100 Geometry MicroSims

Prompt

I am a high-school geometry teacher that has just taken a course in creating interactive simulations and animations using p5.js.

Please create a list of the top 100 interactive animations (MicroSims) I can create to teach my students various topics in geometry?

Here is what I want for each of the 100 MicroSim ideas:

I want to you to create a set of ideas for animations or simulations that have controls such as buttons and sliders. As the student will change the controls so they can interact with illustrative geometry example on the screen change. For each MicroSim please provide:

1. The name of the simulation in a level 3 markdown header.
2. The topics that the students will learn about.
3. Detailed description of MicroSim
4. The list of the input controls on the screen and their type (button, slider etc.).
5. Learning objective of the simulation.
6. The level of difficulty (beginner, intermediate, advanced)

For example to illustrate the difference between degrees and radians you might suggest the following example:

Degrees vs. Radians

Topics: Measuring angles, degrees, radians

Students will learn how we can use both degrees and radians to measure an angle. A circle will be place in the center of a drawing region. As the student moves a slider in the controls area a line from the center of the circle will move around the edge of the circle. The slider will range from 0 to 360 and move in a clockwise direction. Arcs of alternating colors will appear on the circle circumference to for radian of length 1.

Input Control: Slider for degree from 0 to 360 with a default value of 45 and an increment of 1 degree.

Learning Objectives: 1. How many degrees are there in a complete circle?
2. How many radians are there in a complete circle? 3. How many degrees are there in 1 radian?

Difficulty: beginner

Response

GPT-5

Awesome—love that you’re building a MicroSim arsenal! Here are 100 p5.js-friendly interactive geometry simulation ideas, each with a clear purpose, controls, and difficulty so you can cherry-pick or build a full course arc.

1. Degrees vs. Radians

Topics: Measuring angles, degrees, radians

Description: Central circle with rotating radius; alternating colored 1‑radian arc marks around the circumference.
Input Controls: Slider (angle 0–360, step 1, default 45)
Learning Objectives: (1) 360° in a circle (2) 2π radians in a circle (3) Convert 1 radian to degrees
Difficulty: Beginner

2. Angle Types Explorer

Topics: Acute, right, obtuse, straight, reflex
Description: Dynamic angle at a vertex; region labels change by range; color changes with type.
Input Controls: Slider (0–360), Toggle (show/hide type labels)
Learning Objectives: Classify angles by measure; relate measure to type thresholds
Difficulty: Beginner

3. Complementary & Supplementary Angles

Topics: Angle pairs, linear pairs
Description: Two connected angles share a line; highlight when sums are 90°/180°.
Input Controls: Two sliders (θ1, θ2 with live sum), Button (snap to 90/180)
Learning Objectives: Identify complementary vs. supplementary; compute missing angle
Difficulty: Beginner

4. Vertical Angles Visualizer

Topics: Vertical angles, congruence
Description: Two intersecting lines; opposite angles track and stay equal.
Input Controls: Sliders (line slopes), Checkbox (show equality marks)
Learning Objectives: Recognize vertical angle congruence; reason from intersection geometry
Difficulty: Beginner

5. Angle Bisector Builder

Topics: Constructions, angle bisector
Description: Compass-and-straightedge style arcs constructing the bisector.
Input Controls: Slider (angle), Button (animate construction), Checkbox (show loci)
Learning Objectives: Construct and verify a bisector; understand locus of equidistant points to rays
Difficulty: Intermediate

6. Triangle Drag Lab

Topics: Triangle types, side/angle relationships
Description: Draggable vertices; real‑time classification (scalene/isosceles/equilateral; acute/right/obtuse).
Input Controls: Drag handles (A, B, C), Checkboxes (show side lengths/angles)
Learning Objectives: Classify triangles; observe constraints across drags
Difficulty: Beginner

7. Triangle Inequality Tester

Topics: Triangle inequality
Description: Three segments with sliders; feedback if construction is possible.
Input Controls: Three sliders (a, b, c), Button (attempt build)
Learning Objectives: Understand and test triangle inequality conditions
Difficulty: Beginner

