Geometry and shit.

i jsut wanted to make a geometry thread. for beatuful geomitry scthaff. i am bored. so i made this.

i messed it up a bit, can u see where

{{{god, i am really bored}}}}

Did someone buy you a spirograph Norc?

Probably one of the most intellectually beautiful figures in geometry. Can you recognize what it demonstrates?

it demonstrates that I am thick

A Rennie Macintosh design !

Got lots of Rennie Macintosh windows and doors round here- the genuine articles I mean not copies- he did a lot work here. Beautiful stuff. I should try to get some photos.

Im so fond of stained glass windows as well ! People are so lucky if they have originals, especially as people are so fond of Modernising & knocking down lovely old buildings.

halfwise wrote:Probably one of the most intellectually beautiful figures in geometry. Can you recognize what it demonstrates?

Oh yeah! I think you could make a case that all geometry evolved directly from the Pythagorians,
and The Theorem was their crowning achievement.

Ahh yes but did Pythagoris make stained glass windows and doors?

"Everest" do double glazing

Pettytyrant101 wrote:Ahh yes but did Pythagoris make stained glass windows and doors?

No, but if he'd had a good patent attorney he'd have gotten a royalty on every corner!

most of his work is in Glasgow? the art school and the Willow tea room which I dont know if still exists. he and his wife were quite some characters.

Yes there is tons of stuff and his own gallery in Glasgow.
Fortunetly he did quite a few jobs in my area throughout his life, particualry iron work and windows. Some of which still survive in situ.

i always wondered what banksy did in his spair time

Forgeries of Old Masters.

halfwise wrote:Probably one of the most intellectually beautiful figures in geometry. Can you recognize what it demonstrates?

pytagoras?!

kinda love making these crop circles

Norc wrote:

halfwise wrote:Probably one of the most intellectually beautiful figures in geometry. Can you recognize what it demonstrates?

pytagoras?!

Yes!

All the white triangles in both squares are identical with short sides of a and b, and a hypotenuse of c. So the big squares have sides of a + b, so the area of each square is (a + b) (a + b)= a^2 + 2ab + b^2. Now if you recognize that each pair of white triangles makes a rectangle of area (ab) then you'll recognize the picture on the right as a^2 + 2ab + b^2. If you subtract the area of the 4 white triangles, which is 2ab, you'll get a^2 + b^2.

But the second picture of the same square also has 4 white triangles that add up to an area of (2ab), and the remainder is a square of area c^2. Therefore a^2 + b^2 = c^2 QED.

Or in pictures:

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?

i know my shit bro.

It lets you pick up chicks in math bars.

The closest Scottish equivelent to a maths bar is keeping score at darts.

Well first off, your vicar wasn't lying. He didn't say you'd get answers if you asked, only that you wouldn't if you didn't.

What it gives us is so broad reaching it's hard to not take it all for granted. Going back to the ancients, it gave us a way to measure our world in more than one dimension.

It had been know for a very long time that a triangle with sides in a ratio of 3-4-5 would be a perfect right triangle. That fact was used to lay out squares and survey land through a series of tricks, but it didn't solve the general problem that always popped up: If you you can only measure two sides of a triangle, can you calculate the length of the other side?

Without the ability to calculate the distance to places we can't go directly think of how little we would know. The distance across rivers, the height of mountains, the size of the earth, the distance to the moon and stars. In a practical level, every carpenter's square has scales for calculating these lengths and angles derived directly from the Theorem. It would be very hard to design a two story house without the Theorem.

The shape and dimension of books. Printing. Basically anything with right angles in it has been designed with assistance from the Pythagorean Theorem.

Although we tend to take it for granted, it really is as magical as the ancient Pythagoreans believed.

Wouldnt intuition lead to books being book shaped even if you were ignortant of the theorem? I mean, one page after the other doesnt seem a huge leap on one tablet after another, or to require maths knowledge.
I mean loads of man made things had right angles before pythagoras came along.
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.

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