Showing 12 results
Confidence Intervals
Construct confidence intervals using $ar{x} pm z^* rac{sigma}{sqrt{n}}$ to estimate population parameters. Visualize how confidence level, sample size, and variability affect interval width, and interpret what it means to be 95% confident about capturing the true parameter.
Hypothesis Testing
Conduct hypothesis tests by calculating test statistics and p-values to evaluate null hypotheses. Visualize Type I and Type II errors, significance levels, and the decision-making process for rejecting or failing to reject the null hypothesis based on sample evidence.
Least Squares Regression Line
Calculate the least squares regression line $hat{y} = a + bx$ that minimizes the sum of squared residuals. Visualize how the slope $b = r rac{s_y}{s_x}$ and intercept relate to correlation, and interpret the line's predictive power for bivariate data.
Scatter Plot & Correlation
Create scatter plots to visualize bivariate relationships and calculate correlation coefficient $r$ to measure linear association strength. Explore how outliers, direction, form, and strength affect correlation, and understand why correlation does not imply causation.
CRISPR-Cas9 Mechanism 3D Visualizer
Visualizes the complete CRISPR-Cas9 genome editing process, tracking PAM recognition, DNA unwinding, gRNA matching, and the double-strand break in 3D.
Solid of Revolution 3D Visualizer
Interactive Calculus visualizer converting 2D function areas into 3D volumes of revolution using Disk and Washer methods.
Special Relativity: Time Dilation & Length Contraction
Visualizes the counter-intuitive effects of velocity approaching the speed of light, exploring time dilation and length contraction through a moving observer frame.
Le Chatelier's Principle & Equilibrium
Simulates Le Chatelier's Principle allowing users to inject molecules, change volume/pressure, and shift temperature to observe real-time equilibrium shifts (N2O4 \u21CC 2NO2).
Atwood Machine & Inclined Plane Dynamics
Interactive 3D simulation of a dual-mass Atwood machine on an inclined plane. Visualizes tension, friction, and Newton's laws dynamically.
Clausius-Clapeyron Vapor Pressure Plotter
Explores the exponential relationship between temperature and vapor pressure, generating real-time linear ln(P) vs 1/T plots based on intermolecular forces.
Lotka-Volterra Predator-Prey Dynamics
Mathematical ecology simulator charting the cyclic phase space between predators and prey. Manipulate birth/death rates to find stable orbits or extinction events.
Improper Integrals & p-Series Convergence
Calculus visualizer demonstrating the paradox of infinite boundaries yielding finite areas (Gabriel's Horn). Dynamically integrate 1/x^p as the bound approaches infinity.