FYI, there is a very simple reason this works. In every row and column the following is true. 1. there is a 1 in a ones position and a tens position. 2. there is a 5 in the ones and the tens position. 3. there is an 8 in the ones and tens position. 4. there is a 2 in the ones and tens position (this accounts for all 8 numbers in any row and will always yield the same sum no matter the order) 5. The diagonal also follows the previously outlined pattern, but of course if you make the diagonals first, you can fill in the rest with what's left over. If you replace any of these four numbers (and all instances of itself) with any number you choose and follow the same process, you will still get a perfect square. Having said that, the additional properties of these numbers create the other effects. effect one: turning upside down. when turning these numbers upside down, the only thing that changes is whether it is in the ones or the tens place. Since there is one occurrence of each of these numbers in a ones position, and one in the tens position in all cases, this evens itself out. effect two: reflection The ones and eights when reflected also only change from ones to tens, or tens to ones because they are mirror images in themselves. Like effect one, this still has no effect on the sum. The 5 and the 2 are slightly different. The 5 and 2 not only change from ones to tens, or tens to ones (which creates no effect) but they also change from 2 to 5 or 5 to 2. This also has no effect since the number of 2's in ones place or tens place, as well as the number of 5's in ones or tens place is not effected by this trade off. In conclusion, if you create two diagonals that follow the rules of a 125 and 8 in the ones place and tens place (and hundreds, and thousands. ten thousands and so on) and then fill in the rest of the grid following the same criteria, you can replicate this effect. You can also replace your 8 or 1 with 0 ( or add another column and row to facilitate adding zeroes) as long as you are willing to have numbers that begin with 0 (such as 01, 02, 05, or 08) I can't believe I made this comment so detailed...wow
Nice visual representation of the format. The reason there are 16 distinct entries is because, if you consider the row/column/diagonal sum, which can be written as 10*(1+2+5+8) + (1+2+5+8), each entry essentially chooses one of the numbers 1,2,5,8 (4 choices) for the one's place and again one of the numbers 1,2,5,8 (4 choices) for the ten's place. This gives exactly 4x4 = 16 distinct entries for the whole square.
Normal, upside-down, and reflected, all the numbers in the diagonals, the rows, and the columns all add up to 176. And the current number of numberphile videos is 176. OMG!!!!!!
I JUST realized how simple that square is. 176=11*16. He uses two pairs of numbers to achieve this in each section - a number and itself backwards, which is the two digits times 11, and then two multiples of 11. He just has to make sure they add up to 16, and that they are all backwards numbers, which is most numbers.
I think i figured out how it works. Basically, all the numbers are made up of either 1,2,5, or 8, which are all reverse able. When you add all the numbers, you'll always be adding 1,2,5,8 in the ones column, and 1,2,5,8 on the tens column, so it's the same any direction yo add the numbers.
Ah, this is the sort of thing I love about maths - spent the morning doing proofs with hyperbolic trig, and now I'm watching a video about something simple yet beautiful. Love the video, as always, and the paper/pen combo's really growing on me now. Thanks, @numberphile
I just spotted something else. If you add up all the sides that make up the numbers, they all equal 36. For example, the number 5, as he has written it, has five sides. Number one has one side. Number two has five sides. Eight has seven sides. Etc. Add up all sides in the same manner that he gets 176 and the number of 'sides' equals 36.
If you divide numbers into segments, as in seven-segment indicators: 5 has 5 segments, 2 - also has 5 segments, 1 has 2 segments, 8 has all 7 segments and so on. And then add up the number of segments in each cell, you will also get a magic square: 10. 9. 7. 12. 9. 10. 7. 12. 7. 7. 14. 10. 12. 12. 10. 4.
@ThrashMetalForces see brown paper link in the video description for my discussion of the brown paper question... we are changing markers, but I am not re-recording everything done with the old ones.. I don't have time and neither do the professors....
In fact you can add ANY combination of ANY numbers in there and it will ALWAYS give the same result! That's awesome! It even works when you multiply them too, including upside down or sideways.
Thank you for all the work you do Brady. I am a mathematics student and although your videos don't replace class time they really help me to have a better understanding of topics and get more out of my classes. Plus videos like this help me to get my tutoring students to look a math in a different and fun way. Keep up the great work.
