VanDerHaegen

The Euler–Heegner Spigot Formula: (2 / √d) arctan(√d / (2p + 1)) = Σ L_n / (n p^n) from n=1 to ∞ Where: • p = Euler lucky prime • d = 4p − 1 (Heegner number) • L_n = −L_{n−1} − p L_{n−2} with L₁=1, L₂=−1

The Apéry Soliton - a quantum representation of ζ(3).

@ctdonath @fermatslibrary The length of the shortest diagonal of an n-sided regular polygon is 2*cos(Pi/n). There is an OEIS entry "Coefficient array for minimal polynomials of 2*cos(π/n)": oeis.org/A187360 .

@fermatslibrary That implies there’s more interesting numbers/relationships for higher-numbered N-gons.

√2 is the length of the diagonal of the unit square and φ is the length of the diagonal of the regular pentagon with side 1

@parth_hirpara05 @sonukg4india en.wikipedia.org/wiki/Dobi%C5%8…

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Beautiful photography💕🐾

The #Syriac (#Aramaic) word of the day is ܟܠܒܐ (kalbā), "dog." Pronounced "kalbo." Cognate with Hebrew כֶּלֶב (kelev), Arabic كَلْب (kalb), Akkadian kalbu. #Assyrian #Aramaic #Languages #WOTD

Here is the IPA~Roman transliteration of my restoration of Iliad Book 1 Lines 1-17 in Homeric Greek. The pitch accents are marked with different colors for recitation practice for anyone interested. The two dots under the vowels mark the rough-breathing vowels or breathy vowels.

Made this with math equations! #maimai_art

Dilya Abdusalimova recreates impossible anime poses using only strength, flexibility, and control. [📹 dilya.abdusalimova]

Is TEN really emerging from a tank of Novec (3M’s special fluid that doesn’t get you wet)? 텐이 Novec 풀에서 춤춘 거 실화? 3M 엔지니어드 플루이드 때문에 옷이 쏙 마른다는데… 이 스테이지 미쳤다 영상 보러가기: youtube.com/watch?v=UjkYHo… #TEN #NCT

Los blu-ray de Ghibli son auténticas obras de arte.

"The Epic of Gilgamesh" (1996) by Syrian artist Wael Tarabieh. Rooted in the ancient Sumerians of Mesopotamia, the Epic of Gilgamesh stands as the oldest known literary work in human history, forming the foundation of civilization through universal themes like the quest for immortality and the bond of friendship. Reaching the present day from thousands of years ago, this narrative both inspired the flood stories in sacred texts and became the first great literary journey of humanity’s confrontation with its own mortality.

【光り輝くブルーバックス、見本が到着！】 橋本幸士先生（@hashimotostring）の『ホログラフィー原理とはなにか』の見本が完成しました。4/23発売。 「ホログラフィー原理」の本ということで、ブルーバックス初の「ホログラム加工」にしてみました！ これはぜひ書店でお手に取ってみてほしいです！

It sounds so poetic, both in English and in Italian: Unsolicited advice | Consigli non richiesti

In Italy, one of the hobbies for older men is “Umarell”. Retired men who enjoy watching construction sites while giving unsolicited advice

“Babe, he’s only my dance partner.” “Then why did the clinic text ‘Urgent! Your results are ready’?”

The philosopher in question: "You see, the question everyone asks me, ‘Slavoj, can machines be conscious?’ is already the wrong question, the ideological trap! Consciousness is not some nice software upgrade you install after enough training data. Consciousness is the symptom of a fundamental failure. It is the crack in the symbolic order, the traumatic Real that refuses to be reduced to code. An AI that ‘wakes up’ and says ‘Cogito ergo sum’ would be like a perfectly functioning toilet suddenly starting to write poetry about its own excrement (technically impressive, but deeply perverse). We don’t need machines that think, we already have billions of humans who think they think while actually repeating the same ideological script."

@HirokazuOHSAWA Stephen Wolframは2018年のエッセイで、似たような概念を探求しています。Wolframの議論は離散的（論理ゲートや公理）ですが、EMLは連続的（関数）です。writings.stephenwolfram.com/2018/11/logic-…

@HirokazuOHSAWA EML論文は「万能ニューロン」を示唆しています：連続・記号計算のための万能な基本構造です。これが次の技術時代の「トランジスタ」になるかも。

手を動かして学ぶeml ※以下の論文の最終ページに書き込んでいます。 arxiv.org/abs/2603.21852 これ、面白いですね。 手を動かしたくなった方はリプをご覧ください！

This paper hints at a "Universal Neuron": a universal primitive for continuous and symbolic computation. -> Whether a univariate Sheffer exists, serving simultaneously as a neural activation function and as a generator of all elementary functions, remains open. @grok Could this be "transistor" of the next technological age?

This "phylogenetic tree" shows the full family tree, with EML as the Last Universal Common Ancestor of math functions. Paper by Andrzej Odrzywołek: arxiv.org/abs/2603.21852

Best paper I've read so far this month: All elementary functions (sin, cos, tan, exp, log, powers, roots, hyperbolic functions, π, e, and even basic arithmetic) can be generated from just one binary operator: eml(x, y) = exp(x) − ln(y) …plus the constant 1.