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MSET99 Talk Other Math sites Front Page Movie shortcuts Personal info Privacy Policy Guest book News sites Recommend this site Sites for teachers Sites for parents Education & Parenting	Memory and Matching Arithmetic Algebra Logic Fractals Probability Visual Illusions Calculus Math Magic Combinatorics Combinatorial Games Puzzles & Games Geometric Fallacies Social Sciences Elementary Geometry Geometry Outline Mathematics Miscellaneous Demonstrations Interactive Mathematics Activities Memory and Matching Match answers Memory - Easy Memory - Medium Memory - Hard Arithmetic 2 Pails Puzzle 3 Jugs Puzzle 3 Jugs Puzzle in Barycentric Coordinates 3-Term Arithmetic Progression Abacus in Various Number Systems Algorithm for Computing LCM Aliquot Game Arithmetic Operations in Various Bases Broken Calculator Coin Game Collatz Conjecture Counting and Grouping Distributive Law EAN-13 Encoding Equivalent Fractions Even, Odd and Total Number of Digits Euclid's Game Farey Fractions Flipping Items Simultaneously Geometric view of the Sieve of Eratosthenes ISBN Encoding Kaprekar's Iterations and Numbers Lattice Multiplication Long Multiplication Less, Equal, More Make An Identity Napier Bones Plain Multiplication table up to 20×20 Sieve of Eratosthenes Sieve of Squares Soroban in Various Number Systems Suan Pan in Various Number Systems Sums and Products Sums of Powers of Digits Two Simple Equations Universal Product Code Zeros and Nines Algebra Averages, Arithmetic and Harmonic Means Binary Color Device Breaking Chocolate Bars Candy Game: Integer Iterations on a Circle Chebyshev polynomials Complex Numbers: A Dynamic Tool Constructible Numbers Counting Chips On a Circle Counting Triangles Counting Triangles II Divisibility Problem Dots and Fractions Ducci Sequences Egyptian Multiplication First Geometric Interpretation of Complex Numbers Four Pegs That Form a Square Frieze Patterns Geometric Construction of Roots of Quadratic Equation Graph and Roots of a Third Degree Polynomial Graph and Roots of Quadratic Polynomial Heads and Tails (counting, invariance) Identities in the Multiplication Table Integer Iterations on a Circle II (superposition principle) Integers and Rectangles Integers and Rectangles: a Proof by Induction Integers and Rectangles: Two Simple Proofs Interest Calculations Josephus Flavius Game Langford and Skolem Sequences Letter Count in a Sentence Lights Out Logistic Model Loop or Halt Mean Values Merlin's Magic Squares (modular arithmetic, boolean and linear algebra) Mini Lights Out Minimax Principle Minimax Theorem Modular Arithmetic Nine Squares Parrondo Paradox Via Simpson Paradox Peasant Multiplication Pennies in Boxes Plus or Minus (parity, invariance) PolygonalNumbers Proizvolov's Identity Pythagorean Triples Pythagorean Triples Calculator Quasigroup on a Triangular Grid Rectangle on a Chessboard Right Replacement Self-descriptive Strings Self-documenting Sentences Sierpinski's Gasket and Dihedral Symmetry Signs and Sums in a Sequence Signs in a Matrix Simple Cellular Automaton Simpson Paradox Solitaire in Two Colors Squares and Circles (parity, invariance) Squares, Circles, and Triangles (modular arithmetic, invariance) Steinhaus' Problem Sum of Consecutive Integers is Triangular Sum of Consecutive Odd Numbers is Square Sum of Consecutive Triangular Numbers is Square Toads And Frogs Puzzle (counting, logic, problem solving) Two Colors in Two Rows Two Colors in Two Rows II What's next? Word Problems Logic Lewis Carroll's Bilateral Diagrams Lewis Carroll's Trilateral Diagrams Lewis Carroll's Logic Game Venn Diagrams I Venn Diagrams II Fractals All Peano Curves Apollonian Gasket Color Cycling on the Mandelbrot Set Cantor sets Dot Patterns, Pascal Triangle and Lucas Theorem Emergence of Chaos Fractal Curves and Dimension Iterated Function Systems Iterations in the Mandelbrot Set Koch's Snowflake Mandelbrot Set and Indexing of Julia Sets Plane Filling Curves: Hilbert's and Moore's Plane Filling Curves: Peano's and Wunderlich's Sierpinski Gasket By Common Trema Removal Sierpinski Gasket Via Chaos Game Sierpinski Gasket by Trema Removal The Chaos Game: Address Space vs IFS Variations on the Theme of Tremas Variations on the Theme of Tremas II Probability Bertrand's Paradox Binomial Distribution Birds On a Wire Buffon's Noodle Chess Players Truel Conditional Probability and Independent Events Family Statistics Lewis Carroll's pillow problem Monty Hall Dilemma Parrondo Paradox Random Clock Hands Stick Broken Into Three Pieces (Cartesian Coordinates) Stick Broken Into Three Pieces (Trilinear Coordinates) Who Needs Monty? Visual Illusions Assimilation Illusion Balls and Shadows Illusion Brick Wall Illusion Bulging Lines illusion Circular Poggendorff Illusion Continuous Line Illusion Cube Counting Ambiguity Day's Sine Illusion Delboeuf Illusion Distorted Lines Illusion