Love Thy Squares: The Magic Squares!

Pankaj Khanna 9424810575 Previous/Next  Blog Posts: (1)  Beauty Squarely  Introduction & Kuber Yantra (2)  Murphy Radio!? अले वाह!!  My first Experience of Magic Square. (3)  Decoding the Quadratum Mirabile ! How to solve 3x3 Magic Squares. (4)  Lo Shu Square  History of Chinese Magic Square. (5)  The Unhurried Odyssey of a Turtle! ! History of Magic Squares in short. (6)  Varahmihir's Magic Square : Brief Introduction. (7)  Khajuraho Magic : Introduction. (8) Chautisa Yantra : Mytho-math Spice. A video of a schoolboy making a Magic Square in barely ten seconds has been going viral for a while. Since then my family, friends, and even my former students have formed a teasing committee of their own. They keep taunting me with great enthusiasm: "Arre, you can’t even unlock your phone in ten seconds, and this kid finishes a Magic Square before you’ve even found your spectacles! Stop blogging about Magic Squares, you old magician-wit...

Pankaj Khanna 9424810575 Previous/Next  Blog Posts: (1)  Beauty Squarely  Introduction & Kuber Yantra (2)  Murphy Radio!? अले वाह!!  My first Experience of Magic Square. (3)  Decoding the Quadratum Mirabile ! How to solve 3x3 Magic Squares. (4)  Lo Shu Square  History of Chinese Magic Square. (5)  The Unhurried Odyssey of a Turtle! ! History of Magic Squares in short. (6)  Varahmihir's Magic Square : Brief Introduction. (7) Khajuraho Magic : Introduction. And once we’ve gazed upon the brilliance of Varahamihira’s legendary square in the last blog post; the stage lights shift, the curtains rise again, and our next Star steps forward: The enigmatic Khajuraho Square !  Though subdued and hidden in the erotic poetry written in the stones more than a thousand years ago; it tells through the lovely numbers about the glory of Indian Mathematics and Magic Squares. This  little adorable Magic Square is a great example o...

Pankaj Khanna 9424810575 Previous/Next  Blog Posts: (1)  Beauty Squarely  Introduction & Kuber Yantra (2)  Murphy Radio!? अले वाह!!  My first Experience of Magic Square. (3)  Decoding the Quadratum Mirabile ! How to solve 3x3 Magic Squares. (4)  Lo Shu Square  History of Chinese Magic Square. (5)  The Unhurried Odyssey of a Turtle! ! History of Magic Squares in short. (6) Varahmihir's Magic Square : Brief Introduction. Varāhamihira was the sixth-century genius who mixed astronomy, astrology, mathematics, weather science, and his sheer brilliance into one cosmic cocktail. Prolific writer of masterpieces like Brihatsamhita ( बृहतसंहिता) and Panchasiddhantika( पंचसिद्धांतिका), perhaps he could predict monsoons, earthquakes, eclipses—basically everything except when his ink pot would run dry! His calculations were so sharp that even the planets must have felt shy deviating from their paths! A scholar at King Vikramāditya’s court at Ujjain, he...

Pankaj Khanna 9424810575 Previous/Next  Blog Posts: (1)  Beauty Squarely (2)  Murphy Radio!? अले वाह!! (3)  Decoding the Quadratum Mirabile ! (4)  Lo Shu Square (5) The Unhurried Odyssey of a Turtle! ! We’ve already taken a tour through the Kuber Yantra, visited the legendary Lo Shu Square, met the famous fabled Turtle, and even had a friendly chat with the Magic Squares themselves. The Turtle and  these mysterious grids  have slowly and quietly travelled across Continents, crossed Dynasties, impressed Emperors, baffled Sages, and—every now and then—caused a scholar to spill tea on his manuscript out of excitement. Just like an equivalent of Eureka Moment of Archimedes! Now let us appreciate the contribution of Indians, Arabs and Europeans towards Magic Squares in this short blog post which is a kind of a trailler of a long Web Series to be released in many installment now onwards. Magic Squares by Indians: Centuries later afte...

