I've got it on my Linux computer too. 🙂
Volume 4 is currently absorbing me. But had to refer to Volume 1 for the difficult concept of action.
But Sumerian mathematics has caught my current attention,
3^2 + 4^2 = 5^2
and
3^3 + 4^3 + 5^3 = 6^3
makes a lot of sense in Cuneiform. 🙂
Volume 4 is currently absorbing me. But had to refer to Volume 1 for the difficult concept of action.
But Sumerian mathematics has caught my current attention,
3^2 + 4^2 = 5^2
and
3^3 + 4^3 + 5^3 = 6^3
makes a lot of sense in Cuneiform. 🙂
Here's an example of a 'Magic Square':
The numbers in a magic square are special, and from ancient times have been connected with the magical and supernatural world.
In what way is this magic square special?

The numbers in a magic square are special, and from ancient times have been connected with the magical and supernatural world.
In what way is this magic square special?
Too easy, my friend. Babylonian mathematics, base 60. 😀
We shouldn't look down on the Ancients. Maybe they knew something.
I don't mind putting my hand in my pocket to explore ancient mysteries. Who were the "Three Wise Men"? And what were they up to? 😕
Current explorations reveal that "Czech and Speake's" Frankincense and Myrrh aftershave smells quite good. But pricey. About a £100 a bottle. I don't know where the Gold went. 🙁
We shouldn't look down on the Ancients. Maybe they knew something.
I don't mind putting my hand in my pocket to explore ancient mysteries. Who were the "Three Wise Men"? And what were they up to? 😕
Current explorations reveal that "Czech and Speake's" Frankincense and Myrrh aftershave smells quite good. But pricey. About a £100 a bottle. I don't know where the Gold went. 🙁
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Here is the magic in 15.all the numbers are divisible by 4
No, certain numbers are divisable by 4. 🙂
Fermat's Last Theorem - Wikipedia
The special case n = 4, proved by Fermat himself, is sufficient to establish that if the theorem is false for some exponent n that is not a prime number, it must also be false for some smaller n, so only prime values of n need further investigation.
Fermat's Last Theorem - Wikipedia
But you can divide every one of those numbers by 4. How do you mean "certain"?
Okay, I'm not sharp enough to even grasp the explanation.
Math..who needs it! 🙂
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The first magic square to be seen in Europe was contained within an engraving by artist and mathematician Albrecht Dürer in his work 'Melancholia'.
It includes the date of publication, 1514, as two entries in the middle of the bottom row.
Melancholia
It includes the date of publication, 1514, as two entries in the middle of the bottom row.

Melancholia
The construction of even number magic squares, like the one above, is apparently quite a challenge and involves the use of an algorithm (or two).
Odd number magic squares, like the one I first posted, are fairly easily constructed using simple methods.
@ Discopete: Keep looking at the numbers, ignore Steve's divisible by 4 malarky, and consider his earlier Babylonian clue.
Odd number magic squares, like the one I first posted, are fairly easily constructed using simple methods.
@ Discopete: Keep looking at the numbers, ignore Steve's divisible by 4 malarky, and consider his earlier Babylonian clue.
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I was a bit slow last night! Perhaps because the numbers seemed uninteresting. 😱
But have got it now. How big can you make these things and they still work? 😕
Hardy was visiting his maths friend Ramanujan and got a taxi to Putney, IIRC.
Ramanujan wondered what the Taxicab number was...
"1729" said Hardy. "Seems an uninteresting number."
"Oh no. 1729 is an extremely interesting number." Said Ramanujan.
What was amazing about Ramanujan, is he pretty much invented Elliptic curves. He was trying to solve Fermat. And his intuition was right, because the Wiles proof was based on elliptic curves. Funny things. Almost organic.

But have got it now. How big can you make these things and they still work? 😕
Hardy was visiting his maths friend Ramanujan and got a taxi to Putney, IIRC.
Ramanujan wondered what the Taxicab number was...
"1729" said Hardy. "Seems an uninteresting number."
"Oh no. 1729 is an extremely interesting number." Said Ramanujan.
What was amazing about Ramanujan, is he pretty much invented Elliptic curves. He was trying to solve Fermat. And his intuition was right, because the Wiles proof was based on elliptic curves. Funny things. Almost organic.
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Math is by far not my strong suite, but if we have a long and hard look at everything in known existence I find the only number that is completely unrealistic is "0".Idealism belongs to mathematics. Empty space would be purposeless, energy transfer would not be possible and the Universe would not exist. Discontinuity is not allowed in Nature. The interstellar medium has had many names during the centuries. I strongly dislike the name vacuum, it reflects an unphysical view, the view of a bunch of mathematicians.
In terms of math complexity I usually draw the line at ohms law.
But for me, fluid dynamics and mass falls under a segment within "dimensional understanding".
Things like mass density and fluid dynamics is easy to just imagine to a molecular level, since there's no shortage of comparisons in everyday life. Everyone can think and understand what lower or higher mass entails, likewise with fluids of higher or lower viscosity.
Perhaps I may be misinterpreting, but I find this somewhat condescending.Hey, this is beautifully said!
Just because I avoid most theory on the basis of cumbersome, poorly worded and inflated text, it does not translate to me being an illiterate.
Atomic matter comprising massive, highly compressed, hard nuclei makes up a much more dispersive and slower medium.
Quite, but if you look at it at a lower level you will see that the electrons around nucleus will have higher activity with increasing mass. Even if the end result is like you say a "slower medium" that is more because of the amount and distance between the atoms interacting with each other, I guess it could be said that the medium itself is actually "faster" since the level of activity is higher.
Everyone should feel free to correct my potential misunderstandings.
Physicists don't actually claim to know how forces can propagate through a vacuum.
Such forces can only be described in terms of mathematical artifacts.
Force is tricky to deal with mathematically so you never see it mentioned.
However, the ability of EM waves to travel in vacuum is a fact.
A mathematical fact.
KaffiMann,
Well said. Correctly formulated.
Vacuum is a volume with lower density of mass. There is more distance between the fragments of matter, but there is still matter.
Well said. Correctly formulated.
N101N, since I'm already forced to break things down and nitpick, I can allow myself to correct my own definition by adding: The formulation is correct, within the constraints of current science and understanding.
Hope it's all good wherever you are.
Hope it's all good wherever you are.
The 'magic number' of a 3 x 3 magic square is indeed 15.Here is the magic in 15.

But I'd like someone else to tell me what is magic about this particular square in terms of the arrangement of the numbers within it.
The magic 3 x 3 square.
Sum of rows, columns, diagonales is 15.
I am impressed to see, it uses 1,2,3,4,5,6,7,8,9.
Sum of rows, columns, diagonales is 15.
I am impressed to see, it uses 1,2,3,4,5,6,7,8,9.
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