https://traceanim.com/blog/Teaching maths and science with animationen https://traceanim.com/blog/how-to-create-math-slideshttps://traceanim.com/blog/how-to-create-math-slides Sat, 24 Oct 2026 08:00:00 +0000Create math slides that move: type an equation, get its graph, add a live slider, reveal each step on a click and present. A free, step-by-step guide. https://traceanim.com/blog/best-launch-angle-45-degreeshttps://traceanim.com/blog/best-launch-angle-45-degrees Fri, 23 Oct 2026 08:00:00 +0000The proof that 45° gives the longest throw, why 30° and 60° land in the same place, and why real throws use less: launch height and air resistance. https://traceanim.com/blog/brachistochrone-curvehttps://traceanim.com/blog/brachistochrone-curve Fri, 23 Oct 2026 08:00:00 +0000Why a ball on a cycloid beats one on a straight ramp (3.17 s against 3.76 s for a 20 m drop), the 1696 challenge behind it, and how to animate the race. https://traceanim.com/blog/fourier-series-square-wavehttps://traceanim.com/blog/fourier-series-square-wave Fri, 23 Oct 2026 08:00:00 +0000Add sin x, sin 3x / 3, sin 5x / 5… and a square wave appears. The formula, why only odd harmonics, the 9% Gibbs overshoot, and a click-by-click slide. https://traceanim.com/blog/interactive-math-slideshttps://traceanim.com/blog/interactive-math-slides Fri, 23 Oct 2026 08:00:00 +0000What makes a maths slide interactive, what PowerPoint, GeoGebra and Desmos each do well, and how to build click-by-click slides with live sliders. https://traceanim.com/blog/pythagorean-theorem-lessonhttps://traceanim.com/blog/pythagorean-theorem-lesson Fri, 23 Oct 2026 08:00:00 +0000A ready-to-teach Pythagorean theorem lesson: the areas picture, a proof students can follow, common mistakes, check questions, and how to animate it. https://traceanim.com/blog/slope-y-mx-b-lessonhttps://traceanim.com/blog/slope-y-mx-b-lesson Fri, 23 Oct 2026 08:00:00 +0000A slope lesson students can see: rise over run, what m and b do to a line, the usual mistakes, check questions, and live sliders for m and b. https://traceanim.com/blog/unit-circle-lessonhttps://traceanim.com/blog/unit-circle-lesson Fri, 23 Oct 2026 08:00:00 +0000A unit circle lesson plan: sine and cosine as coordinates, special angles, signs in each quadrant, the sine wave unrolled, common mistakes and checks. https://traceanim.com/blog/free-body-diagram-newtons-second-lawhttps://traceanim.com/blog/free-body-diagram-newtons-second-law Fri, 23 Oct 2026 08:00:00 +0000How to teach free-body diagrams step by step, a worked example (30 N push, 10 N friction, 5 kg: a = 4 m/s²), the classic mistakes and check questions. https://traceanim.com/blog/solving-linear-equations-lessonhttps://traceanim.com/blog/solving-linear-equations-lesson Fri, 23 Oct 2026 08:00:00 +0000Teach solving linear equations as undoing steps: a balance-based lesson, worked examples, the classic sign mistakes, check questions and animated steps. https://traceanim.com/blog/solving-quadratic-equations-factoringhttps://traceanim.com/blog/solving-quadratic-equations-factoring Fri, 23 Oct 2026 08:00:00 +0000Solve quadratic equations by factoring: the zero-product rule, the product–sum method, a worked example, common mistakes and checks, with the graph alongside. https://traceanim.com/blog/graphing-quadratic-functions-vertex-formhttps://traceanim.com/blog/graphing-quadratic-functions-vertex-form Fri, 23 Oct 2026 08:00:00 +0000Teach vertex form y = a(x − h)² + k: what a, h and k do to a parabola, completing the square, the sign trap with h, and live sliders to explore it. https://traceanim.com/blog/derivative-slope-of-tangent-linehttps://traceanim.com/blog/derivative-slope-of-tangent-line Fri, 23 Oct 2026 08:00:00 +0000Introduce the derivative as the slope of the tangent line: secants that shrink, the limit (f(x+h) − f(x))/h, a worked example with x², mistakes and checks. https://traceanim.com/blog/riemann-sums-area-under-curvehttps://traceanim.com/blog/riemann-sums-area-under-curve Fri, 23 Oct 2026 08:00:00 +0000A Riemann sums lesson: left, right and midpoint rectangles under y = x², exact numbers for 8 rectangles, how the error shrinks, mistakes and checks. https://traceanim.com/blog/taylor-series-approximationhttps://traceanim.com/blog/taylor-series-approximation Fri, 23 Oct 2026 08:00:00 +0000How Taylor series build eˣ and sin x from polynomials term by term, how accurate a few terms are, the small-angle approximation, and a click-by-click slide. https://traceanim.com/blog/exponential-growth-decay-lessonhttps://traceanim.com/blog/exponential-growth-decay-lesson