개요
Illustrations Without Words
Contains many dynamic illustrations WITHOUT words, segment lengths, and angle measures. In these applets, the slider governs all applet dynamics. These applets can be used to help a student informally & visually discover a mathematics concept and/or meaningfully recall a certain concept. Enjoy!
목차
Writing Prompts: Definitions & Theorems
- Congruent Segments: Quick Exploration
- Congruent Angles: Definition
- Midpoint Definition
- Segment Bisector Definition
- Perpendicular Bisector Definition
- Perpendicular Bisector Definition
- Angle Bisector Definition (I)
- Complementary Meaning?
- Supplementary Angles (Quick Exploration)
- Triangle Altitude Illustrator and Definition Writing Prompt
- Triangle Median Illustrator & Definition Writing Prompt
- Equilateral Action!!!
- Equiangular Action!!!
- Regular Polygon Action!
- Proof Prompt (A)
- Proof Prompt (B)
- Proof Prompt (C)
- Proof Prompt (D)
- A Special Theorem: Part 2 (V2)
- A Special Theorem: Part 2 (V3)
- A Special Theorem: Part 2 (V4)
- Another Special Theorem: Part 1 (V2)
- Another Special Theorem: Part 1 (V3)
- Slope Triangle Rotation (VA)
- Slope Triangle Rotation (VB)
Parallel Lines & Related Angles
- Vertical Angles Theorem
- Exploring Corresponding Angles (V2)
- Alternate Interior Angles Theorem (V1)
- Exploring Alternate Interior Angles (V2)
- Alternate Interior Angles Theorem (V3)
- Alternate Exterior Angles Theorem (V1)
- Exploring Alternate Exterior Angles (V2)
- Alternate Exterior Angles Theorem (V3)
- Same Side Interior Angles Theorem
- Exploring Same Side Exterior Angles
- Solution to Parallel Lines & Angles Problem
- Effortless Trisections
- Special Pair of Lines in the Coordinate Plane
Polygons & Angles: Interior & Exterior Angles
- Triangle Angle Theorems
- Triangle Angle Theorems (V2)
- Triangle Angle Theorems (V3)
- Obvious Corollary
- Triangle Exterior Angle
- Angles of a Right Triangle
- Acute Angles of a Right Triangle
- Quadrilateral Angle Theorems
- Pentagon Angle Theorems
- Hexagon Angle Theorems
- Heptagon Angle Theorems
- Octagon Angle Theorems
- Exploring Polygon Angles: Triangle through Octagon
- GoGeometry Action 40!
- GoGeometry Action 58!
Polygons: Exterior Angles Only
- Triangle: Exterior Angles
- Exterior Angles of a Triangle
- Quadrilateral: Exterior Angles
- Exterior Angles of a Quadrilateral
- Pentagon: Exterior Angles
- Polygons: Exterior Angles
- Polygons: Exterior Angles - REVAMPED
- Exterior Angles (Revisited)
- Exterior Angles of a Pentagon
- Exterior Angles of a Hexagon
- Exterior Angles of a Heptagon
- Exterior Angles of an Octagon
- Exterior Angles (Revisited) V2
Quadrilaterals: Theorems & Properties
- Parallelogram: Theorem 1
- Parallelogram: Theorem 2
- Parallelogram: Theorem (3)
- Parallelograms (I)
- Parallelogram Diagonals
- Special Quadrilateral: Theorem 1
- Special Quadrilateral: Theorem 2
- Special Quadrilateral: Theorem 3
- Special Quadrilateral: Theorem 4
- Quad Midpoints Action!
- Rhombus Action!
- Rhombus Diagonals
- Rectangle Action!
- Rectangle Diagonals
- Square Action!
- Isosceles Trapezoid Action!
- Trapezoid Median: 2 Discoveries
- Isosceles Trapezoid Diagonals
- Isosceles Trapezoid Midpoints
- Kite Action!