It's also mirrored across the diagonal (top-left to bottom-right) axis. At 3:55, for example, the bottom-left corner is 28 while the top-right corner is 85. Row 4 column 2 is the mirror of row 2 column 4, etc.
if im not mistaken all the number in a horizontal row, vertical row and diagonal row have the same digits two 1's, two 2's, two 5's, two 8's. i like it!
Yes, The Professor forgot to mention that each number should be unique. Also, this magic square is indeed interesting - also, easy to construct and to prove. Anyone should see a pattern in it after a while - if you consider both digits of each number separately. Great clip!
If you take the separate numbers in each row or column and add them us (e.g. 1+1+2+2+5+8+8+5) they all add up to 32, as do the diagonals. It also works upside down and at 90 degrees.
Boxes of four numbers work too for this, and another cool thing is that this magic square uses all of the posible 2 digit combinations of the four digits 1,2,8, and 5
@quosmo1 I would say count segments, since that's what a lot of the square is based upon. And there's 38 of them in each row/col/diagonal. :) Key is, each r/c/d contains 1, 2, 5, 8, two of each.
Roger, you've constructed that square so that each set of four has exactly one 1,2,5,8 in both the tens place and the ones place. Can a magic square be constructed using any four digits in the same way? For example, 1,3,6,7?
I get it. Each row/column/diagonal etc. has a 2, a 5, an 8, and a 1 in both the tens and ones place. I bet you could extend that to three digits. That'd be really cool
I think if you rotate each number in it's position 90 degrees and look at it from either side it still works too, like the left edge of the upside down version becomes the top row after rotating each number 90 degrees counterclockwise, 28 + 82+55+11=176
That happens because in every row and in every column, he used the same digits. Every row/column has 2 Ones, 2 Twos, 2 Fives and 2 Eights. Actually every row/column have all 4 digits in the 10's and all 4 digits in the 1's. (1X,2X,5X,8X...X1,X2,X5,X8). So if every row has the same digits, of course the pencil strokes will add up.
I learned of this concept as something called an IXOHOXI. The name (when written in all caps) is the same forwards, backwards, upside down, and in a mirror. The IXOHOXI I first saw used 1s, 6s, 8s, and 9s.
1, 2, 3... etc are symbols that represent a specific value 0 does not represent a value, 0 represents the absence of value. That's like saying no car is a car.
@sjsawyer take an x sudoku, divide it in to 9 3*3 sections and add (number -1)*9 from the magic square below to each number based on where they are. So the center 9 numbers add 36, the top right 9 add 63 and so on. 834 159 672 You can even use a similar trick to make a 27*27 or 81*81 magic square.
zeroes can also be mirrored, which allow 5 by 5 reversible magic squares 10 25 58 81 02 52 08 21 10 85 08 10 85 22 51 81 52 10 05 28 25 81 02 58 10 This works upside down and mirrored (no diagonals)
i may be late to the party but you may notice that all the same digits are used: 1,2,5,8. the reason being that the vertical reflection for these digit are equal to themselves or one another when flipped. 1=1. 2=5. 5=2. and 8=8. No imagine that each line that you draw across the square has to use each digit once and only once for each decimal place. By this i mean 52 and 82 can not be in the same line while 15 and 18 can not be in the same line because the repeated. so long as you follow this rule for the 4x4 square the sum of the numbers can equal 176 and if you've flipped your square, you still follow that rule. try it out
i think every magic square will still stay the same if you reflect it or rotate it because it is just the way numbers add. commutativity and associativity of addition.
Precisely speaking, this works because he's only used the digits '1', '2', '5' and '8'. And 176 is simply 1+10+2+20+5+50+8+80. So any combination of the above mentioned digits in units and tens places(exactly once) will sum up to 176. For example 12+25+58+81=176(each numebr 1,2,5,8 exactly once in units place and tens place) He also missed out, the sum of corners, sum of 2x2 corner sub-squares also come to 176. Not saying that this is not that amusing.
