This work brings how we can generate Pythagoren triples and Magic square using some interesting tables. These Pythagorean triples again generate Palindromic-Type Pandigital Patterns and Magic Squares. The first table generates 9 blocks, the second table generates 99 blocks, the third table generates 999 blocks, and so on. In case of magic square these are … Continue reading Generating Pythagorean Triples, Palindromic-Type Pandigital Patterns, and Magic Squares
Category: Magic Squares
Block-Wise Construction of Magic and Bimagic Squares of Orders 39 to 45
This paper brings block-wise construction of magic squares of order 39 to 45. In order to construct these magic squares we applied the previous known magic squares of orders 3 to 14, except order 12. The order 22 is also used. In each case these are written again. Specially, in case of magic square of … Continue reading Block-Wise Construction of Magic and Bimagic Squares of Orders 39 to 45
Different Digits Magic Squares and Magic Sums Number Patterns
Magic squares are generally constructed using sequential or concutive numbers such as 1, 2,..., n^2. Here in this work, we shall write magic squares using non consecutive different digits numbers. This work, we have done for the magic squares of orders 5, 7, 8, 9 and 10. As commonly, the entries are not in a … Continue reading Different Digits Magic Squares and Magic Sums Number Patterns
Block-Wise Construction of Magic and Bimagic Squares of Orders 25 to 36
This paper summarizes some of the results done by author in previous works on different ways are writing block-wise magic squares. The details can be seen in the links given below. The work is for the magic squares of orders 12 to 36, i.e., for the orders 12, 15, 16, 18, 20, 21, 24, 25, … Continue reading Block-Wise Construction of Magic and Bimagic Squares of Orders 25 to 36
Block-Wise Construction of Magic and Bimagic Squares of Orders 12 to 24
This paper summarizes some of the results done by author in previous works on different ways are writing block-wise magic squares. The details can be seen in the links given below. The work is for the magic squares of orders 12 to 36, i.e., for the orders 12, 15, 16, 18, 20, 21, 24, 25, … Continue reading Block-Wise Construction of Magic and Bimagic Squares of Orders 12 to 24
Magic Rectangles in Construction of Block-Wise Pan Magic Squares
The idea of magic rectangles is used to bring pan magic squares of orders 15, 21, 27 and 33, where 3x3 blocks are with equal sums entries, and are semi-magic squares of order 3 (in rows and columns). The magic squares of orders 12, 18, 24, 30 and 36 are calculated, with the property that … Continue reading Magic Rectangles in Construction of Block-Wise Pan Magic Squares
Magic Crosses
The idea of magic rectangles is well known in literature. Using this idea we brought for the first time in history a new concept on magic crosses. The work is divided in two groups. One on orders (odd, odd) and another on orders (even, even). Within the orders (odd, odd), the work is on magic … Continue reading Magic Crosses
Letters and Numbers in Terms of Magic Squares of Order 4
This work brings 26 letters from A to Z and 10 numbers from 0 to 9 in terms of blocks of pan diagonal magic squares of order 4. The construction is in such a way that each letter and number is formed by equal magic sums of magic squares of order 4. Similar kind of … Continue reading Letters and Numbers in Terms of Magic Squares of Order 4
Block-Wise Equal Sums Magic Squares of Orders 6k
In this paper, block-wise magic squares of orders 12, 18, 24, 30 and 36 are constructed. The construction is in a such way the each block is a magic square of order 6 with equal magic sums. Below are examples and link of download the complete work: Link for download the complete work: Block-Wise Equal Sums … Continue reading Block-Wise Equal Sums Magic Squares of Orders 6k
Letters and Numbers in Terms of Magic Squares of Order 6
This work brings 26 letters from A to Z and 10 numbers from 0 to 9 in terms of blocks of magic squares of order 6. The construction is in such a way that each letter and number is formed by equal magic sums of magic squares of order 6. Similar kind of work with … Continue reading Letters and Numbers in Terms of Magic Squares of Order 6
OM: Religious Symbol of Hinduism – 32 Magic Squares of Equal Magic Sums
Link of complete work: Representations of Letters and Numbers With Equal Sums Magic Squares of Order 4
SWASTIKA (Religious Symbol): Hinduism – Buddhism – Jainism
Link of complete work: Representations of Letters and Numbers With Equal Sums Magic Squares of Order 4
Equal Sums Magic Squares of Order 6×6: Initial of Inder Jeet Taneja (IJT)
Equal Sums Magic Squares of Order 4×4: Initials of Inder Jeet Taneja (IJT)
Block-Wise Equal Sums Pan Magic Squares of Order 4k
This paper brings block-wise pan magic squares multiple of 4. The representations are in such a way that each block of order 4 is a perfect magic square of order 4 with equal sums. The work is written for the magic square of order 4, 8, 12, ..., 32. Applying the same procedure the … Continue reading Block-Wise Equal Sums Pan Magic Squares of Order 4k
Perfect Square Sum Magic Squares
This paper shows how to create magic squares with a perfect square number for the total sum of their entries. This has been done in two ways: Firstly, by using the sum of consecutive odd numbers, and secondly, by using the sum of consecutive natural numbers, and secondly, by using consecutive natural numbers. In the … Continue reading Perfect Square Sum Magic Squares
Pythagorean Triples and Perfect Square Sum Magic Squares
This work brings the idea how we can achieve prefect square sum magic squares using primitive and non primitive Pythagorean triples . By perfect square sum magic square, we understand that the total sum of entries of a magic square is a perfect square. The work is divided in two parts, one on primitive triples and another on non primitive … Continue reading Pythagorean Triples and Perfect Square Sum Magic Squares
Magic Square Type Extended Rows Palprimes of Order 5×5, 7×7 and 9×9
This work brings magic square type palindromic primes (palprimes) numbers of order axa, in such a way that rows, columns and principal diagonals are all palprimes along with extended row of rows. This kind of palprimes are named as "magic square type palprimes" or "palprime distributions" of order axa. This work is limited to palprime distributions of … Continue reading Magic Square Type Extended Rows Palprimes of Order 5×5, 7×7 and 9×9
Magic Squares with Perfect Square Number Sums
This short paper shows how to create magic squares in such a way that total sum of their numbers becomes a perfect square. This has been done in two ways: Firstly, Take the sum of odd numbers, and secondly, take the numbers in a sequential way. In the first case, for all orders of magic … Continue reading Magic Squares with Perfect Square Number Sums
Multi-Digits Magic Squares
In this work, magic squares are written in multi-digits formats. In some situations, different digits are considered according to order of magic squares. Magic squares related to combination with repetitions are also considered. In each case study is extended to palindromic magic squares. Full Work: Multi-Digits Magic Squares