they used the metre, which you struggle to wrap your head around until you realize that if you take a 1 metre pendulum and swing it so that the arc is precisely 1 second (at the the 30th parallel for an exact second due to gravitational variations) you will find that the distance of the arc defines a cubit perfectly. Now you have a
Re: (Score:2)
Oh come on. The base of the Pyramid is 755.9 feet long. Twice that is nowhere near 314 feet. Even a casual glance at the Great Pyramid would tell you that its base is a bit bigger than 157 feet anyway.
The circumference is 3023.6 feet, which is kind of close to pi*1000 so
Re: (Score:2)
If you can't get something so simple and easily checked correct, why should I believe any of the rest of that?
Indeed you are right, my apologies, I was actually busy and in the middle of something else and it has been just over a year since I looked at these calculations. It's not exactly dinner conversations with friends so in what context would I ever bring such a thing up. I'm still wrapping my head around the mastery of it so, it's on me, my error which I will correct.
Please note the IIRC part.
Oh come on. The base of the Pyramid is 755.9 feet long. Twice that is nowhere near 314 feet. Even a casual glance at the Great Pyramid would tell you that its base is a bit bigger than 157 feet anyway.
Well I didn't recall correctly. The Great Pyramid uses Three units of measurement, foot, cubit and metre. It was
Re: (Score:2)
Plant a pole, and mark the tip's shadow location at sunrise on any given day and again the location at sunset. Line joining these two points is East-West.
Fixed that for you.
Use the 3-4-5 triangle from a 10 unit long loop of a rope and mark off North and South. ... ... when I see what my little brothers learn at school (and how it is taught, which is t
You can use a rope based compass and construct the perpendicular, much easier than constructing 2 triangles
But: always good to keep such simple knowledge alive
Re: (Score:2)
Re: (Score:2)
right triangles do not Pythagoras make. They knew clever geometric techniques, but you need more evidence to show they understood good ole' P's theorem.
Right. one day's experience of life on a farm will teach you that there are other ways to solve problems than the academic way. One day's experience of academia will teach you that academics will take 5,0
Re: (Score:2)
Yeah, that's the thing: engineers make shit work. You find out that X moves this way and Y moves that way, and you connect X to Y and things happen.
Scientists figure out why X and Y move the way they do and how they interact to form the strange and unexpected output when combined. Then engineers use that new information to slap together a new machine.
We don't bother proving things. We just figure that wood expands, pressing water from wet wood is really hard, and water is apparently incompressible (
Re: (Score:2)
Those in ancient Britain were also complete illiterates, so building on 5,000 years of maths would have required far greater smarts than today's people.
We don't know that. We only assume it. E.g. if they were writing on deer skins, everything is rotten away now in that climate.
The argument seems to be... (Score:5, Insightful)
Stonehenge contains right triangles; the right triangles obey the Pythagorean theorem; therefore whoever built Stonehenge must have known the Pythagorean theorem.
But ALL right triangles obey the Pythagorean theorem (which is the whole point of the theorem), so this would be true whether the people who built them knew about the theorem or not.
Re:The argument seems to be... (Score:4, Interesting)
Not quite.
A "Pythagorean triangle" is a right-angled triangle where the sides all have integer length. This guy claims to have found some of those, in particular there's a rectangle of stones that mark important sunrise/sunset events and moonrise/moonset events which, when you cut it in half, is Pythagorean.
Which seems odd to me. If the stones are determined by the calendar events, that's the reason why they have those proportions, not Pythagoras' theorem. The builders may have discovered this integer ratio relationship and found it interesting, but I doubt it's the other way around.
Re: (Score:2)
Basically the put four stones around the circumference of a circle, which forms a rectangle. So if all three sides of a right triangle happen to be integer values then it's Pythagorean? But just decrease the length of each integral unit until you it's fuzzy enough and you can't measure it accurately, and any right triangle drawn on the ground can be Pythagorean.
To me, the Pythagorean Theorem is about a^2 + b^2 = c^2, even if not an integer, and a proof that this is true. Merely noticing that 3^2 + 4^2 = 5
Re: (Score:2, Insightful)
"A "Pythagorean triangle" is a right-angled triangle where the sides all have integer length. "
Is that a school thing, a math thing, or a new math thing?
Surely if you use the right unit of measure any triangle can have integer length.
Re: (Score:2)
One side can have integer length, but the other two sides need not. It depends on the angle (that is, either of the acute angles), the sides are integers for only some choices.
Re: (Score:2)
Ah, here we go. [wolfram.com] Apparently this is a standard term.
Re: (Score:2)
I've always called that a Pythagorean triple, but I was going from what the second link said. I figured it might be a usage I wasn't aware of.
