All of the squares given by Nagarjuna are 4×4 magic squares, and one of them is called Nagarjuniya after him. Nagarjuna gave a method of constructing 4×4 magic square using a primary skeleton square, given an odd or even magic sum. Incidentally, the special Nagarjuniya square cannot be constructed from the method he expounds.
Full Answer
How many squares in a 4 by 4 grid?
How many squares are there in an 4 x 4 grid. Solution : There are 4 rows and 4 columns in the above figure. So let n =4. Here we using two types of formulas for finding number of squares in an n x n grid as follows. Formula – 1. n2 + (n -1 )2 + (n-2)2 + – – – – – + (n – n)2. Now substitute n = 4 in the above formula.
What is a 4x4 magic square?
The Order for a magic square dimension of the horizontal and vertical axis of the square. Because it's square, these values for a given puzzle are the same. For example, for a 3x3 magic square we say it is an 'order 3' magic square. A 4x4 magic square is order 4, a 5x5 is order 5 and so on. What is the Magic Constant for a Magic Square?
How to create a magic square?
A method for constructing a magic square for odd N is as follows:
- Start in the middle of the top row, and let n = 1;
- Insert n into the current grid position;
- If n = N 2 the grid is complete so stop. Otherwise increment n;
- Move diagonally up and right, wrapping to the first column or last row if the move leads outside the grid. ...
- Return to step 2.
What are magic squares and how are they constructed?
This is because:
- Each row and column of the magic square contains three numbers.
- The square contains nine numbers total, ranging from 1 to 9.
- Each row, column and diagonal adds up to 15.
- All of the numbers in the square add up to 45.
How do you solve 4x4 magic squares?
0:002:10Solve 4x4 magic squares - YouTubeYouTubeStart of suggested clipEnd of suggested clipSo here we have a complete column when we add up these numbers we get 54. So we know that everyMoreSo here we have a complete column when we add up these numbers we get 54. So we know that every other row column and diagonal must also add up to 54 because it's a magic square.
What is magic sum of 4x4 magic square?
The magic square is magic, because the sum of the numbers of each row, each column and both diagonals always give the same result. The sum can be calculated as follows, the (even) size of the square divided by 2 multiplied by the lowest plus the highest number: 4 / 2 x (1 + 16) = 34. What is a 4x4 panmagic square?
How many 4 by 4 magic squares are there?
It is seen that there are in all 468 normalized squares of order 4, and multiplying this number by 2(4!) 2 = 1152, we get for the total number of magic squares of order 4 the number 539,136.
What is the magic square of order 4?
Notice in the rearrangement that the numbers in our original 4 4 magic square stay together. That is, the numbers 16,2,3,13 that appear in the first row will always be together, in some order, in a row or column of a new square.
What is the formula for magic square?
To solve an odd-numbered magic square, start by using the formula n[(n^2+1)/2] to calculate the magic constant, or the number that all rows, columns, and diagonals must add up to. For example, in a 3 by 3 square where n=3, the magic constant is 15.
How do you do the magic square trick?
0:343:57Magic Square Party Trick - Numberphile - YouTubeYouTubeStart of suggested clipEnd of suggested clipIf you go through and check those the second row will add up to 42. And all the columns up to 42 theMoreIf you go through and check those the second row will add up to 42. And all the columns up to 42 the diagonals the 42. The opposite i mean all four in the corners up to 42. Each four in the corner.
How do you draw a magic square of order 4?
3:009:27All About 4 X 4 Magic Square II How Many Patterns? - YouTubeYouTubeStart of suggested clipEnd of suggested clipIf we are talking of 4 by 4 magic square then k is 4 so if you substitute k equal to 4 here 4 timesMoreIf we are talking of 4 by 4 magic square then k is 4 so if you substitute k equal to 4 here 4 times 4 square 16 plus 1 17 upon 2 68 upon 2 this is 34..
What is unique about Ramanujan magic square?
This is a unique magic square because not only do the rows, columns, and diagonals add up to the same number, but the four corners, the four middle squares (17, 9, 24, 89), the first and last rows two numbers in middle (12, 18, 86, 23), and the first and last columns two middle numbers (88, 10, 25, 16) all add up to ...
How do magic squares work?
A magic square is an n x n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. This number is called the magic number. The main diagonals are those that stretch from corner to corner.
What is magic square chart?
A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., arranged such that the sum of the numbers in any horizontal, vertical, or main diagonal line is always the same number (Kraitchik 1942, p. 142; Andrews 1960, p. 1; Gardner 1961, p. 130; Madachy 1979, p.
How to make a magic square?
You can make your own Magic Square in two ways. Try both methods: Enter your own numbers into the Red Squares and then click on "Add Rows". You can experiment with any numbers using any strategy. Put numbers in the top set of squares and click on "Make Square". If you try this method try any numbers you like.
How many variations are there in a fundamenstal square?
Although they may look very different there are actually only three fundamentally different designs. Rotation, reflection, and translocation provides 128 variations for each of these fundamenstal squares for a grand total of 384.
How to make a square in Excel?
Put numbers in the top set of squares and click on "Make Square". If you try this method try any numbers you like. But, to get a conventional square use:#N#Numbers 8, 4, 2, and 1 - in any order in the first four cells.#N#The fifth number is the starting value, usually 1. 1 Numbers 8, 4, 2, and 1 - in any order in the first four cells. 2 The fifth number is the starting value, usually 1.
What are the numbers in the red squares?
The numbers in the Red Squares form the 3x3 magic Square. The numbers beside the Red Squares show the totals for each row. The horizontal and vertical totals are to the right and below in green squares. The other, blue, squares show the diagonal totals - including all of the "broken diagonals". You can make your own Magic Square in two ways.
