Math applets

A working collection of interactive mathematics.

GeoGebra constructions from 2013-2024, organized by mathematical idea, audience, and the kind of interaction they invite.

I'm working to properly credit files that came from other GeoGebra authors. If you see one inaccurately credited, please let me know.

I'm also working to update the functionality of this archive. Some files may not embed properly at the moment.

111published applets
8mathematical domains
15connected to talks

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111 matching applets

GeoGebra preview for Two coins rotate.
two coins rotate

Two coins rotate

A GeoGebra animation exploring two coins rotate.

Probability and statisticsProbabilityMotionAnimation
Audience
High school, General
Interaction
Animation
Credit
Scott Farrar
GeoGebra preview for Aperiodic monotile 2023.
GeoGebra Doodads

Aperiodic Monotile

Explore the geometry of the 2023 hat monotile, a single shape that tiles the plane only aperiodically.

GeometryTilingConstruction
Audience
High school, General
Interaction
Construction, Generative art, Visualization
Credit
Scott Farrar
GeoGebra preview for Bhaskara 2023.
GeoGebra Doodads

Bhaskara 2023

A GeoGebra drag and notice exploring bhaskara 2023.

GeometryPythagorean theoremDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Pattern block areas.
GeoGebra Doodads

Pattern block areas

A GeoGebra drag and notice exploring pattern block areas.

GeometryTilingDrag and notice
Audience
Middle school, High school
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Teardrop reconstruction.
GeoGebra Doodads

Teardrop reconstruction

A GeoGebra construction exploring teardrop reconstruction.

GeometryConstruction
Audience
High school, General
Interaction
Construction, Visualization
Credit
Scott Farrar
GeoGebra preview for Variance kareem carr doodling.
GeoGebra Doodads

Variance kareem carr doodling

A GeoGebra drag and notice exploring variance kareem carr doodling.

Probability and statisticsData and variationDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Inspired by Kareem Carr
GeoGebra preview for 16 point trig.
GeoGebra Doodads

16 point trig

A GeoGebra drag and notice exploring 16 point trig.

TrigonometryDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Sixes Up simulation.
GeoGebra Doodads

Sixes Up simulation

A GeoGebra simulation exploring sixes up simulation.

Probability and statisticsProbabilitySimulation
Audience
High school, General
Interaction
Simulation, Visualization
Credit
Scott Farrar
GeoGebra preview for Tiling from a cutout 20gon.
GeoGebra Doodads

Tiling from a cutout 20gon

A GeoGebra generative art exploring tiling from a cutout 20gon.

GeometryTilingGenerative art
Audience
High school, General
Interaction
Generative art, Visualization
Credit
Scott Farrar
GeoGebra preview for Triangle inequality vector addition.
triangle inequality 2020

Triangle inequality vector addition

A GeoGebra construction exploring triangle inequality vector addition.

GeometryTriangle inequalityAnglesConstruction
Audience
Middle school, High school
Interaction
Construction, Visualization
Credit
Scott Farrar
GeoGebra preview for Bees Bombs Circles.
beesbombscircles

Bees Bombs Circles

A GeoGebra drag and notice exploring bees bombs circles.

GeometryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar adapted from https://beesandbombs.tumblr.com/
GeoGebra preview for Cones from a Circle.
Two Cones

Cones from a Circle

Cut and fold a circle into cone models and compare how radius, arc length, and height move together.

GeometryConesModelingDrag and notice
Audience
High school, General
Interaction
Drag and notice, Modeling, Visualization
Credit
Scott Farrar
GeoGebra preview for Cshearer41 hexagon problem.
GeoGebra Doodads

Cshearer41 hexagon problem

A GeoGebra drag and notice exploring cshearer41 hexagon problem.

GeometryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Problem by Catriona Shearer
GeoGebra preview for Curvature Steering.
GeoGebra Doodads

Curvature Steering

A GeoGebra drag and notice exploring curvature steering.

CalculusMotionDrag and notice
Audience
Calculus
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Grid Variations.
john golden's squirqle grid

Grid Variations

A GeoGebra drag and notice exploring grid variations.

GeometryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
John Golden
GeoGebra preview for Parabolic reflector v2.
parabolic reflector

Parabolic reflector v2

A GeoGebra drag and notice exploring parabolic reflector v2.

GeometryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Pentagon angles.
GeoGebra Doodads

Pentagon angles

A GeoGebra drag and notice exploring pentagon angles.

GeometryAnglesDrag and notice
Audience
Middle school, High school
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Pentagon cycle.
pentagon cycle

Pentagon cycle

A GeoGebra drag and notice exploring pentagon cycle.

GeometryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Sine Wag the Dog.
sine wag the dog circle

Sine Wag the Dog

A GeoGebra drag and notice exploring sine wag the dog.

TrigonometrySine and cosineDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Slicing Pie.
slicing pie

Slicing Pie

A GeoGebra drag and notice exploring slicing pie.

GeometryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Spheres In ARoom.
spheres in a room

Spheres In ARoom

A GeoGebra drag and notice exploring spheres in aroom.

GeometryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Triangle ineq proof question.
triangle ineq proof question

Triangle ineq proof question

A GeoGebra proof exploring triangle ineq proof question.

GeometryTriangle inequalityAnglesProof
Audience
Middle school, High school
Interaction
Proof, Construction, Visualization
Credit
Scott Farrar
GeoGebra preview for Complex Double Num Line.
visualizeComplexDoubleNumLine

Complex Double Num Line

A GeoGebra drag and notice exploring complex double num line.

Complex numbersComplex transformationsDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Complex Squaring mesh.
complexRules

Complex Squaring mesh

A GeoGebra drag and notice exploring complex squaring mesh.

Complex numbersComplex transformationsDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Factorable Quadratics with colored lattice points and a parabola.
GeoGebra

Factorable Quadratics

Drag the coefficient point and watch how a monic quadratic's graph, factorability, and integer roots line up.

Algebra and functionsQuadraticsFactoringDrag and notice
Audience
High school
Interaction
Drag and notice, Visualization
Credit
Scott Farrar
GeoGebra preview for Function Circle1.
GeoGebra Doodads

Function Circle1

A GeoGebra drag and notice exploring function circle1.

Algebra and functionsDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Function Tube.
GeoGebra Doodads

Function Tube

A GeoGebra drag and notice exploring function tube.

Algebra and functionsDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Heartbeats.
GeoGebra Doodads

Heartbeats

A GeoGebra drag and notice exploring heartbeats.

Probability and statisticsDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Lines In ACircle.
GeoGebra Doodads

Lines in a Circle

Animate lines rotating through a circle and watch the paths and envelopes they create.

GeometryCirclesAnimation
Audience
High school, General
Interaction
Animation, Visualization
Credit
Scott Farrar
GeoGebra preview for Messy e.
GeoGebra Doodads

Messy e

A GeoGebra drag and notice exploring messy e.

Number theoryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Messy e 2.
GeoGebra Doodads

Messy e 2

A GeoGebra drag and notice exploring messy e 2.

Number theoryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Swing Hyp Down.
swingHypDown

Swing Hyp Down

Use a swinging right-triangle animation to connect a changing hypotenuse with geometric motion.

GeometryRight trianglesAnimation
Audience
High school, General
Interaction
Animation, Visualization
Credit
Scott Farrar
GeoGebra preview for 7ths and 13ths 2017.
GeoGebra Doodads

7ths and 13ths 2017

A GeoGebra drag and notice exploring 7ths and 13ths 2017.

Number theoryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Bounding Box Sine.
sine bounding box

Bounding Box Sine

A GeoGebra drag and notice exploring bounding box sine.

TrigonometrySine and cosineDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Bounding Box Sine.
sine bounding box

Bounding Box Sine

A GeoGebra drag and notice exploring bounding box sine.

TrigonometrySine and cosineDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Circle inversion interactive.
GeoGebra Doodads

Circle Inversion

Drag points through an inversive geometry construction and see lines, circles, and distances transform.

GeometryInversionDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice, Construction, Visualization
Credit
Scott Farrar
GeoGebra preview for Cobweb chaos v2.
cobweb chaos

Cobweb Chaos

Use a cobweb diagram to watch repeated function iteration settle, cycle, or become chaotic.

Algebra and functionsIterationDrag and notice
Audience
High school, General
Interaction
Drag and notice, Animation, Visualization
Credit
Scott Farrar
GeoGebra preview for Collatz webbing.
collatz

Collatz webbing

A GeoGebra generative art exploring collatz webbing.

Number theoryIterationGenerative art
Audience
High school, General
Interaction
Generative art, Visualization
Credit
Scott Farrar
GeoGebra preview for Complete Graph Turning.
octagons

Complete Graph Turning

A GeoGebra generative art exploring complete graph turning.

GeometryGenerative art
Audience
High school, General
Interaction
Generative art, Visualization
Credit
Original author unknown
GeoGebra preview for Complex sequence 1.
complex sequences

Complex Sequence

Follow an iterated complex sequence as its orbit draws structure, repetition, and divergence in the plane.

Complex numbersIterationDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice, Animation, Visualization
Credit
Scott Farrar
GeoGebra preview for Imperfect loops.
graphing challenge\imperfect loops

Imperfect loops

A GeoGebra drag and notice exploring imperfect loops.

Algebra and functionsDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Incenter Spirographs.
GeoGebra Doodads

Incenter Spirograph

Animate a triangle and trace its incenter into a family of geometric, spirograph-like curves.

GeometryTriangle centersAnimation
Audience
High school, General
Interaction
Animation, Generative art, Visualization
Credit
Scott Farrar
GeoGebra preview for L and w ratio recttriarea.
RectTriArea

L and w ratio recttriarea

A GeoGebra drag and notice exploring l and w ratio recttriarea.

GeometryArea and perimeterDrag and notice
Audience
Middle school, High school
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Machine learning gradient descent.
GeoGebra Doodads

Machine Learning Gradient Descent

A three-dimensional sketch of an optimization path descending across a mathematical surface.

CalculusOptimizationModelingSimulation
Audience
Calculus
Interaction
Simulation, Modeling, Visualization
Credit
Scott Farrar
GeoGebra preview for Married Joint.
tax brackets

Married Joint

A GeoGebra modeling exploring married joint.

Algebra and functionsTax policyModeling
Audience
High school, General
Interaction
Modeling, Visualization
Credit
Scott Farrar
GeoGebra preview for Min distance to edges.
triangle centers 3blue1brown

Min distance to edges

A GeoGebra construction exploring min distance to edges.

GeometryTriangle centersAnglesConstruction
Audience
Middle school, High school
Interaction
Construction, Visualization
Credit
Scott Farrar, inspired by 3Blue1Brown
GeoGebra preview for Octagons.
GeoGebra Doodads

Octagons

A GeoGebra generative art exploring octagons.

GeometryGenerative art
Audience
High school, General
Interaction
Generative art, Visualization
Credit
Scott Farrar
GeoGebra preview for Rect Tri Area Color.
equiAreaEstimate

Rect Tri Area Color

A GeoGebra construction exploring rect tri area color.

GeometryArea and perimeterAnglesConstruction
Audience
Middle school, High school
Interaction
Construction, Visualization
Credit
Scott Farrar
GeoGebra preview for Tax Brackets.
tax brackets

Tax Brackets

See marginal tax brackets as a piecewise model rather than a single rate applied to all income.

Algebra and functionsTax policyModelingModeling
Audience
High school, General
Interaction
Modeling, Visualization
Credit
Scott Farrar
GeoGebra preview for Trapezoid areas.
trapezoid areas

Trapezoid areas

A GeoGebra drag and notice exploring trapezoid areas.

GeometryDrag and notice
Audience
Middle school, High school
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Triangle centers.
triangle centers 3blue1brown

Triangle centers

A GeoGebra construction exploring triangle centers.

GeometryTriangle centersAnglesConstruction
Audience
Middle school, High school
Interaction
Construction, Visualization
Credit
Scott Farrar, inspired by 3Blue1Brown
GeoGebra preview for Triangle ineq sfsu.
GeoGebra Doodads

Triangle ineq sfsu

A GeoGebra construction exploring triangle ineq sfsu.

