(9) Durer Square.
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.
Brief Introduction.
(7) Khajuraho Magic: Introduction.
(8) Chautisa Yantra: Mytho-math Spice.
(9) Dürer Square from Europe: A part of an Engraving.
The Magic Square—our wandering “Turtle”—inched its way across continents, taking a leisurely 550 years to reach Europe after the Perfect Figure of Khajuraho had already appeared in India. But finally, in the sixteenth century, Europe proudly announced, “Ah! We have one too!”
Enter the famous Dürer Square—a masterpiece with a tale as intriguing as its sums. While most of Europe was busy dodging plagues and calamities, Albrecht Dürer, the German Artist and Mathematician, seems to have said, “Misery? Later. For now, let me arrange these numbers just right for my gloomy Melencolia I.”
And thus, another legend of magic squares was born—slow turtle, fast charm.
(Engraving Melancolia I. Dürer Square lives here in the right top corner Kholi! Enlarge to see.)
If you ever thought Renaissance artists only painted or engraved angels, saints, and people staring dramatically into the distance; be introduced to Albrecht Dürer, : The man who slipped a 4×4 mathematical square into one of the moodiest artworks ever made. Yes, while everyone in his famous engraving Melencolia I looks like they need a strong cup of coffee or a long nap; Dürer quietly dropped the magic square into the corner! Perhaps suggesting: "Solve this… you’re really melancholy...maybe the mood will be uplifted...and my work too!” Hopefully, this blog too;)
Dürer’s square has its own charming quirks, but let’s be honest—it’s not a Perfect Magic Square. The Khajuraho Square, meanwhile, is a full-fledged Pandiagonal / Panmagic / Diabolic / Nasik marvel—the gold standard of perfection, as we saw in Khajuraho Magic.
Still, the two share delightful similarities. Both are engraved masterpieces—one carved in stone, the other etched on paper. Both lie tucked away like Easter eggs inside great works of art. Both are mathematical showstoppers. Each is a 4×4 magic square using the numbers 1 to 16, and both boast the same magic sum: 34.
In short, they’re twin milestones—one shining for India, the other for Germany and Europe. A double delight for math lovers everywhere. And truth be told, there’s still plenty of magic left to extract from these two legends.
Now for the differences—because even magical twins have their oddities:
1. Anonymous vs. Celebrity:
Khajuraho’s creator remains a mystery; Dürer, on the other hand, is a Renaissance rockstar with a verified profile.
2. One vs. Many:
Khajuraho Square exists in a single ancient stone. Melencolia I and its Dürer Square appear in museum after museum across Europe.
3. Documented vs. “I-Think-I-Remember”:
Khajuraho’s dimensions are lost to scholarship (and possibly to time). I recall it being roughly 25 × 25 cm in my last visit years ago. (Shall visit again soon just to size up the famed figures!)
Melencolia I? Its 24.2 × 18.8 cm measurements are well documented. Dürer’s square itself is smaller—more pocket-sized genius.
4. Ageless vs. Dated (Literally):
Khajuraho carries no date—almost proclaiming, “I am timeless.”
Dürer boldly stamped 1514 in the bottom row, Renaissance-style: like signing an Instagram post with mathematical flair!
5. Patternless vs. Pattern-Proud:
Khajuraho hides its construction secrets well.
Dürer’s square flaunts a clear, deliberate pattern.
6. Hidden Gem vs. Global Celebrity:
Despite UNESCO fame and mathematical perfection, Khajuraho remains oddly obscure even in India.
Dürer’s Square? The most famous magic square on Earth, waiting to be endorsed by Tona Lisa in the next blog post!
7. Unfashionable vs. Trendsetter:
The Chautisa Yantra never went viral—Dürer’s square did. Europe made it fashionable.
8. Heavenly Glow vs. Renaissance Gloom:
The Chautisa Yantra sits amid apsaras and gods, radiating pure celestial joy.
Melencolia, meanwhile, is basically the chaotic dorm room of a stressed Renaissance genius: a brooding winged figure, a ladder to nowhere, a sulking polyhedron straight out of a geometry nightmare—and in the midst of this existential chaos, the unfazed magic square quietly whispers, “Relax….! At least I know what I’m doing!”
Message from the engraving is so clear: Life may be chaotic, but at least this grid is perfectly balanced! And we are mostly interested in this grid only!
(More about it's mathematical beauty in the next blog post.)
Pankaj Khanna
9424810575
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मेरे कुछ अन्य ब्लॉग:
हिन्दी में:
तवा संगीत : ग्रामोफोन का संगीत और कुछ किस्सागोई।
रेल संगीत: रेल और रेल पर बने हिंदी गानों के बारे में।
साइकल संगीत: साइकल पर आधारित हिंदी गाने।
कुछ भी: विभिन्न विषयों पर लेख।
तवा भाजी: वन्य भाजियों को बनाने की विधियां!
मालवा का ठिलवा बैंड: पिंचिस का आर्केस्टा!
ईक्षक इंदौरी: इंदौर के पर्यटक स्थल। (लेखन जारी है।)
अंग्रेजी में:
Love Thy Numbers : गणित में रुचि रखने वालों के लिए।
Epeolatry: अंग्रेजी भाषा में रुचि रखने वालों के लिए।
CAT-a-LOG: CAT-IIM कोचिंग।छात्र और पालक सभी पढ़ें।
Corruption in Oil Companies: HPCL के बारे में जहां 1984 से 2007 तक काम किया।
