Interactive Math Animations: Geometry and Trigonometry | Shikkha Web

Grade 8–10

Pythagorean Theorem

The Pythagorean theorem explained: formula a² + b² = c², two proofs you can watch, the converse, Pythagorean triples and 10 worked examples. Drag the triangle yourself.

Grade 10–11

Trigonometric Ratios and the Unit Circle

Drag a point round the unit circle and watch sin, cos and tan change. Standard angle table, ASTC signs, identities, radians and graphs, with solved examples.

Grade 9–11

Quadratic functions and their graphs

Drag the vertex and change a, b, c to see how a quadratic function graph moves. Learn factoring, completing the square, the quadratic formula and discriminant.

Grade 9–10

Circle theorems

All the circle theorems with drag-and-check diagrams: angle at the centre, same segment, semicircle, cyclic quadrilateral, chords, tangents and alternate segment.

Grade 9–10

Heights and distances: elevation and depression angles

What angle of elevation and angle of depression mean, how the height-and-distance formula works, and how two observations solve a tower's height without ever measuring it — with an interactive simulation and solved problems.

Grade 9–11

Probability: experimental vs theoretical probability

What probability means, how the sample-space formula P(E) = n(E)/n(S) works, and why experimental frequency edges closer to theoretical probability the more you flip, roll or draw — with a coin, dice and coloured-ball simulator.

Grade 10–11

Arithmetic and Geometric Sequences

Learn the arithmetic and geometric sequence formulas for the nth term and sum, Gauss's pairing trick, and the sum-to-infinity formula a/(1−r), with a drag-and-slide bar-chart simulation and worked examples.

Grade 9–10

Mean, Median and Mode

Learn the mean, median and mode formulas, why the median resists an outlier while the mean does not, and the grouped-data median/mode formulas, by dragging points on a number line, with worked examples.

Grade 7–11

Sets and Venn Diagrams

Shade union, intersection, difference and complement on a live Venn diagram, drop numbers into regions, check n(A ∪ B) and test De Morgan’s laws, with solved problems.

Grade 8–10

Linear equations: graphs, slope and simultaneous pairs

See slope, intercepts and angle on a straight line, then graph two linear equations to find where they meet. Learn the ratio test for one, none or infinite solutions.

Grade 10–12

Graphs of sin, cos and tan

Plot y = A sin(Bx + C) + D with sliders: see amplitude, period, phase shift, range and the asymptotes of tan live. Trigonometric graphs with solved examples.

Grade 9–10

Completing the Square and the Quadratic Formula

Watch algebra tiles complete the square, then solve quadratic equations, find the vertex and see why the formula works. Free interactive simulation with solved examples.

Grade 7–10

Area of a Circle: Proof, Formula and Solved Problems

Cut a circle into slices, slide them into a rectangle and watch the area become πr². Free interactive simulation with circumference, pi, sectors, arcs and solved problems.

Grade 8–10

Volume and Surface Area of Solids: Cube, Cuboid, Cylinder, Cone, Sphere

Rotate six solids in 3D, unfold their nets and pour a cone into a cylinder to see why it takes exactly three. Free simulation with volume, CSA and TSA formulas and solved problems.

Grade 8–10

Similar Triangles: Scale Factor, AA, SSS, SAS and Shadow Heights

Scale a triangle with a slider and watch angles stay equal, side ratios stay k and area grow by k². Free interactive similar triangles simulation with AA, SSS, SAS tests and shadow problems.

Grade 9–11

Coordinate Geometry: Distance, Midpoint, Slope, Section Formula and Locus

Drag points on a grid and watch the distance formula, midpoint, slope and section formula update live. Free coordinate geometry simulation with the perpendicular-bisector locus and solved problems.

Grade 11–12

Conic Sections: Circle, Ellipse, Parabola and Hyperbola

Tilt a plane through a double cone and watch a circle, ellipse, parabola or hyperbola appear, with its standard equation, foci and eccentricity. Free conic sections simulation with solved problems.

Grade 9–11

Function Transformations: Shifts, Stretches and Reflections

Pick x², |x|, √x, sin x or 2^x and drag sliders for a, b, h and k. Watch shifts, stretches, squeezes and reflections move the graph, with the parent faded behind. Free simulation with solved problems.

Grade 11–12

Derivative as the Slope of a Tangent: Secant to Tangent

Drag a point P on x², x³, sin x, eˣ or 1/x and shrink the gap h to zero. Watch the secant become the tangent and its slope become the derivative, with the derivative graph below. Free simulation.

Grade 11–12

Riemann Sums and Integration: Area Under a Curve

Cut the area under x², x³, sin x, eˣ or √x into up to 100 strips and compare left, right, midpoint and trapezoid sums with the exact integral. Watch the error melt away. Free simulation.

Grade 11–12

Limits and the ε–δ Definition: A Visual Guide

See the epsilon-delta definition of a limit. Pick a function, shrink ε and watch the δ band follow it, with left and right limits, a hole, sin x / x and a jump where no δ works. Free simulation.

Grade 11–12

3D Vectors: Sum, Dot Product and Cross Product

Drag to rotate two 3D vectors. See the sum as a parallelogram, the dot product as a shadow and an angle, and the cross product as a perpendicular arrow whose length is the area. Free simulation.

Grade 11–12

Matrix Transformations: Rotation, Reflection, Shear and the Determinant

Change a 2×2 matrix and watch the grid, a unit square and an F-shape move. See where i-hat and j-hat land, the determinant as signed area, and the inverse. Free simulation.

Grade 11–12

Complex Numbers: Sum, Product, Powers and Roots on the Argand Plane

Drag two complex numbers on the Argand plane. See the sum as a parallelogram, the product as a rotation and stretch, conjugates, powers as a spiral and roots of unity. Free simulation.

Grade 9–12

Binary Number System: Place Value, Conversion and Addition

Flip bits and see decimal, binary, octal and hex change together. Watch conversion by repeated division by 2, regrouping into octal and hex, and binary addition with carries. Free, with worked examples.