Interesting that an 11x11 magic square has a magic sum of 671, being 11x61, and this square has the magic sum of 176, being 16x11. 16 is 8+8 and 61 is 30.5+30.5. 3+0+5=8. 1+7+6=14, and 1+4=5. With 11, you have a digit sum of 2. Just something interesting in this with the 2,5, and 8(i.e. 2+5=7; 2+8=10, which reduces to 1; and 5+8=13, which reduces to 4, etc.), especially since they share similar properties, just as 1, 4, and 7 do(1+4=5; 1+7=8; and 4+7=11, which reduces to 2; etc.), and 3, 6, and 9, also(3+6=9; 3+9=12, which reduces to 3; and 6+9=15, which reduces to 6; etc.). They also have similar multiplicative properties(i.e. 4x7=28, and 2+8=10, which reduces to 1; 7x7=49, and 4+9=13, which reduces to 4; 2x8=16, which reduces to 7; 5x8=40, which reduces to 4; etc.). If you make an addition and multiplication table, with the numbers 1-9, and reduce all the results to their single digit sums (like I've previously shown), you'll notice some interesting patterns. This is all sort of a tangent, but I just wonder how it might tie the inherent nature of 2, 5, and 8.
Isn't it an even MORE magic square because if you look at the right numbers in a column it adds up to 16, and if you look at the left numbers in that same column it also adds up to 16? And that holds true for every column! Even rows! Also upside down! And mirrored!
@ishouldtellyou714 yes,thats interesting but if you think about it it makes sense, it always 10 +20+50+80 in the tens places and 1+2+5+8 in the ones place, the diagonals are the only hard part, and you can't make a 4x4 magic square without the center2x2 square that doesnt add up to the magic constant.
Also adding the 4 opposing ends of the 2 inner rows or columns, even the diagonals = 176 and the outer 4 corners too. wow 176 / 2 = 88 and no mater how many times another 7 is put in the middle then divided by 2 will be all 8's. for example 177776 divided by 2 is 88888 also if the 7 is removed. 16 divided by 2 = 8 888....always the same mirrored, reversed, and rotated. those crazy 8's do you think the birth-date of America was a coincidence?
5 22 18 28 15 2 12 8 25 if you write the numbers in words then do another square based on the number of letters (in the same positions) you also get a magic square (consisting of the numbers 3 to 11), plus the number of letters in the magic sums (when written in words) in both is 9 which is 3 x 3
he went for the diffirent kind of magic the one where nothing special happens however your being distracted by something else so it looks like something special did happen
I also find astonishing, that the numbers in the magic square consist of only 4 different digits, beeing 1,2,5 and 8. Or is that a property of ALL magic squares?
Really interested in who came up with it. And how he did it. I mean, I can't imagine someone trying out numbers for this reason exactly, not the reverse/mirror reading thing at least.
That magic square has only 1s, 2s, 5s and 8s in it. Every one of these numbers is used 8 times. 4 times at the start, 4 times at the end. the number of total different, two number combinations with these 4 numbers. is exactly 16 (= the amount of squares) Every row has two of each number. flipping or mirroring won't change that. I'm sorry that's all the connections I found why I don't think someone randomly "dreamed" this magic square up.
FYI, there is a very simple reason this works. In every row and column the following is true.
1. there is a 1 in a ones position and a tens position.
2. there is a 5 in the ones and the tens position.
3. there is an 8 in the ones and tens position.
4. there is a 2 in the ones and tens position
(this accounts for all 8 numbers in any row and will always yield the same sum no matter the order)
5. The diagonal also follows the previously outlined pattern, but of course if you make the diagonals first, you can fill in the rest with what's left over.
If you replace any of these four numbers (and all instances of itself) with any number you choose and follow the same process, you will still get a perfect square.
Having said that, the additional properties of these numbers create the other effects.
effect one: turning upside down.
when turning these numbers upside down, the only thing that changes is whether it is in the ones or the tens place. Since there is one occurrence of each of these numbers in a ones position, and one in the tens position in all cases, this evens itself out.
effect two: reflection
The ones and eights when reflected also only change from ones to tens, or tens to ones because they are mirror images in themselves. Like effect one, this still has no effect on the sum. The 5 and the 2 are slightly different. The 5 and 2 not only change from ones to tens, or tens to ones (which creates no effect) but they also change from 2 to 5 or 5 to 2. This also has no effect since the number of 2's in ones place or tens place, as well as the number of 5's in ones or tens place is not effected by this trade off.