8. SSS Congruence Playground

Topics: Triangle congruence (SSS)
Description: Build two triangles from three sides; rotation/translation allowed; congruence check.
Input Controls: Sliders (a,b,c for Δ1; a,b,c for Δ2), Buttons (align, overlay)
Learning Objectives: See that SSS determines a unique triangle up to rigid motion
Difficulty: Intermediate

9. SAS Congruence Animator

Topics: Triangle congruence (SAS)
Description: Fix two sides and included angle; show uniqueness.
Input Controls: Sliders (side1, side2, included angle), Button (randomize)
Learning Objectives: Understand SAS uniqueness; role of included angle
Difficulty: Intermediate

10. ASA/AAS Congruence Explorer

Topics: Triangle congruence (ASA, AAS)
Description: Two angles + a side build a triangle; contrasts ASA vs. AAS.
Input Controls: Sliders (A, B, side c), Checkbox (show ambiguity)
Learning Objectives: Why ASA/AAS determine triangles; when ambiguity arises
Difficulty: Intermediate

11. SSA Ambiguity (The Ambiguous Case)

Topics: Law of sines, SSA non‑congruence
Description: Fix two sides and a non‑included angle; show 0/1/2 solutions.
Input Controls: Sliders (a, b, angle A), Buttons (show both solutions)
Learning Objectives: Recognize ambiguous case; interpret geometric conditions
Difficulty: Intermediate

12. Medians & Centroid

Topics: Triangle medians, centroid properties
Description: Draw medians; centroid tracks at 2:1 ratio.
Input Controls: Draggable triangle, Checkbox (length ratios), Button (animate medians)
Learning Objectives: Centroid location; median partition ratio
Difficulty: Intermediate

13. Perpendicular Bisectors & Circumcenter

Topics: Circumcenter, circumscribed circle
Description: Show perpendicular bisectors and circumcircle; note acute/right/obtuse cases.
Input Controls: Draggable triangle, Checkbox (distance to vertices), Toggle (acute/right/obtuse shading)
Learning Objectives: Equidistance to vertices; circumcenter position by triangle type
Difficulty: Intermediate

14. Angle Bisectors & Incenter

Topics: Incenter, incircle
Description: Angle bisectors intersect; draw incircle tangent to sides.
Input Controls: Draggable triangle, Checkbox (angle bisector rays, tangency points)
Learning Objectives: Equidistance to sides; construct incircle
Difficulty: Intermediate

15. Altitudes & Orthocenter

Topics: Altitudes, orthocenter
Description: Show altitudes and intersection; track movement with shape.
Input Controls: Draggable triangle, Toggle (extend lines), Checkbox (orthic triangle)
Learning Objectives: Orthocenter location across triangle types
Difficulty: Intermediate

16. Euler Line Explorer

Topics: Centroid, circumcenter, orthocenter, Euler line
Description: Plot major centers; draw Euler line & ratio relations.
Input Controls: Draggable triangle, Checkbox (show nine‑point circle)
Learning Objectives: Identify triangle centers; relationships along Euler line
Difficulty: Advanced

17. Midsegment Theorem

Topics: Triangle midsegments, similarity
Description: Connect midpoints; highlight parallelism and 1/2 scaling.
Input Controls: Draggable triangle, Checkbox (show similarity scale)
Learning Objectives: Prove/observe midsegment properties
Difficulty: Beginner

18. Interior & Exterior Angle Sum

Topics: Triangle angle sum, exterior angle theorem
Description: Angle “unfold” animation; exterior equals sum of two remote interiors.
Input Controls: Draggable triangle, Buttons (unfold, reset)
Learning Objectives: Triangle sums; exterior angle relation
Difficulty: Beginner

19. Polygon Angle Sums

Topics: Interior/exterior sums, n‑gons
Description: Regular/irregular polygon with variable n; live sums.
Input Controls: Slider (n: 3–12), Checkbox (regular), Button (diagonal triangulation)
Learning Objectives: Derive (n−2)·180°; exterior sum 360°
Difficulty: Beginner