- SSSS: Similar Quads?
- AAA: Similar Quads?
- Trapezoid Median (Midsegment) Action!
- Thebault Action!!!
- Square Problem
- 3 Squares Problem
- Square Action! (Proof Problem 1)
- Harmonic Mean In an Isosceles Trapezoid
- Cut-The-Knot Action (4)!
- Cut-The-Knot-Action (5)!
- Rhombus Action + Sequel = GoGeometry Action 7!
- GoGeometry Action 11!
- GoGeometry Action 12!
- GoGeometry Action 18!
- GoGeometry Action 21!
- GoGeometry Action 22!
- GoGeometry Action 23!
- GoGeometry Action 24!
- GoGeometry Action 36!
- Cut-the-Knot-Action 13!
- GoGeometry Action 42!
- Cut-The-Knot-Action 14!
- GoGeometry Action 46!
- GoGeometry Action 47!
- Rhombus Surprise! (GoGeometry Action 57)
- GoGeometry Action 67!
- GoGeometry Action 69!
- Square + Rhombus = Constant Surprise! (GoGeometry Action 71)
- GoGeometry Action 73!
- Parallelogram? Why So? (GoGeometry Action 77)
- Concave Quadrilateral Craziness! (GoGeometry Action 80)
- Square and Quarter Circle Action = GoGeometry Action 81!
- GoGeometry Action 94!
- GoGeometry Action 95!
- GoGeometry Action 96!
- GoGeometry Action 98!
- GoGeometry Action 99!
- GoGeometry Action 102 !
- GoGeometry Action 108!
- GoGeometry Action 114!
- GoGeometry Action 119!
- GoGeometry Action 126!
- GoGeometry Action 130!
- GoGeometry Action 135!
- GoGeometry Action 136!
- GoGeometry Action 139!
- GoGeometry Action 140!
- Parallelogram + 2 Equilateral Triangles: How to Prove?
Triangles: Theorems & Properties
- SAS: Dynamic Proof!
- SSS: Dynamic Proof!
- SSS: Dynamically Illustrated
- ASA Theorem?
- HL: Hypotenuse-Leg Action!
- Similar Right Triangles (V1)
- Similar Right Triangles (V2)
- AA Similarity Theorem
- SAS ~ Theorem
- SSS ~ Theorem (V1)
- SSS ~ Theorem (V2)
- Parallel Lines Proportionality Theorem
- Triangle-Angle Bisector Theorem
- A Special Triangle & Its Properties (I)
- Converse of IST (V1)
- Isosceles Triangle Medians
- Special Line through Triangle V1 (Theorem Discovery)
- Special Line through Triangle V2 (Theorem Discovery)
- Triangle Midsegment Action!
- Triangle Midsegment
- Another Special Triangle and its Properties (II)
- Converse of IST (II)
- Isosceles Triangle: Surprising Theorem!
- Special Right Triangle (I)
- Special Right Triangle (II)
- Another Special Right Triangle (Guided Discovery)
- Incenter & Incircle Action!
- Incenter + Incircle Action (V2)!
- Medians and Centroid Dance
- Circumcenter & Circumcircle Action!
- Midpoint of HYP
- 3 Special Points!
- 9 Point Circle Action
- 9-Point Circle Action (Part 2)
- 9-Point Circle Action (Part 3B)
- 9-Point Circle Action (Part 4)
- 9-Point Circle Action (Part 5)
- More Triangle Action!!!
- Triangle Median & Circles Action!!!
- 4 Triangles Action!!!
- Desargues Action!!!
- GoGeometry Action 10!
- GoGeometry Action 14!
- GoGeometry Action 17!
- GoGeometry Action 18!
- Cut-The-Knot-Action 8!
- GoGeometry Action 20!
- Cut-The-Knot Action 9!
- Carnot Action! = GoGeometry Action 27!
- GoGeometry Action 29!
- GoGeometry Action 30!
