Geometry and shit.

Eldorion wrote:It lets you pick up chicks in math bars.

no it doesn't. unless your benedict playing hawking

people have yet to appriciate my magnificant geometric crop-circles.

I liked that last one Norc- reminds me of the magnetic lines coming off the sun.
But my heads in enough trouble trying to work out the signfigance of what old Pyhtagoras is on about (and Dave for that matter .)

i know the formula. that's it. though if i dig out some notes, i can probably prove it in three different ways though not that i am bothered finding out right now..

Pettytyrant101 wrote:Wouldnt intuition lead to books being book shaped even if you were ignortant of the theorem?

I don't think so. The understanding of the right angle as a basis for engineering things to be mass produced is fundamental to even imagining them, and has it's roots in the theorem. As book binding progressed, the tools are designed around the same principles as the carpenter's square, and I suspect they were from the beginning. Before that, rolled scrolls were the norm.

I mean loads of man made things had right angles before pythagoras came along.

Maybe not as many as you think. Although the historical dates for Pythagoras are in the 500's BCE, I'm sure you know from your religious history that this is exactly the time of the fall of the Babylonian Empire, who had a complex mathematical understanding going back over a thousand years earlier. A lot of their mystical mathematical wisdom passed to the mystery cult of the Pythagoreans. There is supposedly documentation on old clay tablets that the Babylonians were familiar with the basic proof of the Theorem.

And didnt some ancient wise person work out the earths circumfrence from shadows and wells- I seem to have a vague recollection of something sort of along those lines.

Yes, using the Pythagorean Theorem!

(see this another problem with asking questions- you get answers that just mean more bloody questions! )

I know!

Norc wrote:people have yet to appriciate my magnificant geometric crop-circles.

If I ever see those in my fields, somebody is going to be in BIG TROUBLE!

i knew u were trouble when you walked in
so shame on me now
drew shapes that i'd never seen
now i'm lying on the cold hard grass

David H wrote:

Norc wrote:people have yet to appriciate my magnificant geometric crop-circles.

If I ever see those in my fields, somebody is going to be in BIG TROUBLE!

she's behind the sofa dave

Thanks for that anmswer david, but, tablets have right angled corners and they go back to at least 4000bc.
Although your point on Babylon is interesting as there were certainly plenty of mathmatical and in particular atsronomical schools in that culture.

Its also worth noting that -

The perimeter of the base of the Great Pyramid equals the circumference of a circle whose
radius equal to the height of the pyramid.

if we let the base of the Great
pyramid be 2 units in length, then

pyramid height =


So:


Perimeter of base = 4 x 2 = 8 units


Then for a circle with radius equal to pyramid height
.


Circumference of circle = 2

7.992

So the perimeter of the square and the circumference of the circle agree
to less than 0.1%.
Since the circumference of the circle (2
)
nearly equals the perimeter of the square (


2 8

we can get an approximate value for ,




4 /
= 3.1446

which agrees with the true value to better than 0.1%.




Now, obviously, beng a buckie riddled idiot, I havent a clue if thats right or not. But if so it would seem to indicate the Egyptians of circa 2500bc had a pretty good grasp of mathmatics too.

I doubt if anybody will really ever know when the Pythagorean Theorem in it's most general sense was ever first proved, or even postulated. It's sort of like asking who first thought of monotheism.

Try this: try drawing a perfect square. When you draw the second side and form the first right angle, isn't it suddenly very interesting how long the diagonal is? It's square root of two. In a time before irrational numbers, when even fractions were magical, that's a great mystery, probably older than pi.

Found this while looking for the crabbit thread, the missingness of which is making me crabbit.

But Petty, I can't follow what you are saying about the pyramid because I don't know what your strange symbol you are copying and pasting stands for. Looks like square root of phi, but what does it mean?

As far as the importance of the pythagorean theorem, all surveying, and all vector calculations (which means half of physics) is based completely on the pythagorean theorem. It's more used than pi. Once you get past basic arithmetic/algebra it's the most used bit of mathematics there is. The basis of trigonometry and much of geometry. In fact, it's possibly used even more than algebra.

saw this thread and thought "this looks like a thread i would have made", clicks it.. oh yes

 

halfwise wrote:
But Petty, I can't follow what you are saying about the pyramid because I don't know what your strange symbol you are copying and pasting stands for.  Looks like square root of phi, but what does it mean?

I don't recognize the symbol either, but he's clearly doing a golden ratio calculation here. You'll notice that the value of his symbol is about 1.618.

As far as the importance of the pythagorean theorem, all surveying, and all vector calculations (which means half of physics) is based completely on the pythagorean theorem.  It's more used than pi.  Once you get past basic arithmetic/algebra it's the most used bit of mathematics there is.  The basis of trigonometry and much of geometry.  In fact, it's possibly used even more than algebra.

