Here's todays Daily Sanskrit Wisdom post—this time featuring Aryabhata’s geometric formula for the area of a circle, showing how succinctly ancient Indian mathematicians expressed mathematical truths in verse form.
🔺 Daily Sanskrit Wisdom
🧠 Geometry in Verse – Aryabhata’s Genius
Today’s shloka shares a profound geometric formula by Aryabhata (circa 499 CE), revealing how ancient Indian minds calculated the area of a circle using precise approximations long before modern notation.
📜 Shloka of the Day (Aryabhata – Geometry of Circles)
"चतुरधिकं शतमष्टगुणं द्वासष्टिस्तथा सहस्राणाम्।
अयुतद्वयविष्कम्भस्यासन्नो वृत्तपरिणाहः॥"
— From Aryabhatiya, Ganitapada (Verse 10)
🪔 Word-by-word Translation
| Sanskrit | English | German |
|---|---|---|
| चतुरधिकं (caturadhikaṁ) | Four more than (i.e., 4 + 100 = 104) | Vier mehr als (104) |
| शतम् (śatam) | Hundred | Hundert |
| अष्टगुणं (aṣṭaguṇaṁ) | Multiplied by eight | Achtfach multipliziert |
| द्वासष्टि (dvāsaṣṭi) | Sixty-two | Zweiundsechzig |
| तथा (tathā) | Then / likewise | Dann / ebenso |
| सहस्राणाम् (sahasrāṇām) | Of thousands | Von Tausenden |
| अयुतद्वय (ayuta-dvaya) | Two ten-thousands (20,000) | Zwei Zehntausender (20.000) |
| विष्कम्भस्य (viṣkambhasya) | Of the diameter | Des Durchmessers |
| असन्नः (asannaḥ) | Approximated / nearly equal | Näherungsweise gleich |
| वृत्तपरिणाहः (vṛtta-pariṇāhaḥ) | Circumference of a circle | Umfang eines Kreises |
🌐 Full Translation
EN:
"Add four to one hundred (104), multiply by 8 (832), and then add 62,000. This gives the approximate circumference of a circle whose diameter is 20,000."
DE:
"Füge vier zu hundert hinzu (104), multipliziere mit acht (832) und addiere 62.000. Dies ergibt den ungefähren Umfang eines Kreises mit dem Durchmesser 20.000."
🔍 Interpretation
Aryabhata provides an approximation of π here. Using:
This is astonishingly close to the actual value of π. While the verse appears poetic, it's a coded algorithm for calculating circular dimensions. Aryabhata also developed sine tables, defined the concept of zero, and laid the foundation for trigonometry.
Would you like me to visualize this with an infographic or circular diagram? We can also continue with trigonometric functions from Aryabhata or Bhaskara next—just say the word!
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