- Incircle + Excircle = GoGeometry Action 31!
- GoGeometry Action 32!
- Cut-The-Knot Action 10!
- Finsler-Hadwiger Sequel! (GoGeometry Action 33)
- GoGeometry Action 34!
- Cut-The-Knot-Action 12!
- GoGeometry Action 35!
- GoGeometry Action 37!
- GoGeometry Action 38!
- GoGeometry Action 39!
- GoGeometry Action 41!
- GoGeometry Action 43!
- GoGeometry Action 44!
- GoGeometry Action 45!
- GoGeometry Action 51!
- GoGeometry Action 53!
- Euler Line Surprise! = GoGeometry Action 54
- GoGeometry Action 60!
- GoGeometry Action 63!
- GoGeometry Action 64!
- GoGeometry Action 66!
- GoGeometry Action 68!
- GoGeometry Action 74!
- GoGeometry Action 75!
- GoGeometry Action 76!
- GoGeometry Action 78!
- GoGeometry Action 79!
- GoGeometry Action 82!
- GoGeometry Action 83!
- Cut-the-Knot Action 15!
- Equilateral Triangle + Semicircle = ? (GoGeometry Action 88)
- GoGeometry Action 89!
- GoGeometry Action 90!
- GoGeometry Action 91!
- GoGeometry Action 93!
- GoGeometry Action 97!
- GoGeometry Action 101 !
- GoGeometry Action 103!
- GoGeometry Action 104!
- GoGeometry Action 105!
- GoGeometry Action 106!
- GoGeometry Action 107!
- GoGeometry Action 109!
- SolveMyMaths Action 1!
- Viviani Action! (REVAMPED)
- GoGeometry Action 110!
- GoGeometry Action 112!
- GoGeometry Action 113!
- GoGeometry Action 115!
- GoGeometry Action 116!
- GoGeometry Action 117!
- Blanchet Action = GoGeometry Action 118!
- GoGeometry Action 120!
- GoGeometry Action 121!
- GoGeometry Action 124!
- GoGeometry Action 125!
- Cut-The-Knot Action 18!
- Cut-The-Knot Action 19!
- GoGeometry Action 127!
- Incircle Extension = GoGeometry Action 132!
- Incircle Extension 2 = GoGeometry Action 133!
- GoGeometry Action 134!
- GoGeometry Action 138!
Circle Theorems
- Congruent Circles: Definition
- Circle Tangent-Types Illustrator
- Properties of Tangents Drawn to Circles (A)
- Properties of Tangents Drawn to Circles (B)
- Int+Ext Tangent Action!
- Diameters & Chords I (VA)
- Diameters & Chords I (VB)
- Congruent Chords: Quick Investigation
- Congruent Chords (I)
- Inscribed Angle Theorem (V1)
- Proof Exercise: Inscribed Angle Theorem (Case 1)
- Proof Exercise: Inscribed Angle Theorem (Case 2)
- Proof Exercise: Inscribed Angle Theorem (Case 3)
- Inscribed Angle Theorem Dance: Take 2!
- Inscribed Angle Theorem: Corollary 1
- Where to Sit? (I)
- Thales' Theorem (VA)
- Thales' Theorem (VB)
- Inscribed Angle Intercepts Semicircle
- Cyclic Quadrilaterals (IAT: Corollary 3)
- Angle Formed by Chord & Tangent (I)
- Angle Formed by Chord & Tangent (II)
- Angle Formed by 2 Chords (I)
- Angle Formed by 2 Chords (II)
- Crossing Chords: Proof Hint
- Angles from Secants and Tangents (V1)
- Angle From 2 Secants (V2)
- Secants: Proof Hint
- Congruent Chords Action (A)
- Equidistant Chord Action
- Butterfly Theorem Action!
- Not Your Everyday Chord & Tangent Theorem
- Cut-The-Knot Action (2) !!!
- Square, Tangent, and Two Congruent & Tangent Circles
- GoGeometry Action 1!