20. Regular Polygon Sandbox

Topics: Central/inscribed angles, apothem
Description: Regular n‑gon; show radius, apothem, central angle, perimeter.
Input Controls: Slider (n), Slider (radius), Checkbox (show apothem)
Learning Objectives: Connect polygon parameters; area via ½ap
Difficulty: Intermediate

21. Parallel Lines & Transversals

Topics: Corresponding/alternate interior/exterior angles
Description: Move a transversal; angle pairs highlight equality.
Input Controls: Sliders (line spacing, angle), Checkbox (labels)
Learning Objectives: Identify angle relationships; infer parallelism
Difficulty: Beginner

22. Distance & Midpoint in the Plane

Topics: Coordinate geometry
Description: Two draggable points; compute distance and midpoint dynamically.
Input Controls: Drag points, Checkbox (grid, formula overlay)
Learning Objectives: Apply distance/midpoint formulas; connect algebra & geometry
Difficulty: Beginner

23. Slope as Rate of Change

Topics: Slope, rise/run, angle of inclination
Description: Interactive right triangle on a line; slope & angle displayed.
Input Controls: Drag line points, Checkbox (rise/run triangles)
Learning Objectives: Interpret slope geometrically; slope–angle link via tan
Difficulty: Beginner

24. Circle Basics (r, d, C, A)

Topics: Radius, diameter, circumference, area
Description: Circle with dynamic radius; live formulas.
Input Controls: Slider (radius), Toggle (show sector/segment)
Learning Objectives: Relate r, d, C, A; visualize proportional changes
Difficulty: Beginner

25. Arc Length & Sector Area

Topics: Circle arc length, sector area
Description: Select central angle; highlight arc & sector.
Input Controls: Sliders (radius, angle), Checkbox (radians/degrees)
Learning Objectives: Compute arc length & sector area from angle units
Difficulty: Beginner

26. Inscribed Angles

Topics: Inscribed vs. central angles
Description: Move point on circumference; compare inscribed to central angle subtending same arc.
Input Controls: Drag points, Checkbox (double‑angle relation)
Learning Objectives: Inscribed angle is half central; arc dependence
Difficulty: Intermediate

27. Cyclic Quadrilaterals

Topics: Opposite angles, circle theorems
Description: Quadrilateral with vertices on circle; sums of opposite angles shown.
Input Controls: Drag vertices, Checkbox (show arcs)
Learning Objectives: Opposite angles supplementary; properties of cyclic figures
Difficulty: Intermediate

28. Tangent–Radius Perpendicular

Topics: Tangents to circles
Description: Tangent line at point of contact; radius perpendicular visible.
Input Controls: Drag tangent point, Slider (radius), Checkbox (perp marker)
Learning Objectives: Tangent ⟂ radius at contact point
Difficulty: Beginner

29. Power of a Point

Topics: Chords, secants, tangents
Description: External/internal points with chord/secant/tangent products.
Input Controls: Drag point, Checkbox (measure products), Button (random chords)
Learning Objectives: Verify equal products; compare configurations
Difficulty: Advanced

30. Thales’ Theorem

Topics: Right angles in semicircle
Description: Inscribed angle subtending diameter stays 90°.
Input Controls: Drag point on circle, Checkbox (angle measure)
Learning Objectives: Recognize right triangle in semicircle
Difficulty: Beginner

31. Transformations: Translation

Topics: Rigid motions, vectors
Description: Shape translated by vector; coordinates update.
Input Controls: Sliders (Δx, Δy), Drag vector tail
Learning Objectives: Map points under translation; preserve distance/angle
Difficulty: Beginner

32. Transformations: Rotation

Topics: Rotation about a point
Description: Rotate a polygon around a center by θ.
Input Controls: Slider (angle), Drag rotation center, Button (snap 90°)
Learning Objectives: Rotation mapping; orientation and invariants
Difficulty: Beginner

