Number theory was the one area of mathematics on which Pierre de Fermat (1607–65) worked throughout his life, and he found it ‘very beautiful and very subtle’.

Among other results, he said that the Polygonal Number Theorem (which asserts that every natural number is the sum of at most $n$ $n$-gonal numbers) was ‘a most beautiful and wholly general proposition […] this marvellous proposition’.

(He offered no proof of this result, but claimed to have one in a marginal note to Diophantus' Arithmetica; this was the same book in which he noted what became known as Fermat's Last Theorem.)

Fermat also seems to have counted magic squares and analogous configurations as part of number theory, and wrote that: ‘I know hardly anything more beautiful in arithmetic than these numbers that some call planetary and others magic’. (The term ‘planetary’ is derived from certain treatises linking the magic squares to planets used in talismans.)

He said he had found a rule to find magic cubes (one of his examples is in the attached image) and also determined how many different ways each such cube can be arranged, which he called ‘one of the most beautiful things in arithmetic’.

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[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

#Fermat #NumberTheory #HistMath #MathematicalBeauty #MagicSquare

Abū’l-Wafāʾ al-Būzjānī (940–77/8 CE) wrote one of the earliest extant treatises dedicated to magic squares, focused on constructions. He repeatedly referred to the aesthetic value of the methods of he described.

For instance, he wrote about a method of constructing a magic square of order 4:

‘It is possible to arrive at the magic arrangement in this square by means of methods without displacement showing regularity and elegance [niẓām wa-tartīb ḥasan نظام وترتيب حسن]’ (trans. Sesiano)

Such a method with ‘regularity and elegance’ was: (1) place the number 1 in a corner, 2 and 3 adjacent to the opposite corner, and 4 diagonally adjacent to 1; (2) place 5 to 8 in reverse order in positions horizontally symmetrically opposite to 1 to 4; (3) place $17 − n$ diagonally two places away from $n$ for $n = 1,\ldots,8$ (see attached image).

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[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

#MagicSquare #HistMath #MathematicalElegance #elegance #aesthetics

#ThisWeeksFiddler, 20251219
This week the #puzzle is: Happy (Almost) New Year from The Fiddler! #MagicSquare #primes A magic square is a square array of distinct natural numbers, where each row, each column, and both long diagonals sum to the same “magic number.” ,,, A prime magic square is a magic square consisting of only prime numbers. Is […]

https://stuff.ommadawn.dk/2025/12/24/thisweeksfiddler-20251219/

ハンカチを走る安全ピン〔マジック・手品・一発芸・種明かし〕

https://magic-secrets.net/%e3%83%8f%e3%83%b3%e3%82%ab%e3%83%81%e3%82%92%e8%b5%b0%e3%82%8b%e5%ae%89%e5%85%a8%e3%83%94%e3%83%b3%e3%80%94%e3%83%9e%e3%82%b8%e3%83%83%e3%82%af%e3%83%bb%e6%89%8b%e5%93%81%e3%83%bb%e4%b8%80%e7%99%ba/?feed_id=871&_unique_id=687c59201cad5&Mastodon

#100magic #magic #magicsquare #タネ明かし #マジック #一発芸 #手品 #日用品マジック #日用品マジック #100magic #magic #magicsquare #タネ明かし #マジック #一発芸 #手品

Constructing Odd Order Magic Squares

https://pballew.blogspot.com/2025/06/a-unique-approach-for-odd-order-magic.html

#magicsquare #pballew #math

🎉 Exciting news for Watchit! 🎉

We’re thrilled to share that Watchit has been featured in the "Upcoming" section on Magic Square’s platform! 🚀✨ This is a big milestone in our journey to create a space where creators can connect directly with their audience and monetize their content fairly and transparently.

Check out our project here and start following: https://magicsquare.io/store/app/watchit

A huge thank you to everyone for your support—this is just the beginning! 💪

#Watchit #MagicSquare #ComingSoon

আমার তৈরি গেম - Result is 15, ডাউনলোড লিংকঃ https://play.google.com/store/apps/details?id=com.whiteflower10001.Result_is_15

আপনাকে ৩ X ৩ বর্গক্ষেত্রে ১ হতে ৯ পর্যন্ত সংখ্যাগুলি প্রতিটি এমনভাবে ব্যবহার করতে হবে - যাতে কোনও সংখ্যা পুনরাবৃত্তি না হয়, এবং

⬅️ ডান হতে বামে, প্রতি সারিতে পৃথকভাবে, তিনটি সংখ্যার যোগফল হবে ১৫,
⬇️ উপর হতে নিচে, প্রতি কলামে পৃথকভাবে, তিনটি সংখ্যার যোগফল হবে ১৫,
↘️ কোনাকুনিভাবে, উভয় দিকে, তিনটি সংখ্যার তিনটি সংখ্যার যোগফল হবে ১৫

#MathPuzzle, #MagicSquare, #SlidingPuzzle, #MathGame, #PuzzleGame, #EducationalGame

Super Programs 1 for the ZX81

https://www.youtube.com/watch?v=c3kWrS6o5JE

#SuperPrograms1 #ZX81 #SuperPrograms #Collection #Compilation #InvasionFromJupiter #Skittles #MagicSquare #Doodle #Kim #LiquidCapacity #InternationalComputersLimited #ICL #SinclairResearch

Good morning. Smol Arcee craves violence!

#3rdPartyTransformers #MagicSquare #PeachGirl #Arcee #GoodMorning #ToyPhotography