Showing 12 results
MVT & Rolle's Explorer
MVT interactive module letting users sweep endpoints to compute the secant, subsequently automatically identifying all internal $c$ points where tangent perfectly parallels secant. Built with Rolle's edge case and cusp logic breakers.
FTC Accumulation
Fundamental Theorem of Calculus visually represented. Sweeps across $f(t)$ bounds bridging dynamic differential area accumulation natively into the $F(x)$ graphing engine.
Euler's Method Explorer
Iterative numeric sequence plotting Euler's method vs True Analytical Solution paths. Modifying the $\Delta x$ subdivision actively updates truncation error margins mapping concave dynamics across polynomial and sinusoidal shift patterns.
Radius of Convergence
Convergence mapping UI tracking power series expansion endpoints. Computes spatial Ratio test limits rendering absolute, conditional intervals visually over 1D axis coordinate models to distinguish $[a, b)$ limits structurally.
Arc Length Geometry
Integration geometric summation modeling arc length via continuous reduction of $ds = \sqrt{dx^2 + dy^2}$ discrete limits approaching exact mathematical integrals. Reveals consistent finite approximation underestimation behavior against true curved lines.
Binomial Probability Model
Interactive Binomial exact probability mass function visualizing discrete histograms. Demonstrates dynamic skew based on fixed $n, p$ ratios and overlays large-sample normal convergence boundaries visually calculating exact vs cumulative density outcomes.
Confidence Intervals
Visualization generating multiple dynamic Confidence Interval margin 'nets' drawn from random standard errors. Empirically validates the meaning of 95% confidence by revealing the random capture vs failure rate against an unknown stationary population parameter line.
Linear Regression (LSRL)
Interactive graphical Least Squares regression engine visually proving the $e^2$ square-area minimization property via manual vs automatic fitting while actively mapping high leverage outlier penalties.
Chi-Square Test (Goodness of Fit)
Goodness of Fit interaction engine assessing categorical skew. Graphically maps individual $(O-E)^2/E$ penalty variance blocks onto nominal bar distributions to visually sum into absolute $\chi^2$ scalar outcomes linking directly to cumulative significance rejection limits.
Student's t-Distribution
Interactive dynamic rendering of Student's T probability density logic modeling $df$ expansion from 1 stabilizing towards normal Z convergence. Highlights fat tail density displacement explicitly revealing structural variance uncertainty for small sample designs.
Two-Way Independence
Probability matrices displaying Two-Way intersections visualizing Marginal row sums vs Joint cell probabilities dynamically tracking conditional shrinking denominators highlighting Independence verifications mathematically.
Crystal Lattice Structures (FCC/BCC/HCP)
3D rotatable crystal lattice visualizer for SC/BCC/FCC/HCP unit cells. Demonstrates atom-sharing fractions (corner ×1/8, face ×1/2, body ×1), packing efficiency percentages, coordination numbers, and edge-to-radius geometric relationships interactively.