In conclusion, if you create two diagonals that follow the rules of a 125 and 8 in the ones place and tens place (and hundreds, and thousands. ten thousands and so on) and then fill in the rest of the grid following the same criteria, you can replicate this effect. You can also replace your 8 or 1 with 0 ( or add another column and row to facilitate adding zeroes) as long as you are willing to have numbers that begin with 0 (such as 01, 02, 05, or 08)
I can't believe I made this comment so detailed...wow
Nice visual representation of the format. The reason there are 16 distinct entries is because, if you consider the row/column/diagonal sum, which can be written as 10*(1+2+5+8) + (1+2+5+8), each entry essentially chooses one of the numbers 1,2,5,8 (4 choices) for the one's place and again one of the numbers 1,2,5,8 (4 choices) for the ten's place. This gives exactly 4x4 = 16 distinct entries for the whole square.
And let us take sum time to reflect upon the product (b^1+1)(1+2+5+8).
This is no longer a magic square, this is a magic tesseract
Brilliant.
No it's not
Pfft, well it doesn't literally make sense but metaphorically it does.
+Walavouchey *sense
and I suggest googling the definition of metaphor.
Ahh, sorry for trying. I don't want to go any deeper into definitions, but I suggest trying to understand the joke.
I've been showing these videos to friends who always claimed they HATE MATHS, they don't anymore. Absolutely inspiring, thank you
I thought this was a Parker Square of a video
but it was not even if you look at it in a mirror or upside down.
Normal, upside-down, and reflected, all the numbers in the diagonals, the rows, and the columns all add up to 176. And the current number of numberphile videos is 176. OMG!!!!!!
@@projpotat8965 we were never separated
@wildsabes great to hear! thank you and cheers for showing your friends!
The mirror bit was definitely a surprise.
I JUST realized how simple that square is. 176=11*16. He uses two pairs of numbers to achieve this in each section - a number and itself backwards, which is the two digits times 11, and then two multiples of 11. He just has to make sure they add up to 16, and that they are all backwards numbers, which is most numbers.
It might have been smart to use thin paper and a marker that bleeds through, so you could have turned the paper around.
This is my favourite magic square.
1111
1111
1111
1111
or
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
Mine is
666|666|666|666
666|666|666|666
666|666|666|666
666|666|666|666
1 1 1
1. 1. 1
1. 1. 1
1. 1. 1.
here is mine
3652463.4 3652438.4 3652470.4 3652445.4 3652372.4 3652422.4 3652379.4 3652429.4 3652386.4 3652411.4
3652388.4 3652413.4 3652395.4 3652420.4 3652447.4 3652397.4 3652454.4 3652404.4 3652461.4 3652436.4
3652469.4 3652444.4 3652451.4 3652426.4 3652378.4 3652428.4 3652385.4 3652435.4 3652387.4 3652412.4
3652394.4 3652419.4 3652376.4 3652401.4 3652453.4 3652403.4 3652460.4 3652410.4 3652462.4 3652437.4
3652375.4 3652425.4 3652452.4 3652427.4 3652459.4 3652434.4 3652391.4 3652441.4 3652393.4 3652418.4
3652450.4 3652400.4 3652377.4 3652402.4 3652384.4 3652409.4 3652466.4 3652416.4 3652468.4 3652443.4
3652456.4 3652431.4 3652458.4 3652433.4 3652390.4 3652440.4 3652392.4 3652442.4 3652374.4 3652399.4
3652381.4 3652406.4 3652383.4 3652408.4 3652465.4 3652415.4 3652467.4 3652417.4 3652449.4 3652424.4
3652457.4 3652432.4 3652464.4 3652439.4 3652396.4 3652446.4 3652373.4 3652423.4 3652380.4 3652405.4
3652382.4 3652407.4 3652389.4 3652414.4 3652471.4 3652421.4 3652448.4 3652398.4 3652455.4 3652430.4
Leonard Gotlibowski yes, just, yes
Love Prof Bowley! Glad to see he's not off our screens yet. Great vid!
I think i figured out how it works. Basically, all the numbers are made up of either 1,2,5, or 8, which are all reverse able. When you add all the numbers, you'll always be adding 1,2,5,8 in the ones column, and 1,2,5,8 on the tens column, so it's the same any direction yo add the numbers.
