Euclid's Muse

Newton needs your help! Newton is trying to prove Kepler’s theory on planet orbits; that the area will remain constant anywhere on the orbital. Newton took the integral of the arc length to solve for the area that the planet sweeps over. The length will change in respect to the area as the area remains constant.

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Allow to see derivative of any function you choose

Learn limits n’ stuff

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The green line represents your equation while the pink line represents the derivative of the equation.

Above is a graph of the miles ran by the runner and the time in minutes it has taken her to complete those miles. Drag the runner across the function F(X)= ln(1000X) to represent how many miles she has run. Then you are able to calculate the speed (Minutes per mile) of the runner by finding the derivative of the graph at that exact point.

Relating the position to the velocity of a flying rock from a catapult.

Explore how a geometric approximation beneath the curve compares to the definite integral at variable bounds.