GeometryTriangle inequalityAnglesConstruction
Audience
Middle school, High school
Interaction
Construction, Visualization
Credit
Scott Farrar
GeoGebra preview for Triangular coin probability.
triangular coin game

Triangular coin probability

A GeoGebra simulation exploring triangular coin probability.

Probability and statisticsProbabilitySimulation
Audience
High school, General
Interaction
Simulation, Visualization
Credit
Scott Farrar
GeoGebra preview for 03 Rect Overflow freeplay.
RectTriArea

03 Rect Overflow freeplay

A GeoGebra drag and notice exploring 03 rect overflow freeplay.

GeometryArea and perimeterDrag and notice
Audience
Middle school, High school
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Area Max 01.
RectTriArea

Area Max 01

A GeoGebra drag and notice exploring area max 01.

GeometryArea and perimeterOptimizationDrag and notice
Audience
Middle school, High school
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Completing the Square.
complete the square

Completing the Square

Drag through a visual model of completing the square and watch the algebraic structure take shape.

Algebra and functionsCompleting the squareDrag and notice
Audience
High school, General
Interaction
Drag and notice, Visualization
Credit
Scott Farrar
GeoGebra preview for Forks and knives.
GeoGebra Doodads

Forks and knives

A GeoGebra drag and notice exploring forks and knives.

GeometryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Perfsqtrinomials.
complete the square

Perfsqtrinomials

A GeoGebra drag and notice exploring perfsqtrinomials.

Algebra and functionsQuadraticsDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Perpxsect.
perpendicular x sect makers

Perpxsect

A GeoGebra construction exploring perpxsect.

GeometryConstruction
Audience
High school, General
Interaction
Construction, Visualization
Credit
Scott Farrar
GeoGebra preview for Quadratic ancestors.
quadratic ancestors

Quadratic ancestors

A GeoGebra drag and notice exploring quadratic ancestors.

Algebra and functionsQuadraticsDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Rect Tri Area Gray.
equiAreaEstimate

Rect Tri Area Gray

A GeoGebra construction exploring rect tri area gray.

GeometryArea and perimeterAnglesConstruction
Audience
Middle school, High school
Interaction
Construction, Visualization
Credit
Scott Farrar
GeoGebra preview for Rectangle Pouring.
RectTriArea

Rectangle Pouring

A GeoGebra drag and notice exploring rectangle pouring.

GeometryArea and perimeterAnglesDrag and notice
Audience
Middle school, High school
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Simpsons diversity.
GeoGebra Doodads

Simpsons diversity

A GeoGebra drag and notice exploring simpsons diversity.

Probability and statisticsData and variationDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Taxes on Consumers.
Econ Taxes

Taxes on Consumers

A GeoGebra modeling exploring taxes on consumers.

Algebra and functionsTax policyModeling
Audience
High school, General
Interaction
Modeling, Visualization
Credit
Scott Farrar
GeoGebra preview for Various forecasts.
GeoGebra Doodads

Various forecasts

A GeoGebra simulation exploring various forecasts.

Probability and statisticsData and variationSimulation
Audience
High school, General
Interaction
Simulation, Visualization
Credit
Scott Farrar
GeoGebra preview for Walking Machine.
GeoGebra Doodads

Walking Machine

A GeoGebra animation exploring walking machine.

GeometryMotionAnimation
Audience
High school, General
Interaction
Animation
Credit
Scott Farrar
GeoGebra preview for Haga's Theorem.
GeoGebra Doodads

Haga's Theorem

A GeoGebra proof exploring haga's theorem.

GeometryProof
Audience
High school, General
Interaction
Proof, Visualization
Credit
Scott Farrar
GeoGebra preview for Kate nowak paper folding.
kate nowak paper folding

Kate nowak paper folding

A GeoGebra drag and notice exploring kate nowak paper folding.

GeometryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Inspired by Kate Nowak
GeoGebra preview for Primative pythag.
primative pythag closed under multiply

Primative pythag

A GeoGebra proof exploring primative pythag.