Duh! Nah, just kidding. You got it.
ok, so can you come up with your own magic square now that you apparently have grasped the concept?
Nice... so 176 is just 16*(10+1)
Ah, this is the sort of thing I love about maths - spent the morning doing proofs with hyperbolic trig, and now I'm watching a video about something simple yet beautiful. Love the video, as always, and the paper/pen combo's really growing on me now. Thanks, @numberphile
I just spotted something else. If you add up all the sides that make up the numbers, they all equal 36. For example, the number 5, as he has written it, has five sides. Number one has one side. Number two has five sides. Eight has seven sides. Etc. Add up all sides in the same manner that he gets 176 and the number of 'sides' equals 36.
It took me a long time to understand what you meant by "side". The number of line segments in each digit.
If you divide numbers into segments, as in seven-segment indicators:
5 has 5 segments,
2 - also has 5 segments,
1 has 2 segments,
8 has all 7 segments and so on.
And then add up the number of segments in each cell, you will also get a magic square:
10. 9. 7. 12.
9. 10. 7. 12.
7. 7. 14. 10.
12. 12. 10. 4.
A brief explanation of the segments:
|
| - this is 1
_
|
_
|
_ - this is 5
And so on.
This is the most awesome thing I've seen today!
@ThrashMetalForces see brown paper link in the video description for my discussion of the brown paper question... we are changing markers, but I am not re-recording everything done with the old ones.. I don't have time and neither do the professors....
In fact you can add ANY combination of ANY numbers in there and it will ALWAYS give the same result! That's awesome! It even works when you multiply them too, including upside down or sideways.
Thank you for all the work you do Brady. I am a mathematics student and although your videos don't replace class time they really help me to have a better understanding of topics and get more out of my classes. Plus videos like this help me to get my tutoring students to look a math in a different and fun way. Keep up the great work.
It's also mirrored across the diagonal (top-left to bottom-right) axis. At 3:55, for example, the bottom-left corner is 28 while the top-right corner is 85. Row 4 column 2 is the mirror of row 2 column 4, etc.
How cool....you guys collaborating!
If I look at your magic square box at any direction, I see, 16 standing eggs and 16 laying eggs. You are genius.
@virumoz he didn't... but maybe he'll tell us... he appears here in the comments section from time to time!
if im not mistaken all the number in a horizontal row, vertical row and diagonal row have the same digits two 1's, two 2's, two 5's, two 8's. i like it!
Yes, The Professor forgot to mention that each number should be unique.
Also, this magic square is indeed interesting - also, easy to construct and to prove. Anyone should see a pattern in it after a while - if you consider both digits of each number separately.
Great clip!
Love you, Roger!
i had heard of magic squares before, but never this one. this one is so awesome!!!!
This is the first Numberphile video to not be about a particular number.
damnnn the marker sound on the paper gives me goose pump
A link to Roger's drawing can be found in the full video description (click "show more" to see it).
If you take the separate numbers in each row or column and add them us (e.g. 1+1+2+2+5+8+8+5) they all add up to 32, as do the diagonals. It also works upside down and at 90 degrees.
I wish roger bowley was my maths teacher! It's just something about the way he talks that leaves me intrigued and interested.
But why? And how?
I love Numberphile! Keep 'em coming!
Boxes of four numbers work too for this, and another cool thing is that this magic square uses all of the posible 2 digit combinations of the four digits 1,2,8, and 5
MIND BLOWN!
There is also a 1,2,5, and 8 in both the 1 and 10's place in every row, column, diagonal, and square.
MIND BLOWN.
this is the one and only thing that i like to watch on youtube, yet i have no idea what they are saying most of the time.
What if we call this due to the unique mirror reflection, assign it a new category the MMS or Mirror Magic Square.
... are there others still to come?
Accidentally, all possible combinations in his square also adds up to his IQ. I thought that was the most impressive.
This is a special magic square.
As opposed to the Parker square, which is a "special" magic square
@quosmo1 I would say count segments, since that's what a lot of the square is based upon. And there's 38 of them in each row/col/diagonal. :) Key is, each r/c/d contains 1, 2, 5, 8, two of each.
Roger, you've constructed that square so that each set of four has exactly one 1,2,5,8 in both the tens place and the ones place. Can a magic square be constructed using any four digits in the same way? For example, 1,3,6,7?
