December 4, 2025
Pi vs Tau: math’s messiest love triangle
What's the Deal with Euler's Identity?
Internet melts down: Pi loyalists vs Tau diehards over the ‘i’ rotation trick
TLDR: The article reimagines Euler’s identity as simple rotations: -1 is a half-turn, fractional powers give i, and e^(iπ) lands at -1. Comments explode into Pi vs Tau debates, deeper math rabbit holes, and praise for the intuitive approach, showing how a clearer picture can make “imaginary” numbers click.
Euler’s identity — the famed “e to the i pi plus one equals zero” — just got a fresh, street‑level explanation: think of -1 as a 180° flip, then take “half flips” to get i, the imaginary unit. The author ditches napkin‑proofs and infinite series for a visual, rotation‑based vibe that makes complex numbers feel like moving points on a map. It’s simple: multiply by -1 for a half turn, raise it to fractions for smaller turns, and suddenly e^(iπ) becomes a clean 180° spin that lands you at -1, then add 1 to hit zero. Accessible? Yep. Controversial? Also yes.
Commenters erupted. One camp wants a cleaner formula, with xeonmc dropping “(-1)^x = cos(πx) + i sin(πx)” like a mic. The real brawl: Pi loyalists vs Tau diehards, as rmunn waves the Tau Manifesto and declares “e^(i·tau) = 1,” because tau makes quarter‑turns and radians feel natural. Meanwhile, zkmon yells “Enter quaternions” and opens the rabbit hole: why is i^i real, what’s up with the unit circle, and why do angles add when you multiply? stared brings receipts with colorful visuals here. And sevensor cheers the intuition: the -1 half‑rotation beats classroom “Maclaurin series” wizardry. Verdict: math TikTok energy — clever, chaotic, and wildly educational.
Key Points
- •Euler’s identity e^(iπ) + 1 = 0 is shown as a special case of Euler’s formula e^(iα) = cos(α) + i·sin(α).
- •Setting α = π (180°) in Euler’s formula yields −1, and moving it to the left side gives the identity.
- •Rotating points can be modeled with trigonometric formulas or by multiplying coordinates by −1 for 180° rotations.
- •Fractional powers of −1 motivate the imaginary unit i as a 90° rotation, leading to complex numbers x + i·y.
- •Rotations by arbitrary angles use radians (2π = 360°) and Euler’s formula; powers of i handle m·90° rotations.