Triple Pendulum vs Learn Graphs

The motion of a triple pendulum is governed by a set of coupled ordinary differential equations. For certain energies its motion is chaotic. This application solves these differential equations using the Runge-Kutta method for the time stepping. You can influence the movement of the pendulum by holding your device in different positions.

Don't just look at graphs — play them. Learn Graphs turns algebra into a game: shape a curve with sliders until it clicks onto the target, quiz yourself on the points that matter, and keep a daily streak going. Every answer is checked by real mathematics computed inside the app. MATCH THE CURVE • 67 hand-crafted challenges across 13 function families • Watch your curve morph live as the match meter climbs • Earn up to 3 stars per challenge — beat par, skip the hints QUIZZES THAT READ THE GRAPH • Tap the intercept, spot the vertex, pick the matching equation • A Daily Mix of 5 questions across the functions you've explored • Wrong answers teach: the correct point lights up on the curve A GRAPHING CANVAS THAT TEACHES • Press and drag to trace any curve — it snaps to intercepts, extrema, and inflection points with their coordinates • Ghost trails show before/after as you change a coefficient • Pin a curve, then bend a second one over it to compare • Type exact coefficients, save your favorite curves, and export them as clean PNG or PDF for homework and slides AN ON-DEVICE AI TUTOR On iPhone and iPad with Apple Intelligence, ask the tutor to explain the curve you're looking at or what your last change did — in plain language, powered entirely on device. The math always comes from the app's own engine, never guessed. EVERYWHERE YOU LEARN • Full iPad experience with a sidebar and keyboard shortcuts • "Function of the Day" Home Screen widget with your streak • Siri & Shortcuts: "Show a quadratic graph in Learn Graphs" • VoiceOver Audio Graphs — hear the shape of any curve • In English, Spanish, Portuguese, French, and German 13 function families: linear, quadratic, cubic, quartic, exponential, logarithmic, square root, cube root, absolute value, hyperbolic, rational, trigonometric (sin, cos, tan, sec, csc, cot), and constant — each with domain, range, intercepts, extrema, inflection points, and asymptotes computed instantly. Perfect for algebra and precalculus students, teachers who want a live demo tool, and parents helping with homework.