I actually love the squeaky sound from those pens. It makes me calm.
I love watching people get excited over numbers.^^
2:39
[Jaw drops]... he's not about to say... he just said... WHAT!
I get it. Each row/column/diagonal etc. has a 2, a 5, an 8, and a 1 in both the tens and ones place. I bet you could extend that to three digits. That'd be really cool
one thing they didn't mention and is essential for a magic square is that the numbers should not be repeated.
I think if you rotate each number in it's position 90 degrees and look at it from either side it still works too, like the left edge of the upside down version becomes the top row after rotating each number 90 degrees counterclockwise, 28 + 82+55+11=176
That happens because in every row and in every column, he used the same digits. Every row/column has 2 Ones, 2 Twos, 2 Fives and 2 Eights. Actually every row/column have all 4 digits in the 10's and all 4 digits in the 1's. (1X,2X,5X,8X...X1,X2,X5,X8).
So if every row has the same digits, of course the pencil strokes will add up.
I learned of this concept as something called an IXOHOXI. The name (when written in all caps) is the same forwards, backwards, upside down, and in a mirror. The IXOHOXI I first saw used 1s, 6s, 8s, and 9s.
just saw the sixty symbols video on this. how interesting that this come up right after
1, 2, 3... etc are symbols that represent a specific value 0 does not represent a value, 0 represents the absence of value.
That's like saying no car is a car.
@sjsawyer take an x sudoku, divide it in to 9 3*3 sections and add (number -1)*9 from the magic square below to each number based on where they are. So the center 9 numbers add 36, the top right 9 add 63 and so on.
834
159
672
You can even use a similar trick to make a 27*27 or 81*81 magic square.
zeroes can also be mirrored, which allow 5 by 5 reversible magic squares
10 25 58 81 02
52 08 21 10 85
08 10 85 22 51
81 52 10 05 28
25 81 02 58 10
This works upside down and mirrored (no diagonals)
i may be late to the party but you may notice that all the same digits are used: 1,2,5,8. the reason being that the vertical reflection for these digit are equal to themselves or one another when flipped. 1=1. 2=5. 5=2. and 8=8. No imagine that each line that you draw across the square has to use each digit once and only once for each decimal place. By this i mean 52 and 82 can not be in the same line while 15 and 18 can not be in the same line because the repeated. so long as you follow this rule for the 4x4 square the sum of the numbers can equal 176 and if you've flipped your square, you still follow that rule. try it out
i think every magic square will still stay the same if you reflect it or rotate it because it is just the way numbers add. commutativity and associativity of addition.
Precisely speaking, this works because he's only used the digits '1', '2', '5' and '8'.
And 176 is simply 1+10+2+20+5+50+8+80.
So any combination of the above mentioned digits in units and tens places(exactly once) will sum up to 176.
For example 12+25+58+81=176(each numebr 1,2,5,8 exactly once in units place and tens place)
He also missed out, the sum of corners, sum of 2x2 corner sub-squares also come to 176.
Not saying that this is not that amusing.
the last few seconds made me laugh XD
Brady must've me gusta'd when Roger said "This is gonna take some time, Brady."
Interesting that an 11x11 magic square has a magic sum of 671, being 11x61, and this square has the magic sum of 176, being 16x11. 16 is 8+8 and 61 is 30.5+30.5. 3+0+5=8. 1+7+6=14, and 1+4=5. With 11, you have a digit sum of 2.
Just something interesting in this with the 2,5, and 8(i.e. 2+5=7; 2+8=10, which reduces to 1; and 5+8=13, which reduces to 4, etc.), especially since they share similar properties, just as 1, 4, and 7 do(1+4=5; 1+7=8; and 4+7=11, which reduces to 2; etc.), and 3, 6, and 9, also(3+6=9; 3+9=12, which reduces to 3; and 6+9=15, which reduces to 6; etc.). They also have similar multiplicative properties(i.e. 4x7=28, and 2+8=10, which reduces to 1; 7x7=49, and 4+9=13, which reduces to 4; 2x8=16, which reduces to 7; 5x8=40, which reduces to 4; etc.). If you make an addition and multiplication table, with the numbers 1-9, and reduce all the results to their single digit sums (like I've previously shown), you'll notice some interesting patterns. This is all sort of a tangent, but I just wonder how it might tie the inherent nature of 2, 5, and 8.
lt's a magic square squared.
