Animations
Each example below is a standalone .eido project holding a single figure that uses stage, animate and assert to demonstrate one geometric result. Every download uses the current .eido format (manifest version: 2) and contains editable Eidolang source.
After downloading, choose Open in the app header and select the file, or drop the .eido file onto the app. You do not have to install anything: the View in Viewer link plays the project in the browser.
The image in each section is a PNG exported from the same figure with Eidograph's export tool and shows one frame of the timeline. Open the file to play the whole animation.
Plane figures
Perpendicular Bisector Theorem
This example shows how to make an animation to demo the perpendicular bisector theorem. P slides along the perpendicular bisector of AB while the live length labels on PA and PB stay equal, and two assertions check the distances and the right angle on every frame.
Download perpendicular-bisector-theorem.eido · View in Viewer
Napoleon's Theorem
This example shows how to make an animation to demo Napoleon's theorem. Vertex C keeps deforming the triangle while the three equilateral-triangle centers stay the vertices of an equilateral triangle.
Download napoleons-theorem.eido · View in Viewer
Thales' Theorem
This example shows how to make an animation to demo Thales' theorem. P travels along the semicircle while the angle subtended at P by the diameter AB stays a right angle.
Download thales-theorem.eido · View in Viewer
Inscribed Angle Theorem
This example shows how to make an animation to demo the inscribed angle theorem. P moves around the major arc while the central angle AOB stays exactly twice the inscribed angle APB.
Download inscribed-angle-theorem.eido · View in Viewer
Perpendicular Chord Bisector Theorem
This example shows how to make an animation to demo the perpendicular chord bisector theorem. The chord AB rotates around the circle while OM stays perpendicular to it and the two half-chord labels stay equal.
Download perpendicular-chord-bisector-theorem.eido · View in Viewer
Isosceles Triangle Base Angles
This example shows how to make an animation to demo the base angles of an isosceles triangle. Apex C slides up and down the axis of symmetry, and the two base angles stay equal at every height.
Download isosceles-triangle-base-angles.eido · View in Viewer
Triangle Angle Sum
This example shows how to make an animation to demo the angle sum of a triangle. A parallel drawn through C folds the three interior angles into a straight angle while vertex C keeps moving.
Download triangle-angle-sum.eido · View in Viewer
Triangle Centroid Theorem
This example shows how to make an animation to demo the centroid theorem. The triangle deforms while the three medians keep meeting at G, which stays at a 2:1 ratio along every median.
Download triangle-centroid-theorem.eido · View in Viewer
Pythagorean Rearrangement Proof
This example shows how to make an animation to demo the Pythagorean theorem. Four congruent right triangles rotate into a second arrangement inside the same square, turning the two smaller squares into one square on the hypotenuse.
Download pythagorean-rearrangement-proof.eido · View in Viewer
Triangle Circumcenter
This example shows how to make an animation to demo the circumcenter of a triangle. The three perpendicular bisectors keep meeting at O, and the circumcircle follows the moving vertex C.
Download triangle-circumcenter.eido · View in Viewer
Radius and Tangent
This example shows how to make an animation to demo the right angle between a radius and a tangent. The point of contact T travels around the circle while the tangent line stays perpendicular to the radius OT.
Download radius-and-tangent.eido · View in Viewer
Power of a Point
This example shows how to make an animation to demo the power of a point. One secant through P rotates while the live labels show that both secant products stay equal.
Download power-of-a-point.eido · View in Viewer
Ptolemy's Theorem
This example shows how to make an animation to demo Ptolemy's theorem. Vertex D slides around the circle while the product of the diagonals and the sum of the opposite-side products stay equal.
Download ptolemys-theorem.eido · View in Viewer
Parallelogram Diagonals
This example shows how to make an animation to demo the bisection of the diagonals of a parallelogram. The parallelogram leans as its angle changes, and both diagonals keep the same midpoint M.
Download parallelogram-diagonals.eido · View in Viewer
Varignon's Theorem
This example shows how to make an animation to demo Varignon's theorem. Vertex D keeps deforming the quadrilateral while the quadrilateral of side midpoints stays a parallelogram.
Download varignons-theorem.eido · View in Viewer
Reflection Shortest Path
This example shows how to make an animation to demo the shortest reflected path. P slides along the mirror while the live route length reaches its minimum exactly where A, P and the reflected point B' are collinear.
Download reflection-shortest-path.eido · View in Viewer
Homothety
This example shows how to make an animation to demo a homothety. The scale factor k grows while every image point stays on a ray from O and every side length is multiplied by k.
Download homothety.eido · View in Viewer
Rotation Is a Rigid Motion
This example shows how to make an animation to demo a rotation as a rigid motion. The triangle turns a full circle around O while assertions check that every side length and angle is preserved.
Download rotation-is-a-rigid-motion.eido · View in Viewer
Ellipse Focal Definition
This example shows how to make an animation to demo the focal definition of an ellipse. P travels once around the ellipse; the two focal distances change but their sum stays constant.
Download ellipse-focal-definition.eido · View in Viewer
Parabola Focus and Directrix
This example shows how to make an animation to demo the focus-directrix definition of a parabola. P moves along the parabola while its distance to the focus stays equal to its distance to the directrix.
Download parabola-focus-and-directrix.eido · View in Viewer
Pantograph Similarity
This example shows how to make an animation to demo how a pantograph linkage enlarges a drawing. The linkage turns while two loci record the stylus path and the pen path, which stays a similar copy scaled by k.
Download pantograph-similarity.eido · View in Viewer
Cycloid from a Rolling Circle
This example shows how to make an animation to demo a cycloid. A circle rolls without slipping along a line while a marked point on its rim traces the cycloid as a locus.
Download cycloid-from-a-rolling-circle.eido · View in Viewer
Unit Circle and Sine Wave
This example shows how to make an animation to demo how the unit circle generates a sine wave. A connector links the rotating point on the circle to the point on the graph, whose height is the sine of the same angle.
Download unit-circle-and-sine-wave.eido · View in Viewer
Circle Inversion
This example shows how to make an animation to demo inversion in a circle. P moves outward along a ray while its image P' moves inward, keeping the product OP × OP' equal to R².
Download circle-inversion.eido · View in Viewer
Solid figures
Cuboid Space Diagonal
This example shows how to make an animation to demo the space diagonal of a cuboid. The height grows while assertions check the base diagonal against a² + b² and the space diagonal against a² + b² + c².
Download cuboid-space-diagonal.eido · View in Viewer
Cone and Cylinder Volume Ratio
This example shows how to make an animation to demo the volume ratio of a cone and a cylinder. A shared radius grows for both solids while the live volume labels stay in a 3:1 ratio.
Download cone-and-cylinder-volume-ratio.eido · View in Viewer
Intersection Circle of Two Spheres
This example shows how to make an animation to demo the circle where two spheres meet. The distance between the centers grows and the common circle shrinks, always lying in the perpendicular bisector plane.
Download intersection-circle-of-two-spheres.eido · View in Viewer
Stella Octangula
This example shows how to make an animation to demo the stella octangula. A second congruent tetrahedron rotates until, at 90 degrees, the two interpenetrate around a regular octahedral core.