33. Transformations: Reflection

Topics: Reflection across a line
Description: Reflect a shape across draggable line.
Input Controls: Drag line endpoints, Checkbox (perpendicular distances)
Learning Objectives: Reflection properties; line of symmetry
Difficulty: Beginner

34. Transformations: Dilation

Topics: Similarity, scale factor
Description: Dilate figure from a center; lengths and area scale.
Input Controls: Slider (scale k), Drag center, Checkbox (area factor k²)
Learning Objectives: Similar figures; scaling effects
Difficulty: Beginner

35. Transformations Composition Lab

Topics: Composition of isometries
Description: Chain multiple transformations; show resulting mapping.
Input Controls: Buttons (add translate/rotate/reflect), History panel
Learning Objectives: Explore equivalences (e.g., two reflections = rotation)
Difficulty: Intermediate

36. Symmetry Finder

Topics: Line & rotational symmetry
Description: Test shapes for symmetries; show axes/centers.
Input Controls: Dropdown (shape), Slider (rotation test), Checkbox (axes)
Learning Objectives: Identify symmetry types/order
Difficulty: Beginner

37. Tessellation by Regular Polygons

Topics: Tiling, angle sums at a point
Description: Try to tile plane with chosen polygon(s); show gaps/overlaps.
Input Controls: Dropdown (polygon), Checkbox (combine shapes), Button (fill)
Learning Objectives: Which regular polygons tessellate and why
Difficulty: Intermediate

38. Escher-Style Glide Reflection

Topics: Isometries, frieze patterns
Description: Build frieze by glide reflection from a motif.
Input Controls: Draw motif, Buttons (reflect/glide), Slider (glide length)
Learning Objectives: Understand glide reflection and pattern symmetries
Difficulty: Advanced

39. Similar Triangles via AA

Topics: Triangle similarity
Description: Two triangles with synchronized angles; scale changes.
Input Controls: Sliders (two angles), Slider (scale), Checkbox (ratio display)
Learning Objectives: AA similarity; proportional sides
Difficulty: Beginner

40. Right Triangle Similarity (Altitude to Hypotenuse)

Topics: Similarity, geometric mean
Description: Drop altitude; show three similar right triangles; geometric mean relations.
Input Controls: Draggable triangle, Checkbox (proportion labels)
Learning Objectives: Proportional segments; mean relationships
Difficulty: Advanced

41. Pythagorean Theorem Dissection

Topics: Area proofs
Description: Square on each side; sliding dissections to show a²+b²=c².
Input Controls: Slider (a, b), Button (animate proof)
Learning Objectives: Visual area proof; dynamic verification
Difficulty: Beginner

42. Pythagorean Triples Explorer

Topics: Integer right triangles
Description: Generate triples; plot lattice triangles.
Input Controls: Buttons (next triple), Checkbox (primitive only)
Learning Objectives: Recognize triples; connect number theory & geometry
Difficulty: Intermediate

43. Converse of Pythagoras

Topics: Triangle classification by sides
Description: Test c² vs a²+b² to classify acute/right/obtuse.
Input Controls: Sliders (a, b, c), Checkbox (classification)
Learning Objectives: Use converse to determine angle type
Difficulty: Beginner

44. Trig on the Unit Circle

Topics: Sine, cosine, tangent
Description: Rotating radius; project x/y; tangent line length.
Input Controls: Slider (angle), Toggle (degrees/radians)
Learning Objectives: Read sin/cos/tan from geometry
Difficulty: Beginner

45. Special Right Triangles

Topics: 30‑60‑90 and 45‑45‑90
Description: Templates with scalable hypotenuse; side ratios displayed.
Input Controls: Slider (scale), Buttons (switch triangle type)
Learning Objectives: Memorize/derive special ratios
Difficulty: Beginner