Pankaj Khanna 9424810575 Previous/Next  Blog Posts: (1)  Beauty Squarely (2)  Murphy Radio!? अले वाह!! (3)  Decoding the Quadratum Mirabile ! (4) Lo Shu Square Which one is older: Hindu Kuber Yantra or Chinese Lo Shu Square? You already know about Kuber Yantra with the Magic Square, Parsi Mohalla and also about Me, Mom and the Murphy Radio;) It's high time we discussed about Lo Shu Square too. The world believes that Lo Shu is the oldest Magic Square but they can't stop me in believing that Kuber Yantra is far more sacrosanct and maybe more ancient too! Still to be fair, let me do justice to such a cute, adorable and profound Lo Shu Square! So here goes the Lo Shu story or the myth or the legend: Born sometime around 4,000 years ago in ancient China, this 3×3 magic square has dazzled Emperors, Monks, Scholars, Artists, Mathematicians and anyone who enjoys numbers that behave so nicely and obediently! The story begins on the banks of the Luo River, where E...

Pankaj Khanna 9424810575 Previous/Next  Blog Posts: (1)  Beauty Squarely (2)  Murphy Radio!? अले वाह!! (3)  Decoding the Quadratum Mirabile ! Quadratum Mirabile means Wonderful Squares! And all the Magic Squares we are going to discuss are indeed Quadratum Mirabile! Let's start by tackling the 3x3 'Quadratum Mirabile' puzzle first! The challenge is simple: Fill a 3x3 square with natural numbers (they can be consecutive or random) such that the sum of the numbers in all three rows, all three columns, and both main diagonals are equal. To develop a reliable mathematical method for completing any 3x3 magic square, we'll use a little bit of algebra. ​First of all we will introduce Variables : Let's represent the numbers in the grid using variables like a, x and y. By establishing relationships between these variables, we can construct the entire square. ​ Start with the Diagonal : A helpful rule of thumb for any order of magic square will be to always begin by...

Pankaj Khanna 9424810575 Previous/Next  Blog Posts: (1) Beauty Squarely (2) Murphy Radio!? अले वाह!! (3)  Decoding the Quadratum Mirabile ! This piece picks up from where the earlier introduction (Beauty Squarely) left off. But beware — this isn’t just a continuation, it’s an evolution! A darker twist laced with humor, where the nefarious meets the hilarious...! If you think scams are a 'digital age' phenomenon, bless your naive heart! ​Our ancestors were just as good at bilking people; they just used pamphlets, flyers, and a 'trusty' P.O. box instead of email and crypto. ​Fraud has always been offline. The internet only gave it fiber-optic speed. Digital fraud is just next generation of Analog fraud! Old timers of my generation may recall the above type of Pamphlets/Flyers distributed with News Papers and Magazines in Seventies. Normally such Pamphlets used to be written in Hindi. Having seen Kuber Yantra earlier, when  chanced upon the above type of...

Pankaj Khanna 9424810575 Next/Previous Articles: (1) Beauty Squarely (2) Murphy Radio!? अले वाह!! (3) Decoding the Quadratum Mirabile ! This new blog series ' Love Thy Square' builds upon the initial mathematical exploration Love Thy Number , and will proceed simultaneously with it. The focus for this series will be the elegant world of Magic Squares: highly structured arrays where the total of the numbers in every row, column, and  the diagonals is the same. This constant sum is named the Magic Constant.  Despite the fact that Mathematics is, let's be honest, already Sorcery;  ancient Mathematicians decided to really rub it in by christening these things 'Magic Squares'.  I mean, 'Mathematical Squares' would have been perfectly fine—a little boring, maybe, but more accurate!  While Magic is sleight of hand, art and entertainment;  Mathematics is much more than that. It is entertainment, Enlightenment and God's chosen language! Calling them 'Magic ...