Interesting Items...

[Deleted member 473]

I was aware of past attempts to "design" the actual ratio of pi.

There was a hoax, based on the bible saying
π=3.

Alabama's Slice of Pi

Did the state legislature of Alabama redefine the value of pi according to Biblical precepts?

www.snopes.com

 

[Black Hole]

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.

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.

 

[gomezz]

The simple beauty of mathematical perfection

 

[Black Hole]

Oh yes, the Euler identity. I was blown over when I saw that derived at school.

 

[MikeSh]

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

Yes, very sad.
Probably careless

You might be interested in this:
Analyzing Video Footage Of Collapse of Massive Arecibo Telescope
It's a Scott Manley video (about 13 mins). He does all things 'space' and is worth a watch - for analysis of some news if nothing else. (I think he is a Scot who has moved to California.)

 

[Deleted member 473]

The simple beauty of mathematical perfection

cos π +ι sin π = -1 + 0

 

[Deleted member 473]

I found this diagram far more interesting:


This is just a wonderful proof of Pythagoras's Theorem.

 

[prpr]

Nice. I've never seen that before.
4(ab/2)+cc = (a+b)(a+b)
2ab+cc = aa+2ab+bb
cc = aa+bb

 

[sine24]

So we are still using that expensive EU stuff?

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.

 

[Deleted member 473]

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.


Perhaps not as elegant, as it requires calculating the area of the yellow square.

 

[trog]

@sine24 And I just laugh at you still posting when they have all chosen to ignore you and cannot see your trolling

 

[gomezz]

I found this diagram far more interesting:

View attachment 5297
This is just a wonderful proof of Pythagoras's Theorem.

That is not a proof. It is an illustration.

 

[Black Hole]

That is not a proof. It is an illustration.

Okay, it requires a few words of explanation, but I say it does prove Pythagoras visually.

 

[Deleted member 473]

That is not a proof. It is an illustration.

You can't prove it anyway, as it is false in most geometries. It is an axiom in Hilbert spaces.

 

[gomezz]

Okay, it requires a few words of explanation, but I say it does prove Pythagoras visually.

Then that proves you are not a mathematician.

 

[gomezz]

You can't prove it anyway, as it is false in most geometries. It is an axiom in Hilbert spaces.

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).

 

[Black Hole]

Then that proves you are not a mathematician.

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.

 

[gomezz]

I never said either of those things.

 

[Deleted member 473]

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.

I think BH was referring to me there.

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).

So, what is your proof of Pythagoras in Euclidean space?

 

[Deleted member 473]

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.