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Paata Ivanisvili

@PI010101 • 7,552 subscribers

Professor of Mathematics @ UC Irvine | Former postdoc @ Princeton | Exploring what AI can (and can’t) do in math.

Shorts

Still excited about these 3Blue1Brown-style videos generated by AI. Here’s a beautiful illustration of a classic analysis problem: Let f be convex, nonnegative on [0,∞), with f(0)>0 and f(x)→0 as x→∞. Place a light source at (0,b) with 0<b<f(0). Rays reflect off the graph of f and the x-axis following the usual laws of optics. Question: can any ray escape to +∞, or do all trajectories eventually come back? Prompt to video

Still excited about these 3Blue1Brown-style videos generated by AI. Here’s a beautiful illustration of a classic analysis problem: Let f be convex, nonnegative on [0,∞), with f(0)>0 and f(x)→0 as x→∞. Place a light source at (0,b) with 0<b<f(0). Rays reflect off the graph of f and the x-axis following the usual laws of optics. Question: can any ray escape to +∞, or do all trajectories eventually come back? Prompt to video

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The longest thick curve on a sphere. Put a rope of prescribed thickness on the unit sphere. How long can it be without overlapping itself? Surprisingly, the answer is known only for thickness sin(π/2n)

The longest thick curve on a sphere. Put a rope of prescribed thickness on the unit sphere. How long can it be without overlapping itself? Surprisingly, the answer is known only for thickness sin(π/2n)

16,594 просмотров

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Navier–Stokes equation (2D incompressible), solved live numerically on a discrete grid ρ (∂u/∂t + u·∇u) = −∇p + μ Δu + f, ∇·u = 0 The ink (the white stuff on the left) is added so you can see the motion of the fluid.

Navier–Stokes equation (2D incompressible), solved live numerically on a discrete grid ρ (∂u/∂t + u·∇u) = −∇p + μ Δu + f, ∇·u = 0 The ink (the white stuff on the left) is added so you can see the motion of the fluid.

Paata Ivanisvili

41,383 просмотров • 2 месяцев назад

72,785 points inside a sphere that form any letter of the alphabet when viewed from different angles

72,785 points inside a sphere that form any letter of the alphabet when viewed from different angles

Paata Ivanisvili

17,813 просмотров • 22 дней назад

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