Re: (Score:2)
Sounds good.
What unit of length would you use for a right triangle with the two shorter sides of length 1 metre (or 1 yard, if you prefer)?
I can't scale sqrt(2) metres to make it an integer...
Re: (Score:2)
but we're talking about right triangles. How many RIGHT triangles can you think of off the top of your head where all 3 sides are integral in any unit of measure? 3:4:5 is the most oft cited and easy to remember. 12:5:13 is the other easy one. I can't think of any others at the moment, but I thought there was one more without going into triple digits. (obviously, since the unit of measure is arbitrary, when we talk about triangle x:y:z, we are talking about all triangles that are geometrically "similar"
Re: (Score:3)
I don't see that in the Tech Times article; the claim there is that the builders of Stonehenge knew the Pythagorean *theorem* (which of course doesn't require integer sides). It does claim that Pythagorean *triangles* will be found elsewhere in Britain, but leaves implicit any connection between Pythagorean triangles and the Pythagorean theorem.
The Telegraph article has a picture of Stonehenge labeled "A bird's eye view of Stonehenge showing the rectangle and Pythagorean triangles", with 56 postholes in th
Re: (Score:2)
I got the moon declinations and phases from https://www.timeanddate.com/mo [timeanddate.com]... [timeanddate.com]. It's a nice calculator, much better than having a Stonehenge in your back yard.
It might be nice but I think in units of Awesomeness it is several orders of magnitude less than actually having Stonehenge in your out back.
Re: (Score:2)
"A "Pythagorean triangle" is a right-angled triangle where the sides all have integer length. This guy claims to have found some of those"
Which is an explendid way to show they did *not* know the Pythagorean theorem. Aegyptians, for instance, knew the nice trick that you can form a right-angled triangle with a 12 units rope, so integer length triangles are expected. We know the Pythagorean theorem, therefore we have no need to limit ourselves to "nice" right-angled triangles: we can build anyone that plea
Re: (Score:2)
What I was thinking. Also, whoever wrote the article (and the person who copied it into /.) got the Pythagorean theorem wrong: "The theorem states that the square of the hypotenuse is equal to the sum of the other two squares on the triangle." That's only true if it's a right triangle, not true for other triangles (unless you're the Scarecrow in the Wizard of Oz: https://www.youtube.com/watch?... [youtube.com]).
Re: (Score:2)
Stonehenge Builders Used Pythagoras' Theorem (Score:2)
Re: (Score:2)
Insensitive clods!
is this new? (Score:5, Informative)
Re: (Score:2)
Apparently he really is an astrologer: https://en.wikipedia.org/wiki/... [wikipedia.org]. His only claim to being an astronomer is that he teaches astronomy, but this is at the "Faculty of Astrological Studies."
Re: (Score:2)
Apparently he really is an astrologer: https://en.wikipedia.org/wiki/... [wikipedia.org]. His only claim to being an astronomer is that he teaches astronomy, but this is at the "Faculty of Astrological Studies."
You can be an astronomer and an astrologer too, as long as you keep the two separate.
It's like physicists who believe in God.
It would have been the Pythagorean Conjecture then (Score:2)
Hopefully (Score:4, Funny)
Re: (Score:2)
That’s why they’re not around anymore - Pythagoras sued them into oblivion.
Igloo analogy (Score:5, Interesting)
The base of an igloo, which is essentially a circle, follows the formula Circumference = pi * Diameter.
After building several hundred igloos, I am sure an Inuit builder would have empirical knowledge that it takes roughly three times as many steps to go around a circle than it takes to walk the diameter. In this way, the Inuit builder would have a very practical understanding of pi without possibly ever defining pi.
Children may use 3-4-5 triangles in wood shop before ever learning about Pythagoras's Theorem.
Some woodworkers have a very practical understanding of specific right triangles without really thinking the maths through.
I would put the Stonehenge builders in the same lot. Lots of empirical knowledge, but maybe less so on the modern-day mathematical definitions.
Re:Igloo analogy (Score:4, Insightful)
Quite.
Maths is not an inherently intellectual-only exercise. It can be determined to within a human margin of error quite easily by empirical evidence.
The same claim goes to the pyramid-builders. But the desert is littered with collapsed and bad pyramids that weren't right or were changed mid-construction. And those are just the ones that got left rather than "Rip it up, it's wrong, that's a billion tons of stone, we can re-use it"...
Though I don't doubt these people were not just Neanderthals bashing clubs against their head, they didn't formalise mathematics in this fashion. Pythagoras did, which is why we know his name and call him a mathematician.