46. Law of Sines

Topics: Trigonometry in any triangle
Description: Compute a/sinA = b/sinB = c/sinC; visualize circles of equal ratios.
Input Controls: Draggable triangle, Checkbox (ratio bars)
Learning Objectives: Apply law; connect to circumcircle diameter
Difficulty: Intermediate

47. Law of Cosines

Topics: General triangles
Description: Show c² = a² + b² − 2ab cos C with a dynamic diagram.
Input Controls: Sliders (a,b,C), Checkbox (dot product link)
Learning Objectives: Compute unknowns; relate to Pythagoras at C=90°
Difficulty: Intermediate

48. Vector Basics

Topics: Vectors, magnitude, direction
Description: Drag vector endpoint; components, magnitude, angle shown.
Input Controls: Drag head, Checkbox (component triangle)
Learning Objectives: Decompose and measure vectors
Difficulty: Beginner

49. Vector Addition (Parallelogram & Tip‑to‑Tail)

Topics: Vector operations
Description: Two vectors combine; both methods animated.
Input Controls: Drag vectors, Buttons (method), Checkbox (resultant)
Learning Objectives: Equivalence of constructions
Difficulty: Beginner

50. Dot Product as Projection

Topics: Dot product geometry
Description: Project u on v; scalar projection visual.
Input Controls: Drag u, v; Checkbox (angle, lengths)
Learning Objectives: Interpret uv cosθ; orthogonality test
Difficulty: Intermediate

51. Loci of Points

Topics: Locus definitions
Description: Animate sets equidistant from points/lines/segments.
Input Controls: Dropdown (locus type), Sliders (distances)
Learning Objectives: Connect constraints to circles, parabolas, strips
Difficulty: Intermediate

52. Apollonius Circle

Topics: Ratio distances
Description: Points P with |PA|/|PB|=k traced as circle.
Input Controls: Drag A, B; Slider (k)
Learning Objectives: See locus is a circle (k≠1) or perpendicular bisector (k=1)
Difficulty: Advanced

53. Polygon Area by Triangulation

Topics: Decomposition, area
Description: Draw simple polygon; auto‑triangulate and sum areas.
Input Controls: Click to add vertices; Button (triangulate)
Learning Objectives: Break complex shapes into triangles
Difficulty: Intermediate

54. Shoelace Formula Demo

Topics: Coordinate area
Description: Compute polygon area via signed sums; show term pairing.
Input Controls: Place vertices; Checkbox (show sums)
Learning Objectives: Apply shoelace; orientation matters
Difficulty: Advanced

55. Cavalieri’s Principle (2D→3D intuition)

Topics: Area/volume comparison
Description: Sweep parallel slices with equal heights; equal areas/volumes.
Input Controls: Slider (slice), Dropdown (shapes)
Learning Objectives: Compare shapes by cross‑sections
Difficulty: Advanced

56. Prisms & Cylinders: Nets & Volume

Topics: Surface area, volume
Description: 3D → net unfold; live SA & V.
Input Controls: Dropdown (shape), Sliders (dims), Button (unfold/fold)
Learning Objectives: Compute SA/V; relate nets to surfaces
Difficulty: Beginner

57. Pyramids & Cones: Nets & Volume

Topics: Surface area, volume
Description: Adjustable slant height; show lateral area and V=⅓Bh.
Input Controls: Sliders (base size, height), Button (unfold)
Learning Objectives: Distinguish base vs. lateral area; volume formula
Difficulty: Intermediate

58. Spheres: Great Circles & Caps

Topics: Sphere geometry
Description: Slice sphere; show great circle radius and cap area/volume.
Input Controls: Slider (slice height), Checkbox (formulas)
Learning Objectives: Visualize spherical sections; formula intuition
Difficulty: Advanced

59. Cross‑Sections of 3D Solids

Topics: Planar slices
Description: Cut solids with a plane; see resulting 2D shapes.
Input Controls: Dropdown (solid), Sliders (plane angle/height)
Learning Objectives: Match solids to cross‑sections
Difficulty: Intermediate