@conferencereport If you add the individual digits they add to 16 and there's two majic squares of those! How cool is that!
A magic square in multiple dimensions, wonderfull.
Isn't it an even MORE magic square because if you look at the right numbers in a column it adds up to 16, and if you look at the left numbers in that same column it also adds up to 16? And that holds true for every column! Even rows! Also upside down! And mirrored!
as well as in every column, diagonal, and mini square
THIS IS AWESOME
Dürer did etchings in wood. "Melancholia" was one such etching.
Actually in every corner 2x2 square sum is also 176 and in central 2x2 square the sum is 176. This works for mirrored and upside down too.
@1212JackJohnson If you multiply the individual digits (e.g. 2 X 5 X 1 X 8 or 5 X 8 X 1 X 2) it equals 80 in all directions.
:)
Amazing! I have got to learn those numbers! :)
You can fill the square in every place with number 1 and have all the same properties
@ishouldtellyou714 yes,thats interesting but if you think about it it makes sense, it always 10 +20+50+80 in the tens places and 1+2+5+8 in the ones place, the diagonals are the only hard part, and you can't make a 4x4 magic square without the center2x2 square that doesnt add up to the magic constant.
Also adding the 4 opposing ends of the 2 inner rows or columns, even the diagonals = 176 and the outer 4 corners too. wow
176 / 2 = 88 and no mater how many times another 7 is put in the middle then divided by 2 will be all 8's.
for example 177776 divided by 2 is 88888
also if the 7 is removed. 16 divided by 2 = 8
888....always the same mirrored, reversed, and rotated. those crazy 8's
do you think the birth-date of America was a coincidence?
@Acid113377 No. They are the only ones that "mirror" - thats why they were chosen!
5 22 18
28 15 2
12 8 25
if you write the numbers in words then do another square based on the number of letters (in the same positions) you also get a magic square (consisting of the numbers 3 to 11), plus the number of letters in the magic sums (when written in words) in both is 9 which is 3 x 3
And if you add up all the lines to draw the numbers you get 34 in all of them!
MAGIC!
(38 if you count 1 and the sides of 8 as having 2 lines)
Whats amazing is that his desk is a chair.
he went for the diffirent kind of magic the one where nothing special happens however your being distracted by something else so it looks like something special did happen
OMFG that is absolutely amazing lol, i wonder if that's a coincidence or if theres some kin of special pattern for getting them
that was beautiful.
Brady, I enjoy all your videos, but something seems missing. Can you please up the volume on the marker squeaks? I can't get enough of them.
I also find astonishing, that the numbers in the magic square consist of only 4 different digits, beeing 1,2,5 and 8. Or is that a property of ALL magic squares?
And the units in each column/row add up to 16 and all the tens digits in each column/row add up to 16 :3
What a legend
actually, it's 38, because in a 7-segment display, the number 1 uses two segments.
That's what I /said/. I quote, "The 'magic number' is the sum of all the numbers, not the sum of the digits of each number."
He was making the square in his comment. Each one is a separate box.
Really interested in who came up with it. And how he did it. I mean, I can't imagine someone trying out numbers for this reason exactly, not the reverse/mirror reading thing at least.
wait a moment.. in every row are exactly 35 lines!! he didn't mention that :)
That interesting that each number repeats twice in the same row, column, ect
That magic square has only 1s, 2s, 5s and 8s in it. Every one of these numbers is used 8 times. 4 times at the start, 4 times at the end. the number of total different, two number combinations with these 4 numbers. is exactly 16 (= the amount of squares) Every row has two of each number. flipping or mirroring won't change that.
I'm sorry that's all the connections I found why I don't think someone randomly "dreamed" this magic square up.
MY GOD! IT TRULY IS A MAGIC SQUARE!!!!
Incredible
My question is,What is the point or functionality of a magic square?
Also,how do you pick what numbers to enter in each box ?
great stuff
every line that he added in order to get 176 had a 1,2,5,8 in both the tens and the ones place
My mind is blown!
There is still one more way to do it. If you were to count each line making up the blocky numbers you will find that it yet again equals 176.