Fri, 23 Oct 2026 08:00:00 +0000Teach exponential growth and decay with y = a·bˣ: doubling, half-life, compound interest, why exponential beats x², common mistakes and check questions. https://traceanim.com/blog/systems-of-equations-graphinghttps://traceanim.com/blog/systems-of-equations-graphing Fri, 23 Oct 2026 08:00:00 +0000Teach systems of linear equations by graphing: the intersection as the solution, one, none or infinitely many solutions, substitution as a check, and mistakes. https://traceanim.com/blog/expanding-brackets-lessonhttps://traceanim.com/blog/expanding-brackets-lesson Fri, 23 Oct 2026 08:00:00 +0000Teach expanding brackets with the area model: why (a + b)² = a² + 2ab + b², not a² + b², the difference of two squares, mistakes and check questions. https://traceanim.com/blog/adding-vectors-head-to-tailhttps://traceanim.com/blog/adding-vectors-head-to-tail Fri, 23 Oct 2026 08:00:00 +0000Teach vector addition: head-to-tail drawings, adding components, the magnitude with Pythagoras, a river-crossing example, common mistakes and checks. https://traceanim.com/blog/simple-pendulum-periodhttps://traceanim.com/blog/simple-pendulum-period Fri, 23 Oct 2026 08:00:00 +0000Teach the simple pendulum period formula T = 2π√(L/g): what changes the period and what does not, the small-angle limit, worked examples and checks. https://traceanim.com/blog/wave-speed-equation-lessonhttps://traceanim.com/blog/wave-speed-equation-lesson Fri, 23 Oct 2026 08:00:00 +0000Teach the wave equation v = fλ: wavelength, frequency, period and amplitude on one animated wave, examples with sound and light, mistakes and checks. https://traceanim.com/blog/circular-orbit-speed-lessonhttps://traceanim.com/blog/circular-orbit-speed-lesson Fri, 23 Oct 2026 08:00:00 +0000A lesson on circular orbits: gravity as the centripetal force, orbital speed v = √(GM/r), the ISS at 7.7 km/s and 92 minutes, geostationary orbit, and mistakes. https://traceanim.com/blog/ohms-law-circuits-lessonhttps://traceanim.com/blog/ohms-law-circuits-lesson Fri, 23 Oct 2026 08:00:00 +0000Teach Ohm’s law V = IR with a live circuit: current, voltage, resistance, series and parallel resistors, power, the classic misconceptions and checks. https://traceanim.com/blog/custom-math-animationshttps://traceanim.com/blog/custom-math-animations Wed, 21 Oct 2026 08:00:00 +0000Points, vectors and curves that move with time: write a rolling wheel or a sliding ladder in six lines of calculator maths, or let the AI write it. https://traceanim.com/blog/animate-math-without-codehttps://traceanim.com/blog/animate-math-without-code Tue, 20 Oct 2026 08:00:00 +0000A practical guide to animated maths slides: what to animate, how to reveal ideas one click at a time, and how to build it without Python or Manim. https://traceanim.com/blog/newtons-method-animationhttps://traceanim.com/blog/newtons-method-animation Tue, 20 Oct 2026 08:00:00 +0000Teach Newton's method visually: follow each tangent down to the x-axis, compare it with bisection, and see why it converges so fast, or fails. https://traceanim.com/blog/euler-method-direction-fieldshttps://traceanim.com/blog/euler-method-direction-fields Tue, 20 Oct 2026 08:00:00 +0000A visual lesson on differential equations: draw the direction field, follow solution curves, then watch Euler’s method step away from the exact solution. https://traceanim.com/blog/qam-constellation-diagramshttps://traceanim.com/blog/qam-constellation-diagrams Tue, 20 Oct 2026 08:00:00 +0000What a constellation diagram shows, why 256-QAM needs a cleaner channel than QPSK, Gray coding, noise and phase errors, with animated examples. https://traceanim.com/blog/tcp-three-way-handshake-diagramhttps://traceanim.com/blog/tcp-three-way-handshake-diagram Tue, 20 Oct 2026 08:00:00 +0000Teach the TCP handshake with a sequence diagram that plays one message per click: SYN, SYN-ACK, ACK, sequence numbers, and what happens when a packet is lost. https://traceanim.com/blog/fractals-in-the-classroomhttps://traceanim.com/blog/fractals-in-the-classroom Tue, 20 Oct 2026 08:00:00 +0000Three fractals that hook a class: the Koch snowflake step by step, the Sierpinski triangle and the Mandelbrot set, with the maths behind each. https://traceanim.com/blog/logistic-map-chaoshttps://traceanim.com/blog/logistic-map-chaos Tue, 20 Oct 2026 08:00:00 +0000One simple rule, x → r x (1 − x), goes from a steady state to cycles to chaos as r grows. Cobweb diagrams and the bifurcation diagram, explained.