You have to recognise that Stonehenge proper was 3000-2000 BC. Mesolithic posts on the site align to a lunar calendar thousands of years before that.
For thousands of years, people maintained a site with significance to their astronomical observations. Yes, for religious purposes, but they weren't idiots. Likely these people had intelligence not vastly different from our own, but they lacked a more formal education process. The ability to sit in a classroom for 18-20 years and be taught every day is the only thing that's changed. These people weren't stupid, just not formally educated. Plenty of people even today operate on the exact same principle!
How many adults, now, today, could tell you what Pythagoras' Theorem was, state it, understand it, apply it and see it's application to places like Stonehenge? It's by far not everyone.
How many adults, now, today, are going to build something that's still standing in thousands of years, and how intelligent (collectively) would everyone who worked on it have to be to do that?
I find it quite insulting that people think even Stone Age man was some thick-headed caveman. And that EVERY Stone Age person was that thick.
Hilariously, I watched a series on TV a few years ago where a group of people tried to live in an isolated area with no modern facilities and they failed MISERABLY. Literally, they ate through their initial stock of food, they couldn't build a shelter, meat was left to go rotten for days with no preparation and they were SURPRISED by that, they trekked miles to get water and came back with almost nothing, not even food gathered along the way, and when snow hit, they were all evacuated to safety because they didn't bother to make any preparations.
Just being "modern man" doesn't make us collectively intelligent. There are outliers whose knowledge benefits us all, while half of people are of "below average" intelligence (by definition - if you don't understand that, nor do half the population!). That a few thousand years ago, not long enough to have biologically changed us very much at all except under extreme evolutionary pressure, there were people capable of taking a reasonable guess at the length of a side of a basic engineering project? Yeah? And? So what?
We are doing these people a disservice. It's probably why a lot of people just assume that dinosaurs and cavemen lived together.
These people probably didn't even have TIME to sit around and think, let alone formerly school, but it doesn't mean they were stupid. They could probably only burn wood, maybe a primitive oil for light (outside of full moons) - hell we don't know what they might have been doing of an evening, they may be much cleverer than we thought. But likely the night was a loss and most of the day was used for more essential tasks like surviving and gathering food and making weapons.
You're not telling me that you're surprised a Bear Grylls existed back then who had mastered his art after generations and had time to sit and think, even if his village mates were still worshipping trees?
Pick a modern human couple at random, put them back in that environment, and we'd likely not be able to replicate anything of Mesolithic mathematics, cosmology, survival skills, etc. for dozens of generations (if they even live that long).
Outside of w
Re: Igloo analogy (Score:2)
It's interesting that you claim Pythagoras the mystical cult leader was a scientist, but the engineers who built Stonehedge are relegated to only doing it for religious reasons.
Re: (Score:2)
The people who built it almost certainly were more driven by religious reasons, but it's unknown.
The *person* (or handful of people) who designed it probably weren't.
In fact, they probably did it on commission on one religious leader who had no clue.
There's no reason in history to suggest such a pattern has ever changed.
The people who built the pyramids were much more likely to be religious than they were to be architects.
Re: Igloo analogy (Score:2)
Splitting religion from science becomes somewhat nonsensical before the scientific revolution. The builders of stonehenge may have had a version of astronomy steeped in mythic tradition, but they were still essentially building an astral calendar. That's engineering, no matter the stories they may have told about the reasons they felt compelled to do so.
Re: (Score:2)
Re: (Score:2)
Well, but after building Iglus every few month year after year, he surely knows PI is closer to 355/113, don't you think so?
How do they know that? (Score:2)
Nationalistic revisionism (Score:2)
Re: (Score:2)
didn't build houses, didn't settle, Strange that we found so many relicts of houses and villages ...
didn't have a common language Extremely unlikely.
And this huge knowledge didn't reach us because it was destroyed... by Christians.
Only in rare circumstances, most was long forgotten and underground before the Christianization even started.
There are nice BBC movies about recent stone henge research, you find them on youtube. The people living there traded with people from spain, central europe, north italy an
Staring at clouds too long (Score:3)
I really don't see this being far removed from what is being suggested by the article, that standing stones in the British Isles are positioned in a way which is pythagorean. There are hundreds of standing stone circles all over the isles. It would not be hard to cherry pick some of them and shoehorn the hypothesis into. It's the sort of pseudo archeological garbage that Graham Hancock has been doing for years.
Re: (Score:2)
Re: Staring at clouds too long (Score:2)
You're leaving out the part where crop circle design has gotten way more complicated over the years and the classic farmer explanation no longer applies to many of the more complicated "circles".
Re: (Score:2)
Re: (Score:2)
Re: (Score:2)
Lines (Score:2)
Quick, someone test the asinine modern druids who claim religious rights over it, to see if they know the theorem.