- GoGeometry Action 2!
- GoGeometry Action 3!
- GoGeometry Action 4!
- GoGeometry Action 5!
- Geometric Mean Illustration
- GoGeometry Action 6!
- GoGeometry Action 8!
- Cut-The-Knot Action (6)!
- GoGeometry Action 9!
- GoGeometry Action 13!
- GoGeometry Action 15!
- GoGeometry Action 16!
- Cut-The-Knot Action 7!
- GoGeometry Action 19!
- Thales Action + Sequel = GoGeometry Action 25!
- GoGeometry Action 26!
- GoGeometry Action 48!
- GoGeometry Action 49!
- GoGeometry Action 50!
- GoGeometry Action 52!
- 60-Degree Sector Surprise! (GoGeometry Action 55)
- Neusis Logic Action = GoGeometry Action 56!
- Quarter Circle Surprise!
- GoGeometry Action 59!
- GoGeometry Action 61!
- GoGeometry Action 62!
- GoGeometry Action 70!
- GoGeometry Action 72!
- Geometric Mean Madness! (GoGeometry Action 84)
- Mickey Mouse Theorem! (Cut-the-Knot Action 16)
- More Geometric Mean Action! (GoGeometry Action 86)
- GoGeometry Action 87!
- GoGeometry Action 92!
- A Stronger Conclusion!
- GoGeometry Action 100!
- GoGeometry Action 122!
- GoGeometry Action 128!
- GoGeometry Action 129!
- GoGeometry Action 131!
- GoGeometry Action 137!
- GoGeometry Action 141!
Geometric Constructions
Transformations
Area, Surface Area, Volume
Slope
Functions
- Functions: Input & Output (3)
- Functions: Input & Output (4)
- Half-Life Action!!!
- What Makes a Function Even?
- What Makes a Function Odd?
- Odd Functions (Another Look)
- Odd Functions: Another Look (Take 2)!
- Function Composition: Dynamic Illustrator (1)
- Periodic Function Action!
- Logarithmic Action!
- Logarithmic Action (2)!
- Logarithmic Action (3)!
- Logarithmic Action (4)!
- Logarithmic Action (4)! V2
Vectors
Conic Sections: Definitions & Properties
Trigonometry
- Angle Orientations (Standard Position)
- Coterminal Angles Action!!!
- Special Angles in Standard Position: Intro (V1)
- Special Angles in Standard Position: Intro (V2)
- Special Angles in Standard Position: Intro (V2) - Part 2
- Special Angles in Standard Position: Intro (V3)
- Sine & Cosine Period Action (2)!
- Tangent Period Action (2)!
- Right Triangle Trigonometry: Intro
- Trigonometric Ratios (Right Triangle Context)
- What "CO" in COsine Means
- Law of Sines (& Area)
- Law of Cosines: Discovery
- Bizzare Trig Identity?
- 3 Squares Problem
- Polar Coordinates: Introduction
Illustrations in 3-Space
Calculus Applets
Cool But Not-Often-Seen Theorems
- Equilateral Action (1)!
- Equilateral Action (2)!
- Equilateral Action (3)!
- Napoleon Motion!
- Hexagonal Napoleon Theorem?
- Triangle to Conic?
- Square Problem
- Japanese Theorem for Cyclic Quadrilaterals
- Cyclic Quad Action (II)
- Equilateral Action (4)!
- Equilateral Triangle and Rectangle (Area Problem)
- Van Aubel Action!!!
- Finsler-Hadwiger Action!!!
- Morley Action!
- Quadrilateral Surprise!
- Cut-The-Knot Action !!!
- Cut-the-Knot-Action (3)!
- Cut-The-Knot-Action 11!
- GoGeometry Action 65!
- Hexagonal Surprise! (GoGeometry Action 85)
- GoGeometry Action 111!
- GoGeometry Action 123!
- Cut-The-Knot Action 17!