Where Did The Magic Square Come From?

The Lo Shu Square, also known as the magic square on the turtle shell, is a unique normal magic square of order three, with 1 at the bottom and 2 in the upper right corner. It is obtained from the Lo Shu by rotation or reflection. Magic squares are special mathematical constructs where the rows, columns, and diagonals all add up to the same number. They have been considered since ancient times, with the first recorded magic square being found in ancient China around 5000 years ago.

The legend of “Lo Shu” or “scroll of the river Lo” tells the story of a huge flood that destroyed crops and land. The people offered a sacrifice to the river gods to save them. Magic squares have a long history, dating back to at least 190 BCE in China. At various times, they have acquired occult or mythical significance and have spread across the globe. Examples of this square from the 1st century AD were found in the ruins of Pompeii, and it was still employed during the 19th century in Europe.

Chinese legends claim that a giant turtle with a three-by-three magic square engraved on its back came out of the Lo River to save China from a flood. Leonhard Euler, a famous Swiss mathematician, created an unusual 4×4 magic square using Greek letters instead of numbers. The earliest known magic square is Chinese, recorded around 2800 B.C. Fuh-Hi described the “Loh-Shu”, or “scroll of the river Loh”.

Magic squares have fascinated people throughout history and continue to challenge people around the world. The Chinese probably invented the magic square of three centuries before anyone else, but they have evolved over time.

Is there a formula for magic square?

The magic constant can be calculated by adding all nine numbers in the magic square and dividing by the number of rows, as demonstrated in the provided example. This process yields the magic constant of 15.

How old is the magic square?

The third-order magic square was first discovered by Chinese mathematicians in 190 BCE, and the fourth-order magic square was first documented in India in 587 CE. By the end of the 12th century, the general methods for constructing magic squares were well established, and some of these squares were increasingly used in conjunction with magic letters for occult purposes. In India, all the fourth-order pandiagonal magic squares were enumerated by Narayana in 1356.

Magic squares were made known to Europe through translation of Arabic sources as occult objects during the Renaissance, and the general theory had to be re-discovered independent of prior developments in China, India, and Middle East.

The first unequivocal instance of the 3×3 magic square appears in the chapter called Mingtang (Bright Hall) of a 1st-century book Da Dai Liji (Record of Rites by the Elder Dai), which purported to describe ancient Chinese rites of the Zhou dynasty. These numbers also occur in a possibly earlier mathematical text called Shushu jiyi (Memoir on Some Traditions of Mathematical Art), said to be written in 190 BCE. This is the earliest appearance of a magic square on record; it was mainly used for divination and astrology.

The oldest surviving Chinese treatise that displays magic squares of order larger than 3 is Yang Hui’s Xugu zheqi suanfa (Continuation of Ancient Mathematical Methods for Elucidating the Strange) written in 1275. The contents of Yang Hui’s treatise were collected from older works, both native and foreign, and he only explains the construction of third and fourth-order magic squares while merely passing on the finished diagrams of larger squares.

After Yang Hui, magic squares frequently occur in Chinese mathematics such as Ding Yidong’s Dayan suoyin (c. 1300), Cheng Dawei’s Suanfa tongzong, Fang Zhongtong’s Shuduyan, Zhang Chao’s Xinzhai zazu (c. 1650), and Bao Qishou’s Binaishanfang ji (c. 1880). However, despite being the first to discover the magic squares and getting a head start by several centuries, the Chinese development of the magic squares are much inferior compared to the Indian, Middle Eastern, or European developments.

What is the theory of the magic square?

A magic square puzzle is a square with distinct integers arranged so that the total sum is the same in every row, column, and main diagonal. A magic square puzzle of order n is an organization of n 2 unique integers in a square. The fixed sum in every row, column, and diagonal is known as the magic constant or magic sum, represented by the letter M. The magic constant of a typical magic square depends on the value of n, and the value of the magic sum is calculated using the formula. A magic square of different orders can be created by subtracting each number from (n 2 + 1), creating a complementary magic square, or a normal magic square with consecutive numbers beginning with 1.

What does the magic square symbolize?

A magic square is a type of amulets based on numerology, with numerical arrangements that hold magical meaning. In the Middle East, numbers are as significant as words, making them powerful amulets. The most widely used magic square is the buduh-square, which is an arrangement of numbers 1 through 9, with 5 in the middle and 15 in all directions. The name “buduh” comes from the four letters on the corners of the square, which are noted in the Abjad letter-numerals: b-d-w-h. The power of the buduh square was believed to be so strong that the name itself was enough to invoke that power.