Test the politicians who roll over and let it happen too.
Pythagorean Theorem or Pythagorean Triples? (Score:2)
Re:Down with Pythagoras! (Score:5, Insightful)
That article is possibly the stupidest thing I have ever read in my life.
What would Benjamin Franklin have to say about the absurdity that Alaska, with less than a million inhabitants, has the same Senate power as California, a state with over 38 million people
He'd say, "Good". That's EXACTLY what the Senate was designed for... so that small states would be on an equal footing with the large states.
Re: (Score:2)
Galanty Miller is a long-time contributing writer for the Onion News Network.
So.... Satire, maybe? I can't figure it out. Poe's Law applies.
Re: (Score:2, Insightful)
He'd say, "Good". That's EXACTLY what the Senate was designed for... so that small states would be on an equal footing with the large states.
This is just it. Democracy comes in various flavours. Some representational, some direct, some are tyranny of the minority, but all were designed with a very specific purpose and end goal.
Personally I hate the system in the USA, but there sure is no arguing against the reasons for its creation. There is only arguing if its design was ultimately in the best interest of the people, and in this case that argument depends entirely on which people you are talking about.
Re: (Score:2, Interesting)
That article is possibly the stupidest thing I have ever read in my life.
What would Benjamin Franklin have to say about the absurdity that Alaska, with less than a million inhabitants, has the same Senate power as California, a state with over 38 million people
He'd say, "Good". That's EXACTLY what the Senate was designed for... so that small states would be on an equal footing with the large states.
I can't comment on what Benjamin Franklin would have said then or now; however, it's worth noting that the US is a very different place than it was when the constitution was made.
Look at the name of the US- it's the United STATES; not the United PROVINCES. At the time of founding the states were viewed as... well, states aka NATIONS, not provinces. This was a coming together of different nations to become one. The original US was more of a confederacy than a single nation. Obviously over time the US ha
Re: (Score:2)
Re: (Score:2)
Did you read the article? There's absolutely nothing in it, so, whatever...
Oh, there's one thing in it. This priceless quote:
Heath also contends that the ancient humans who built Stonehenge likely used a rope or another object to represent a time period as it relates to the sun and the moon. He says that this is where the phrase "a length of time" originates from.
If that's the quality of the math in the book then Pythagoras can sleep soundly tonight.
Re:Bullshit. (Score:5, Funny)
Re: (Score:2)
No one knows who they were... or what they were doing.
Re:Bullshit. (Score:5, Interesting)
No calculations necessary. Pure geometry with simple means.
Re: (Score:2)
How do you know Dont-eat-beans didn't rent from Pythagorus?
This does however give me a name for my next Argonian character.
Re:Problem: Pythagoras was not the first to prove. (Score:5, Informative)
Re: Problem: Pythagoras was not the first to prove (Score:2)
I think you're missing the forest for the trees. Ignore the small squares; the larger square demonstrates the proof using a variation of the classic https://www.dbai.tuwien.ac.at/... [tuwien.ac.at]
Re: (Score:2)
The Pythagoreans are reputed to be willing to outright murder people to keep their mathematical secrets.
According to legend, Pythagoras himself was murdered. He could have escaped, but only by crossing a bean field. He hated beans and forbade his followers to eat them. So he stood his ground, faced his pursuers, and was killed.
Disclaimer: I like beans, and eat them almost everyday.
Re: (Score:2)
The Pythagoreans are reputed to be willing to outright murder people to keep their mathematical secrets.
According to legend, Pythagoras himself was murdered. He could have escaped, but only by crossing a bean field. He hated beans and forbade his followers to eat them. So he stood his ground, faced his pursuers, and was killed.
Disclaimer: I like beans, and eat them almost everyday.
That doesn't make sense unless he would somehow have had to eat his way across the bean field to escape.
As I understand it, it was the consumption of beans he objected to, not that he wouldn't walk on them and hurt them.
Re: (Score:2)
Re: (Score:2)
Sounds like a lot of British stuff in so far as, there's some great qualities to it, but it'll be fucked up by someone winging it a bit on one or two critical features *AND* totally fucking up the marketing.
Plus, it will have an inexplicable oil leak from somewhere where no oil should even be.
(Old British motorcycle joke.)
Re: (Score:2)
Re: (Score:2)
No. The beaker culture replaced the earlier culture. Only a few percent of their DNA was imported.
Perhaps they themselves died of as a result of self poisoning by deadly beaker.
Re: (Score:2)
Convincing evidence you got there, Slick. Where can I sign up?
One word: Atlantis.
Argue with that if you can!