60. Volume by Rotation (Washers)

Topics: Solids of revolution
Description: Rotate region around axis; compute with washers.
Input Controls: Draw function/region; Slider (resolution)
Learning Objectives: Visualize volume integrals (calc preview)
Difficulty: Advanced

61. Coordinate Transform: Polar vs. Cartesian

Topics: Coordinates, r–θ mapping
Description: Point moves; simultaneously show (x,y) and (r,θ).
Input Controls: Drag point, Checkbox (grid swap)
Learning Objectives: Convert between systems
Difficulty: Beginner

62. Parametric Curves (Lissajous)

Topics: Parametric motion
Description: Animate tracing with time parameter.
Input Controls: Sliders (ax, ay, phase), Button (play/pause)
Learning Objectives: Interpret parameters geometrically
Difficulty: Intermediate

63. Reflection Across Any Line (Coordinate Proof)

Topics: Analytical reflection
Description: Reflect a point by formula; compare construction vs. algebra.
Input Controls: Drag line, point; Checkbox (algebra steps)
Learning Objectives: Derive reflection formulas
Difficulty: Advanced

64. Rotations by Matrices

Topics: Linear transformations
Description: Multiply vectors by rotation matrix; grid deformation.
Input Controls: Slider (θ), Checkbox (matrix display)
Learning Objectives: Matrix–rotation connection
Difficulty: Advanced

65. Shear Transformations

Topics: Non‑rigid maps, area preservation
Description: Apply shear; track area/perimeter.
Input Controls: Sliders (shear x/y), Checkbox (area calc)
Learning Objectives: Understand shear effects; area invariance
Difficulty: Advanced

66. Conic Sections from a Cone

Topics: Circle, ellipse, parabola, hyperbola
Description: Adjustable cutting plane angle and position; trace conic.
Input Controls: Sliders (tilt, height), Dropdown (view)
Learning Objectives: How conics arise from slicing a cone
Difficulty: Intermediate

67. Parabola as Locus (Focus–Directrix)

Topics: Distance equality
Description: Points equidistant from focus and line; draw parabola.
Input Controls: Drag focus & directrix; Checkbox (distance bars)
Learning Objectives: Locus definition of parabola
Difficulty: Advanced

68. Ellipse: Sum of Distances

Topics: Ellipse definition
Description: Two foci; locus where PF1+PF2 is constant.
Input Controls: Drag foci; Slider (sum), Checkbox (major/minor axes)
Learning Objectives: Ellipse properties and parameters
Difficulty: Advanced

69. Hyperbola: Difference of Distances

Topics: Hyperbola definition
Description: Locus with |PF1−PF2| constant.
Input Controls: Drag foci; Slider (difference)
Learning Objectives: Branches and asymptotes
Difficulty: Advanced

70. Triangle Area via Base–Height

Topics: Area formula
Description: Drag base endpoints and height point; area updates.
Input Controls: Drags (base, altitude foot), Checkbox (right angle marker)
Learning Objectives: Area depends on base & height only
Difficulty: Beginner

71. Parallelogram Area & Base–Height

Topics: Area invariance
Description: Shear a parallelogram; area stays base×height.
Input Controls: Drag vertex, Slider (shear), Checkbox (cut‑paste proof)
Learning Objectives: Invariance under shear
Difficulty: Beginner

72. Heron’s Formula

Topics: Triangle area from sides
Description: Compute area via s(s−a)(s−b)(s−c) and compare to base–height.
Input Controls: Sliders (a,b,c valid), Button (build triangle)
Learning Objectives: Apply Heron; validate numerically
Difficulty: Advanced

73. Circle Chord–Sagitta Relations

Topics: Chord length, sagitta, radius
Description: Move chord; show relationships.
Input Controls: Drag chord endpoints, Slider (radius)
Learning Objectives: Connect sagitta to radius & chord
Difficulty: Intermediate

74. Inscribed Polygon → Circle Area Limit

Topics: Limits intuition
Description: Increase n of regular inscribed polygon; area approaches πr².
Input Controls: Slider (n), Checkbox (error vs. circle area)
Learning Objectives: Approximation and convergence
Difficulty: Intermediate