Who invented the magic square?

The Ramanujan magic square is a unique 3×3 grid invented by Indian mathematician Srinivasa Ramanujan. Each cell contains a number from 1 to 9, and each row, column, and diagonal have the same sum. Ramanujan created different magic squares of the same size but with different magic constants. For instance, he created an even square of 4 x 4 with magic constants of 34 and 35, a 5 x 5 square with magic constants of 65 and 66, and 7 x 7 squares with magic sums of 170 and 175 in two different problems.

What is the oldest known magic square?

The Lo Shu Square, discovered in ancient China around 5000 years ago, is the first recorded magic square. Legend has it that a mystical turtle emerged to rescue people from a flood, revealing a 3×3 grid of nine squares each containing one of the numbers between 1 and 9. The sum of these squares is always 15, regardless of the arrangement of the numbers in each row, column, and diagonal. This arrangement is now known as the 3×3 magic square.

The constant, unchanging nature of mathematics is one of the most satisfying aspects of mathematics. In Ri Masterclass, 10-year-old students are asked to find different arrangements of the integers 1-9 in a 3×3 magic square, and then discuss whether they think they have one solution or eight. This is the simplest possible magic square, of order 3, and it is a testament to the constant and unchanging nature of mathematics.

What is the logic behind magic square?

In recreational mathematics, a magic square of order n is defined as an arrangement of n² distinct integers in a square, where the sum of the n numbers in all rows, columns, and diagonals is a constant, represented by an n × n matrix.

How many magic squares exist?

A 3×3 magic square has 36, 288, 000 possible combinations, which allows for a relatively straightforward approach to testing all of them. In contrast, a 4×4 magic square has 21 trillion possible combinations, making it considerably more challenging to test all of them.

Is there a trick to magic squares?

The magic number of any sized grid can be calculated by dividing the sum of every number on the board by the number of rows. In this case, the magic number is 1+2+.+9 = 45 / 3 = 15. The “middle” most neutral number, 5, works best in the middle of the grid for balance reasons. Lower and higher numbers work well on opposite sides or corners, but it would be near impossible to balance a grid with a 1 in the middle.

Using Google Sheets, the author found a solution for a 4-by-4 square. By splitting the numbers into groups (1-3, 4-6, 7-9), the grid was balanced by ensuring no number of the same group shared a row or column. The middle number was most advantageous, as there was no solution that didn’t put 5 in the middle square.

What are some interesting facts about the magic square?

Magic squares, a mathematical concept, have a long history dating back to at least 190 BCE in China. They have been classified according to their order n as odd, evenly even, oddly even, or associative magic squares, pandiagonal magic squares, and most-perfect magic squares. The classification is based on different techniques required to construct odd, evenly even, and oddly even squares.

In modern times, magic squares have been generalized in various ways, including using extra or different constraints, multiplying instead of adding cells, using alternate shapes or more than two dimensions, and replacing numbers with shapes and addition with geometric operations. The third-order magic square was known to Chinese mathematicians as early as 190 BCE, and the first dateable instance of the fourth-order magic square occurred in 587 CE in India. By the end of the 12th century, the general methods for constructing magic squares were well established.

Magic squares were made known to Europe through translation of Arabic sources as occult objects during the Renaissance, and the general theory had to be re-discovered independent of prior developments in China, India, and Middle East. Ancient cultures with a tradition of mathematics and numerology did not discover the magic squares, such as Greeks, Babylonians, Egyptians, and Pre-Columbian Americans.

The first unequivocal instance of the 3×3 magic square appears in the chapter called Mingtang (Bright Hall) of a 1st-century book Da Dai Liji (Record of Rites by the Elder Dai), which purported to describe ancient Chinese rites of the Zhou dynasty. The 3×3 magic square was mainly used for divination and astrology. The identification of the 3×3 magic square to the legendary Luoshu chart was only made in the 12th century, after which it was referred to as the Luoshu square.

Yang Hui’s Xugu zheqi suanfa (Continuation of Ancient Mathematical Methods for Elucidating the Strange) is the oldest surviving Chinese treatise that displays magic squares of order larger than 3, written in 1275. The treatise only explains the construction of third and fourth-order magic squares, while passing on the finished diagrams of larger squares.

Why is it called magic square?

The magic square, a mathematical construct originating in ancient China, has become a significant cultural element worldwide. The term “magic square” is derived from the concept of a magic constant, which is defined as the sum of all rows, columns, and diagonals within a square matrix. This magic constant is unique in that it remains constant regardless of the specific values assigned to the rows, columns, and diagonals.