How many equivalent squares are there in magic square?
In discussing magic squares, equivalent squares are usually not considered as distinct. The 8 equivalent squares are given for the 3×3 magic square below: 8. 1. 6.
What is the smallest magic square?
The smallest (and unique up to rotation and reflection ) non-trivial case of a magic square, order 3. In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The order of the magic square is the number ...
What is Parker Square?
The Parker Square, named after recreational mathematician Matt Parker, is an attempt to create a 3 × 3 magic square of squares — a prized unsolved problem since Euler. The Parker Square is a trivial semimagic square since it uses some numbers more than once, and the diagonal 232 + 372 + 472 sums to 4107, not 3051 as for all the other rows, columns, or diagonal. The Parker Square became a "mascot for people who give it a go, but ultimately fall short". It is also a metaphor for something that is almost right, but is a little off.
What is the magic square of Jupiter?
The square associated with Jupiter appears as a talisman used to drive away melancholy . It is very similar to Yang Hui 's square, which was created in China about 250 years before Dürer's time. As with every order 4 normal magic square, the magic sum is 34. But in the Durer square this sum is also found in each of the quadrants, in the center four squares, and in the corner squares (of the 4×4 as well as the four contained 3×3 grids). This sum can also be found in the four outer numbers clockwise from the corners (3+8+14+9) and likewise the four counter-clockwise (the locations of four queens in the two solutions of the 4 queens puzzle ), the two sets of four symmetrical numbers (2+8+9+15 and 3+5+12+14), the sum of the middle two entries of the two outer columns and rows (5+9+8+12 and 3+2+15+14), and in four kite or cross shaped quartets (3+5+11+15, 2+10+8+14, 3+9+7+15, and 2+6+12+14). The two numbers in the middle of the bottom row give the date of the engraving: 1514. The numbers 1 and 4 at either side of the date correspond respectively to the letters "A" and "D," which are the initials of the artist.
How to find moment of inertia of a magic square?
The moment of inertia of a magic square has been defined as the sum over all cells of the number in the cell times the squared distance from the center of the cell to the center of the square; here the unit of measurement is the width of one cell. (Thus for example a corner cell of a 3×3 square has a distance of#N#2 , {displaystyle {sqrt {2}},}#N#a non-corner edge cell has a distance of 1, and the center cell has a distance of 0.) Then all magic squares of a given order have the same moment of inertia as each other. For the order-3 case the moment of inertia is always 60, while for the order-4 case the moment of inertia is always 340. In general, for the n × n case the moment of inertia is#N#n 2 ( n 4 − 1 ) / 12. {displaystyle n^ {2} (n^ {4}-1)/12.}
Where did magic squares come from?
Unlike in Persia and Arabia, we have better documentation of how the magic squares were transmitted to Europe. Around 1315, influenced by Arab sources, the Greek Byzantine scholar Manuel Moschopoulos wrote a mathematical treatise on the subject of magic squares, leaving out the mysticism of his Middle Eastern predecessors, where he gave two methods for odd squares and two methods for evenly even squares. Moschopoulos was essentially unknown to the Latin Europe until the late 17th century, when Philippe de la Hire rediscovered his treatise in the Royal Library of Paris. However, he was not the first European to have written on magic squares; and the magic squares were disseminated to rest of Europe through Spain and Italy as occult objects. The early occult treaties that displayed the squares did not describe how they were constructed. Thus the entire theory had to be rediscovered.
What happens when you divide a magic square by a magic constant?
Dividing each number of the magic square by the magic constant will yield a doubly stochastic matrix, whose row sums and column sums equal to unity. However, unlike the doubly stochastic matrix, the diagonal sums of such matrices will also equal to unity.
How many magic carpets are there in order 4?
However, for many other magic squares, the Latin Squares are readily, and helpfully, decomposed into the component magic carpets, e.g., order 4 is best understood as four binary magic carpets; order 8 as 6 binary magic carpets; and order 9 as 4 magic carpets in base 3.
What is a 4x4 magic carpet?
The fundamental 4x4 magic carpet can be represented by dots and spaces. Any line in any direction of length four contains two dots, i.e., it sums to 2; any selected 4x4 area is a pan-magic pattern. We can take four samples of this large carpet, rotate two of them, and make the only four possible order four magic carpets. " S ".
What is a prime number pan magic square?
Regular prime number pan magic squares (larger then order 3), e.g., order 5, are composed of two Magic Carpets, or Latin Squares. For such squares the Latin Square and the Magic Carpet are one and the same. Neither of the two Latin Squares can be decomposed further into more detailed Magic Carpets, and all rows, columns, ...
How many letters are in a 4x4?
Any 4x4 area contains each letter twice in every row, every line, and every diagonal. To make an actual 4x4 magic square the letters in this square would be replaced, respectively by 8, 4, 2, and 1 (see Main 4x4 Page ).
What is the dot in each of the above squares?
The dot in each of the above squares is replaced with its own letter. The four squares are then combined to make the composite square on the left and then the larger carpet on the right.
Is a square a Latin square?
Not a Latin Square. Strictly speaking this is not a "Latin Square". A Latin Square for order N uses N letters N times and each row and each column contains one of each letter. The above square can be converted into two Latin Squares.
Can you use Latin squares in a 4x4?
Because of this limitation, Latin Squares are of only limited use in constructing 4x4 pan-magic squares. There are two other possible 4x4 alphabetical squares and all three are shown below. The third is not even Latin in that, now, only the diagonals contain one of each letter.