Thanks for the explanation of bigger Magic Squares.
Whoah. Wait a minute. 😀
I don't see 15 In there at ALL! 😕
Am I missing something?
Whoah. Wait a minute. 😀
I don't see 15 In there at ALL! 😕
Am I missing something?
mchambin is referring to this 3 x 3 magic square:
And not mine:
However, the magic number for all 3 x 3 magic squares is 15.
I see the 12 x 12 magic square in post #5421uses every number from 1 to 144.
Is this feature possible at any size ?
Once you have a magic square of a given size you can make many more by mean of:
Symmetries.
Adding a constant in each cell.
Multiplying each cell by a constant.
Adding two squares, cell by cell.
I presume the square filled with 1,2,3, ...n^2 is the canonical form of the n x n magic square; It is unique regardless of symmetries.
Can this be confirmed ?
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Simple magic squares are constructed using consecutive integers from 1 to n^2 , where n is the number of integers on one side of the square.
So a 3 x 3 magic square uses the integers from 1 to 3^2, or 1 to 9, as below.
For an order 3 magic square, trial and error in positioning the digits does the job.
By multiplying all the digits by 4, we obtain my magic square:
The base 'magic number' is still 15 though.
So a 3 x 3 magic square uses the integers from 1 to 3^2, or 1 to 9, as below.
For an order 3 magic square, trial and error in positioning the digits does the job.
By multiplying all the digits by 4, we obtain my magic square:
The base 'magic number' is still 15 though.
The answer may lie in this link: Solving Magic Squares
However, there's too much mathematics in there for me!
I do see mention of Steve's 'quartics' though! 😎
There is a lot of information about magic squares in Wikipedia.
Many more ways than I thought to built magic squares.
A magic square filled with 1,2,3, n^2 is called a normal magic square. ( not a "canonical form", like I wrote ).
There are much more normal squares than I thought.
Many more ways than I thought to built magic squares.
A magic square filled with 1,2,3, n^2 is called a normal magic square. ( not a "canonical form", like I wrote ).
There are much more normal squares than I thought.
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Magic Squares may repay study.
I know I talk rubbish most of the time. 😱
But have Lucid moments. 😀
Where I have got to, thanks to Felix Klein is that circles, ellipses and hyperbolas are just the same thing.
I know I talk rubbish most of the time. 😱
But have Lucid moments. 😀
Where I have got to, thanks to Felix Klein is that circles, ellipses and hyperbolas are just the same thing.
My images appear to have gone AWOL so, for completeness, I will paste them here:
IMAGE 1
IMAGE 2
An externally hosted image should be here but it was not working when we last tested it.
Conic sections, like magic squares, have a long history.
Apollonius of Perga commented upon them in the 6th century.
His Treatise on Conic Sections is one of the most important mathematical works to have come down to us from the Ancient World, arguably second only to Euclid’s Elements.
The Conics of Apollonius of Perga — Steemit
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I truly appreciate the encouragement Galu but I can't make head nor tail of this explanation. My math career is a no starter. 🙂
I wasn't expecting you to give, or understand, a mathematical explanation, Pete.
The 'magic' I challenged everyone to spot was that the numbers in my magic square summed to 60 when added in a vertical column, a horizontal column and even diagonally.
Nobody has given me that answer, so you are not alone! 😉
The 'magic' I challenged everyone to spot was that the numbers in my magic square summed to 60 when added in a vertical column, a horizontal column and even diagonally.
Nobody has given me that answer, so you are not alone! 😉
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I had no inclination to add any of the numbers but now that you bring it up, it should have been the most intuitive thing to do! Weird🙄
However, Steve hit on it right away, no?
However, Steve hit on it right away, no?
He didn't describe the magic of the square as requested and as I have just described.
He did mention 'Babylonian' base 60, but he does tend to 'Babble on' a bit! 😀
He did mention 'Babylonian' base 60, but he does tend to 'Babble on' a bit! 😀
Lot of Life in Sumerian Base 60, IMO.
I possibly missed my true Vocation as a Military Commander. 🙂
What are we up against here?
Forbidden Planet - It's still coming! - YouTube
Clearly pop-guns and rifles aren't working. 😕
Either deploy Nuclear weapons or wake Doctor Mobius up. 😀
I possibly missed my true Vocation as a Military Commander. 🙂
What are we up against here?
Forbidden Planet - It's still coming! - YouTube
Clearly pop-guns and rifles aren't working. 😕
Either deploy Nuclear weapons or wake Doctor Mobius up. 😀
Lurking behind our thin, rational facade is an impulsive demon that takes control of us, acts without thinking, and serves its own purposes regardless of the impact to our ultimate well-being.
That demon is your id. 😱
Your id, your lizard-brain, your ‘animal’ impulses, that piece of you evolved in a context wildly different from the one in which you now live.
Why does that remind me of Altaira? 😉
That demon is your id. 😱
Your id, your lizard-brain, your ‘animal’ impulses, that piece of you evolved in a context wildly different from the one in which you now live.
Why does that remind me of Altaira? 😉
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The oldest known mathematical puzzle dates from Archimedes, more than two millennia ago.
The goal of Archimedes’ Stomachion is to determine in how many ways 14 pieces can be put together to make a square.
It has been shown that Archimedes’ puzzle has exactly 536 truly distinct solutions.
The goal of Archimedes’ Stomachion is to determine in how many ways 14 pieces can be put together to make a square.
It has been shown that Archimedes’ puzzle has exactly 536 truly distinct solutions.
KaffiMann,
In this endeavour, mathematics is distractive and it constricts imaginative thinking. Yes, zero is nonsensical and so is infinity.
"Slow and fast" are lousy terms. The space medium is the "fastest" medium by far. "Fast" means high particle velocity / vibration frequency due to low density / resistivity / mass / dispersion / pressure, entailing large amplitudes and short wavelengths, that is, high propagation speed and high energy levels.
Vibration frequencies within a certain range give rise to the much-talked-about light phenomenon. Phenomena merely have mental existence.
Atomic matter, clouds of interstellar dust, black holes... are the concentration of the miniscule particles of the space medium. Well, there is no proof, but the institutionalized tenet of voodoo science is much less convincing.
In this endeavour, mathematics is distractive and it constricts imaginative thinking. Yes, zero is nonsensical and so is infinity.
"Slow and fast" are lousy terms. The space medium is the "fastest" medium by far. "Fast" means high particle velocity / vibration frequency due to low density / resistivity / mass / dispersion / pressure, entailing large amplitudes and short wavelengths, that is, high propagation speed and high energy levels.
Vibration frequencies within a certain range give rise to the much-talked-about light phenomenon. Phenomena merely have mental existence.
Atomic matter, clouds of interstellar dust, black holes... are the concentration of the miniscule particles of the space medium. Well, there is no proof, but the institutionalized tenet of voodoo science is much less convincing.
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