75. Golden Ratio in Geometry

Topics: Φ constructions
Description: Construct golden rectangle/spiral; ratio tracking.
Input Controls: Slider (scale), Button (construct), Checkbox (ratio≈1.618)
Learning Objectives: See Φ in lengths and rectangles
Difficulty: Intermediate

76. Similarity & Scale in the Plane

Topics: Dilations with coordinates
Description: Choose center & factor; track coordinates and lengths/areas.
Input Controls: Drag center, Slider (k), Checkbox (pre‑/image table)
Learning Objectives: Compute images; area scales by k²
Difficulty: Beginner

77. Circle Inversions (Intro)

Topics: Inversion geometry
Description: Map points through inversion circle; see images of lines/circles.
Input Controls: Slider (inversion radius), Drag point/line/circle
Learning Objectives: Qualitative effects of inversion
Difficulty: Advanced

78. Polygon Interior Angle Turning

Topics: Exterior angle sum
Description: Walk around polygon; turning angle accumulates to 360°.
Input Controls: Button (walk), Slider (speed), Checkbox (angle accumulator)
Learning Objectives: Exterior angle sum = 360°
Difficulty: Beginner

79. Spiral Similarity

Topics: Rotation+dilation around a point
Description: Map one segment to another via spiral similarity.
Input Controls: Drag segments; Slider (angle/scale)
Learning Objectives: Combine rotation & dilation about a center
Difficulty: Advanced

80. Triangle Centers Locus (Kiepert/Napoleon)

Topics: Constructed triangle centers
Description: Equilateral triangles on sides; new centers’ loci.
Input Controls: Draggable base triangle, Checkbox (first/second Napoleon)
Learning Objectives: Explore special centers & configurations
Difficulty: Advanced

81. Incircle & Excircles

Topics: Angle bisectors, tangency
Description: Show incircle and three excircles; tangent points.
Input Controls: Draggable triangle, Checkboxes (in/excircles)
Learning Objectives: Understand internal vs. external bisectors
Difficulty: Advanced

82. Polygon Perimeter vs. Area Trade‑off

Topics: Optimization intuition
Description: Fix perimeter; vary shape to see max area (regular).
Input Controls: Slider (n), Drag vertices, Button (regularize)
Learning Objectives: Regular polygon maximizes area for fixed perimeter
Difficulty: Intermediate

83. Isoperimetric Experiment (Circle vs. Polygons)

Topics: Isoperimetric inequality (visual)
Description: Compare area for fixed perimeter shapes; circle leads.
Input Controls: Draw shape, Button (compute perimeter/area), Checkbox (circle reference)
Learning Objectives: Circle’s optimality intuition
Difficulty: Advanced

84. Folding Symmetry (Paper Model)

Topics: Reflection, rotational symmetry
Description: Simulate paper folds; mirror images overlay.
Input Controls: Buttons (fold/unfold), Slider (rotation)
Learning Objectives: Symmetry via physical analogies
Difficulty: Beginner

85. Perimeter vs. Diameter in Regular n‑gons

Topics: Limits to circumference
Description: Compare polygon perimeter to circle circumference.
Input Controls: Slider (n), Checkbox (error plot)
Learning Objectives: Understand polygon → circle limit
Difficulty: Beginner

86. Angle Chasing Puzzles

Topics: Parallel lines, triangles, circles
Description: Random puzzle generator with hints and dynamic reveals.
Input Controls: Button (new puzzle), Buttons (hint/solve)
Learning Objectives: Practice multi‑step reasoning
Difficulty: Intermediate

87. Coordinate Proofs Sandbox

Topics: Proof by coordinates
Description: Place points; system checks parallelism, midpoints, slopes.
Input Controls: Place/move points; Checkboxes (properties to prove)
Learning Objectives: Translate geometric claims into algebraic checks
Difficulty: Advanced

