Interesting Items...

Ouch. I hadn't picked this up in any news:

The Arecibo telescope in Puerto Rico has collapsed less than two weeks after officials announced it was too dangerous to attempt repairs.

The collapse follows two cable failures within four months. First, a support cable wrenched out of its socket on August 10th, then a main cable snapped on November 6th. Two weeks later, the NSF announced that it would dismantle the telescope, while still supporting other onsite facilities, such as the LIDAR facility for geospace research. While engineers had assessed the structure after the first cable failure and replacement parts were on order, the second failure suggested the system could collapse at any time. Each cable is 8.25 centimeters thick and made of 160 wires, but drone footage of the remaining cables to that tower showed individual wires were breaking daily.
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The Arecibo radio telescope in Puerto Rico was a 1,000' dish constructed in a natural depression in the ground, with an antenna assembly suspended over it on cables (it featured in Bond movie Golden Eye). As the dish was fixed, it scanned the heavens with the rotation of the Earth, but its precise direction could be steered to a limited extent by moving the antenna.

The antenna assembly was reported to weigh 900 tons because it was also able to transmit and thus be used as interplanetary radar. A similar construction in China doesn't have transmit capability.

 
The simple beauty of mathematical perfection :)

e^{i\pi }+1=0
 
I found this diagram far more interesting:

pythagoras-figure-2-02.jpeg
This is just a wonderful proof of Pythagoras's Theorem.
 
Nice. I've never seen that before.
4(ab/2)+cc = (a+b)(a+b)
2ab+cc = aa+2ab+bb
cc = aa+bb
 
Scrat said:
So we are still using that expensive EU stuff?
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Not if the EU can help it. Just as well they can't.

Oh how I laugh at the EU nutters here and everywhere who day by day told us THERE CAN'T BE A BORDER ON THE IRISH ISLAND for 5 long years.

Yet their beloved EU put the border up in a matter of hours.

Oh, how I laugh at them.
 
pythagoras-figure-2.png
Or this graphical representation.
cc+2ab=aa+bb+2ab

Yes, we didn't get that diagram in lessons, but I found it later in a book.

The next one dates from the second century CE.

image6.gif
Perhaps not as elegant, as it requires calculating the area of the yellow square.
 
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Scrat said:
You can't prove it anyway, as it is false in most geometries. It is an axiom in Hilbert spaces.
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You would indeed need to specify that your are talking about Euclidean geometry in a full and strict proof. In the world at large I think it is safe to assume this unless talking about global navigation and such like where the context would imply spherical geometry (eg where parallel lines do meet).
 
gomezz said:
Then that proves you are not a mathematician. :D
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Never said I was, especially if your definition of "mathematician" is somebody who takes a demonstration on a Euclidean plane and says it's wrong because it doesn't apply in an arbitrary geometry.
 
Black Hole said:
Never said I was, especially if your definition of "mathematician" is somebody who takes a demonstration on a Euclidean plane and says it's wrong because it doesn't apply in an arbitrary geometry.
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I think BH was referring to me there.🤣🤣🤣
gomezz said:
You would indeed need to specify that your are talking about Euclidean geometry in a full and strict proof. In the world at large I think it is safe to assume this unless talking about global navigation and such like where the context would imply spherical geometry (eg where parallel lines do meet).
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So, what is your proof of Pythagoras in Euclidean space?
 
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Even in 2D space time, ie, a 1D space plus time, Pythagoras takes the form

cc=aa-bb

for suitable dimensions. You can't get more concrete than that.😁

Then, take planes following great circles on their journeys. No Pythagoras there! Distances are measured along great circles, Euclidean distance is irrelevant.
 
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