Number theoryPythagorean theoremProof
Audience
High school, General
Interaction
Proof, Visualization
Credit
Scott Farrar
GeoGebra preview for Angle bisect a trapezoid.
angle bisect a trapezoid

Angle bisect a trapezoid

A GeoGebra construction exploring angle bisect a trapezoid.

GeometryAnglesConstruction
Audience
Middle school, High school
Interaction
Construction, Visualization
Credit
Scott Farrar
GeoGebra applet plotting distances from a point to triangle vertices.
Asilomar 2013

Distances to Vertices

Explore how distances from a movable point to triangle vertices change and what patterns emerge.

GeometryTriangle centersDrag and notice
Audience
High school
Interaction
Drag and notice, Visualization
Credit
Scott Farrar
GeoGebra preview for Epsilon delta.
epsilon delta

Epsilon delta

A GeoGebra drag and notice exploring epsilon delta.

CalculusLimitsDrag and notice
Audience
Calculus
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra graph with curves controlled by visible linear factors.
Asilomar 2013

Painting with Linear Factors

Use factors as visible controls for shaping a graph, adapted from Riley Lark's activity idea.

Algebra and functionsFactoringDrag and notice
Audience
High school
Interaction
Drag and notice, Visualization
Credit
Adapted from Riley Lark
GeoGebra preview for Scaled sine.
Sine unit circle

Scaled sine

A GeoGebra drag and notice exploring scaled sine.

TrigonometryUnit circleSine and cosineDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Sine unit circle oct2013.
Sine unit circle

Sine unit circle oct2013

A GeoGebra drag and notice exploring sine unit circle oct2013.

TrigonometryUnit circleSine and cosineDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra applet showing quadrilaterals that may or may not remain squares when dragged.
Asilomar 2013 companion file

Square Not Square

Compare what stays square, what only looks square, and what changes under dragging.

GeometryQuadrilateralsDrag and notice
Audience
Middle school, High school
Interaction
Drag and notice, Construction
Credit
John Golden
GeoGebra triangle inequality applet with a draggable third point.
Asilomar 2013

Triangle Inequality Drag

Drag segment lengths and watch possible triangles appear, disappear, or collapse at the boundary.

GeometryTriangle inequalityDrag and notice
Audience
Middle school, High school
Interaction
Drag and notice, Construction
Credit
Scott Farrar
GeoGebra preview for Unscaled sine.
Sine unit circle

Unscaled sine

A GeoGebra drag and notice exploring unscaled sine.

TrigonometryUnit circleSine and cosineDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Distances to Vertices.
Color continuum Triangle Centers

Distances to Vertices

Move a point around a triangle and study how its distances to the vertices change together.

GeometryTriangle centersDrag and notice
Audience
Middle school, High school
Interaction
Drag and notice, Visualization
Credit
Scott Farrar
GeoGebra preview for Distances to Vertices.
Color continuum Triangle Centers

Distances to Vertices

A GeoGebra construction exploring distances to vertices.

GeometryTriangle centersAnglesConstruction
Audience
Middle school, High school
Interaction
Construction, Visualization
Credit
Scott Farrar
GeoGebra unit circle diagram with trigonometric segment labels.
Asilomar 2013

Unit Circle Trigonometry

Connect a rotating point on the unit circle to trigonometric values and their geometry.

TrigonometryUnit circleDrag and notice
Audience
High school, Precalculus
Interaction
Drag and notice, Visualization
Credit
Scott Farrar
GeoGebra preview for Triangulation Mics.
Triangulation Mics

Triangulation Mics

A GeoGebra drag and notice exploring triangulation mics.

GeometryDrag and notice
Audience
High school, General
Interaction
Drag and notice
Credit
Scott Farrar
GeoGebra preview for Time Angles.
timeangles

Time Angles

Drag the time slider and use clock hands as a changing angle diagram for noticing and conjecturing.

GeometryAnglesDrag and notice
Audience
Middle school, High school
Interaction
Drag and notice, Animation, Visualization
Credit
Scott Farrar