Learn Graphs vs Make Chirps

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.

This educational app displays gravitational wave chirps created by mergers of massive black holes in several different ways, giving users an intuitive understanding of these exotic disturbances of space-time itself produced by cataclysmic events in distant galaxies. FEATURES: • Simulation: Experience the intricate behavior of gravitational waves through physics simulation of inspiralling black holes that merge to form a final black hole which then “shakes off” its excess energy. • Visualizations: See the essence of gravitational waves via waveform plots, frequency evolutions, and spectrograms, to understand the patterns and how they depend on black hole masses. • Auditory Experience: Listen closely as you hear the evolution of gravitational waves, detecting the characteristic increase in time in strength and frequency. Try varying masses to see how pitch is affected. • Dynamic Animations: Witness the captivating dance of black holes in collision animations. Explore the propagation of these waves through space-time with mesmerizing spiral animations. • Educational Insights: Gain a comprehensive understanding of gravitational waves and the pioneering work of LIGO through informative text pages, enhancing your knowledge of these cosmic phenomena. COMPATIBILITY Compatible with iPhone and iPad, iOS 16 or later. ACKNOWLEDGEMENT Supported by the National Science Foundation with grant PHY-2110181.