Prezactly!  

except that his symbol is 2 x 1.618, and it includes a square rooty thing which comes from nowhere. And he never mentions the golden ratio.

Did the Egyptians know about the golden ratio? Will have to look that one up.

Not sure what you mean Halfy.

Pettytyrant101 wrote:
4 /
=  3.1446

so = 4 / 3.1446 = 1.2720
therefore Φ = 1.2720^2 = 1.6180  That's the golden ratio.

I don't know off hand whether the Egyptians had it by I know the Masons and other mystical geometers claim they did.

Edit: Wikipedia seems to give it a Greek origin, but a lot of Pythagorean stuff has its roots in Egypt, and the mathematical mystery cults didn't leave much in the way of historical records, so it's hard to say but it's certainly possible.  The phi symbol Φ seems to be the standard symbol for the golden mean (much easier than writing it out!), so Petty's copied image  can be written  √Φ meaning "the square root of the golden ratio".

Oh, his equations wrap to the next line, that was messing me up.

The phi symbol Φ seems to be the standard symbol for the golden mean (much easier than writing it out!), so Petty's copied image can be written √Φ meaning "the square root of the golden ratio".- David

Thats exactly hat I meant, yup, without a doubt, that very thing.    {{{{   }}}}}

Pettytyrant101 wrote:

Thats exactly hat I meant, yup, without a doubt, that very thing.   

Good! I'm glad we sorted that out.  

The pyramid thing really comes down to one of the old challenges of early geometry (which was all about constructing drawings with a compass and straightedge) called "squaring the circle". In its day it drove philosophers mad that, while you could divide a line segment into smaller line segments, you could divide squares into smaller squares, triangles into triangles, etc. there was just no way to divide circles into smaller circles. In older times, people devoted their lives to such questions in exactly the same way quantum physicists ponder things now. The human brain is a strange place to live sometimes.

Pettytyrant101 wrote:The phi symbol Φ seems to be the standard symbol for the golden mean (much easier than writing it out!), so Petty's copied image  can be written  √Φ meaning "the square root of the golden ratio".- David

Thats exactly hat I meant, yup, without a doubt, that very thing.    {{{{   }}}}}

I thought it might mean the golden ratio, but since the equations were wrapping I couldn't get the math to work out.

I just want to say that this woman is totally awesome!

Wikipedia wrote:Maryam Mirzakhani (Persian: مریم میرزاخانی‎; born May 5, 1977) is an Iranian mathematician, and a full professor of mathematics (since 1 September 2008) at Stanford University.

Her research interests include Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. In 2014, Mirzakhani became the first woman as well as the first Iranian to be awarded the Fields Medal.

Mirzakhani found international recognition as a brilliant teenager after receiving gold medals at both the 1994 International Mathematical Olympiad (Hong Kong) and the 1995 International Mathematical Olympiad (Toronto), where she was the first Iranian student to finish with a perfect score.

The Fields Medal is like the Nobel Prize for mathematics, and the fact that the first woman ever to win it, from anywhere in the world, came up through the Iranian university system under an Islamic regime while the West was imposing sanctions all around her should be serious food for thought.

looked her up. You expect her to look old and distinguished, but she's in her mid 30's, with a slightly impish air about her.

Pettytyrant101 wrote:Ok I know this question shows me up to be the complete maths thicko that I undoubtedly am, but if you never ask you dont get answers (as my vicar used to say although he was lying as it turned out he didn't in fact have any answers! )
anyway- I understand how jolly clever all this is, but what was the need?What did proving these things mean beyond the abstract? What was driving the Greeks to come up with this stuff? Was there a pressing need or idle curiousty?
I assume its useful for lots of things like construction, but exactly why? What does it allow you do?

While I was trying desperately to find the thread advising Norc on love and dating (yes, I clearly have much else to avoi...uh...do), I came across this reaction to the Pythagorean theorem. So here is my response.

In modern times, mathematics is most akin to art: you set up some rules, and play, and see what comes out. It's constrained freedom.
Physics is most akin to religion: you know the rules are out there, and worship is finding the deeper rules of what is. You can't make up the rules. Most of the "playing" is just applying the mathematics based on rules that align with nature.

Back in the time of the Pythagoreans, mathematics was so undeveloped that the rules had to come from nature, so was more akin to physics. Math was a form of worship of what is.

The Pythagoreans weren't really applying it as far as I know. The later Greeks were definitely applying it: used in construction all the time.

Well, gravity enforces all kinds of practical hidden-mathematics in construction.