Uniformly Chaotic

Binomial & Normal Distribution Explorer Binomial & Normal Distribution Explorer Distribution Binomial (n, p) Normal (μ, σ) n n = 20 p p = 0.50 Normal approx Continuity correction μ σ Query P(X = k) P(X ≤ k) P(X ≥ k) P(a ≤ X ≤ b) k a b Y-scale In Binomial mode, bars show PMF. Gold curve overlays the Normal approximation. Continuity correction shades half‑steps at the interval boundaries. PMF / PDF Normal approx Normal PDF Shaded probability Drag sliders, watch the shaded probability update instantly. ...

Probability Experiment Simulator Probability Experiment Simulator Experiment Coin (H/T) Single die (1–6) Two dice sum (2–12) Card suits (♠ ♥ ♦ ♣) Urn (red/blue) P(Heads) Value: 0.50 With replacement Red Blue With replacement Trials per tick Value: 100 Run Pause Step×1 Step×10 Step×100 Reset Theoretical overlay is shown in gold. Without‑replacement modes auto‑refill when resources are exhausted to keep the experiment going. Experimental Theoretical Compare bars to gold lines; watch frequencies stabilize. Ready.

Shortest Distance Between Skew Lines Shortest Distance Between Skew Lines L₁ point P: x₁ y₁ z₁ L₁ dir V: v₁x v₁y v₁z L₂ point Q: x₂ y₂ z₂ L₂ dir W: w₁x w₁y w₁z Show common perpendicular Show V–W parallelogram Show normal (V×W) Random Swap L₁/L₂ Reset Reset view Tip: Drag to orbit • Scroll/pinch to zoom • Double‑click/tap canvas to reset view. X Y Z Line L₁ Line L₂ Shortest segment Normal V×W L₁: P + tV • L₂: Q + sW Ready.

Plane & Line Intersection Plane & Line Intersection a b c d Normalize normal Random Reset x₀ y₀ z₀ vₓ vᵧ v𝓏 Show normal Reset view Tip: Drag to orbit • Scroll/pinch to zoom • Double‑click/tap to reset view. X Y Z Plane Line Normal Intersection Equation: ax + by + cz + d = 0 • Line: P + tV Ready.

3D Vector Sandbox 3D Vector Sandbox Aₓ Aᵧ A𝓏 Bₓ Bᵧ B𝓏 Normalize A Normalize B Swap A/B Random Show proj₍B₎A Show A×B Show angle arc Show A–B parallelogram Scale (px/unit) Reset view Tip: Drag on the canvas to orbit, scroll to zoom. Axes colors — X:red, Y:green, Z:blue. X Y Z Vector A Vector B proj₍B₎A A×B Double‑click/tap canvas to reset orbit. Ready.

Differential Equation Solver Differential Equation Solver dy/dx = x + y y - x x * y y·sin(x) Custom… x₀: y₀: h: Steps: Method: Euler Runge–Kutta (4) Solve n x y

Riemann Sum & Area Under Curve Riemann Sum & Area Under Curve Preset x^2 sin(x) e^x ln(x) abs(x) 1/x Custom… f(x) Interval a Interval b Subintervals n Method Left Right Midpoint Trapezoid Animate n Reset Absolute area (ignore sign) Grid Show f(x) Auto y-scale Manual y-max Allowed: + − × / ^, parentheses, x, and Math functions: sin, cos, tan, asin, acos, atan, exp or e^x, ln, log, sqrt, abs. f(x) Positive area Negative area Trapezoids Signed vs absolute area toggle is on the ...