88. Perpendicular & Angle Bisectors (Construction Mode)

Topics: Compass–straightedge constructions
Description: Emulate real tools; steps logged.
Input Controls: Tools palette (compass, straightedge), Button (check steps)
Learning Objectives: Master basic constructions and sequencing
Difficulty: Intermediate

89. Rectangle & Rhombus Properties

Topics: Parallelogram families
Description: Deform a parallelogram toward rectangle/rhombus/square; property flags.
Input Controls: Drag vertices; Checkboxes (equal angles/sides/diagonals)
Learning Objectives: See family relations & defining properties
Difficulty: Beginner

90. Trapezoids & Midsegment

Topics: Trapezoid properties
Description: Show midsegment length as average of bases; isosceles traits.
Input Controls: Drag vertices, Checkbox (midsegment math)
Learning Objectives: Compute midsegment; identify isosceles trapezoids
Difficulty: Beginner

91. Circle Tangents from External Point

Topics: Tangent lengths
Description: From P outside circle, draw two tangents; lengths equal.
Input Controls: Drag P, Slider (radius), Checkbox (length equality)
Learning Objectives: Tangents from a point have equal lengths
Difficulty: Beginner

92. Inscribed Polygon Perimeter Convergence

Topics: π approximation
Description: Increase n; compare polygon perimeter to circumference.
Input Controls: Slider (n), Checkbox (error %)
Learning Objectives: Numerical approach to π
Difficulty: Beginner

93. Polygon Diagonals Counter

Topics: Combinatorics in geometry
Description: Show diagonals count n(n−3)/2; draw them.
Input Controls: Slider (n), Checkbox (hide crossings)
Learning Objectives: Derive and verify diagonal formula
Difficulty: Beginner

94. Lattice Point Pick’s Theorem

Topics: Area on grid polygons
Description: Draw lattice polygon; display interior/boundary counts and area.
Input Controls: Click to place vertices (grid locked), Button (compute)
Learning Objectives: A = I + B/2 − 1
Difficulty: Advanced

95. Circle Packing in a Rectangle (Greedy)

Topics: Optimization, area density
Description: Place equal circles; show packing density estimate.
Input Controls: Sliders (rows, cols, radius), Button (pack)
Learning Objectives: Explore packing efficiency and limits
Difficulty: Advanced

96. Voronoi & Delaunay (Geometry of Nearest Neighbors)

Topics: Planar graphs, proximity
Description: Scatter points; show Voronoi cells & Delaunay triangulation.
Input Controls: Click to add/move points; Checkboxes (show/hide structures)
Learning Objectives: Duality and nearest‑neighbor geometry
Difficulty: Advanced

97. Perimeter Walk vs. Straight‑Line Distance

Topics: Triangle inequality (paths)
Description: Compare path along polyline vs. direct segment.
Input Controls: Draw path points; Button (compare)
Learning Objectives: Path length ≥ straight‑line distance
Difficulty: Beginner

98. Circle–Line Intersection Counter

Topics: Intersections, discriminant intuition
Description: Move line; display 0/1/2 intersection points.
Input Controls: Drag line, Slider (radius)
Learning Objectives: Visualize intersection cases
Difficulty: Beginner

99. Polygon Similarity Tester

Topics: Similarity criteria for polygons
Description: Scale/rotate/reflect polygons; compare angle sets and side ratios.
Input Controls: Sliders (scale, rotation), Button (reflect), Checkbox (ratio table)
Learning Objectives: Determine similarity for general polygons
Difficulty: Advanced

100. Proof by Counterexample Lab

Topics: Conjectures, counterexamples
Description: Present geometric conjectures; students manipulate figures to find counterexamples (or support).
Input Controls: Button (new conjecture), Drags (figure), Button (submit example)
Learning Objectives: Distinguish proof vs. example; power of counterexamples
Difficulty: Intermediate

If you want, I can turn any of these into ready‑to‑run p5.js sketches with a standard UI scaffold (panels, sliders, buttons, and a consistent keyboard shortcut scheme). Which 3 do you want first?