Divergent Spirals Illusion Gerbino's Illusion Heaver: A Visual Illusion Height/Width Interplay Illusion Hering Illusion Hermann Grid Illusion Importance of Occluders: Motion Binding Judd Illusion Kanizsa Triangle Müller-Lyer Illusion Necker Cube Occluded Wheel Illusion Orbison Illusion Parallelogram Illusion Perspective Illusion Poggendorff Illusion Poggendorff Illusion II Ponzo Illusion Ponzo Illusion II Reverse Spoke Illusion Revolving Circles Illusion Rotating Top Illusion Scintillating Grid Illusion Shepard's Parallelogram Illusion Shifting Cube Illusion Shimmer Illusion Simultaneous Contrast Illusion Simultaneous Contrast Illusion II Simultaneous Contrast: Koffka's Illusion Simultaneous Contrast: White's Illusion Simultaneous Contrast: White's Illusion, V-Variant Staircase Illusion Twisted Cord Illusion Unfolding Spirals Illusion Wundt Illusion Wundt Block Illusion Zöllner's Illusion Calculus Addition and Subtraction of Functions Cartesian Coordinate System Derivative of Sine and Cosine Distance From a Point to a Straight Line Equations of a Straight Line Estimating Circumference of a Circle Function, Derivative and Integral Graph of a Polynomial Graph of a Polynomial Defined by Its Roots Horner's Method Inflection Points of Fourth Degree Polynomials Lagrange Interpolation Maximum Volume of a Cut Off Box Mistrust Intuition of the Infinite Naturally Discontinuous Functions Riemann Sums - Function Integration Rolle's and Mean Value Theorems Taylor Series Approximation to Cosine Two Circles and a Limit Math Magic An Arithmetic Magic Trick Arithmetic magic matrix Bachet's Magic Trick Barcode Magic Calendar Magic Gergonne's Magic Trick Hummer's Mind Reader Magic in Square Math Telepathy Number Guessing Game Two Numbers Guessing Game Combinatorics 3-Colors Tower of Hanoi Affirmative Action Problem Balanced Incomplete Block Design on a Triangular Grid Bicolor Tower of Hanoi Blithe 12 Cheapest Link & Kruskal's Algorithms - skill practice Chvatal's Art Gallery Theorem Coin change Coloring a Graph Critical Path in a Weighted Digraph de Bruijn Cycle Dominoes on a Chessboard Euler & Hamilton Paths - skill practice Five Lattice Points Flipping Items Simultaneously II Flipping pancakes Gray Codes Group multiplication of permutations Hanoing Happy 8 Hex Can't End in a Draw How to define a permutation Infinite Latin Square Jumping Isn't Everything Latin Squares Leibniz and Pascal Triangles Life-like Automaton With Definable Rules Light Bulbs in a Circle Listing All Combinations Listing All Permutations Listing All Permutations: Johnson-Trotter Method Lucky 7 Make Your Move, Kid! Marriage Problem, simulation Mazes Monotone Number Sequences Number sequences and Pigeonhole Party Acquaintances Permutations as a Product of Transpositions Product of Permutations Project Scheduling Property of the Powers of 2 Recombining Permutations Sam Loyd's Fifteen Scrub Tile Puzzle Shuttle Puzzle Simple Graphs Sliders (slider games on torus, Moebius strip, projective plane, permutations, cycles) Straight Tromino on a Chessboard The Game of Life Tool for Constructing Orthogonal Latin Squares Tower of Hanoi Tower of Hanoi, the Hard Way Two Men of Tibet Universal Coloring Y Can't End in a Draw Combinatorial Games Date Game Fraction Game Grundy's Game Hex 7 Kayles Nim Nimble Northcott's game One Pile Plainim Plainim Misère Scoring Scoring Misère Silver Dollar Game Silver Dollar Game With No Silver Dollar Sticks, Jess realization of Scoring Misère Sticky Problem Sticky Problem II Subtraction Game TacTix Take-Away Games Turning Turtles Wythoff's Nim Wythoff's Nim II Puzzles & Games 3-Chain 4×4×4 Tic Tac Toe (spacial visualization) Achieve the Equilibrium Bulls and Cows Caterpillar Changing Colors (combinatorics, invariance) Color Balls Computer Mastermind (logic and problem solving) Eight Digits Puzzle Farmer and Wife To Catch Rooster and Hen (invariance, city block distance) Fif (multiple representations) Fill a Hexagonal Grid (space visualization) Fish Soup Game (multiple representations) Four Knights (multiple representations) Full House Goat, Cabbage and Wolf to move across a river (multiple representations) Hare and Hounds Jam (multiple representations) Looping Chips (multiple representations) Mastermind (logic and problem solving) Mastermind Variants (logic and problem solving) Mirror Maze Peg Solitaire (logic, problem solving, subproblems) Pick A Label (logic, problem solving) Reverse Solitaire (logic, problem solving, subproblems) Sending scouts into the desert (algebra, geometric series, problem solving) Seven Coins Puzzle (multiple representations) Shuttle Puzzle Practice Solitaire on a Circle (iterations, invariance) Stones in Cups Super Nim Thugs and Bowmen Tiling a Triangulated Hexagon (a proof without words) Toads And Frogs in 2 dimensions (repeated application of same idea) Tromino Puzzle Vector Addition and Subtraction Vowel Movement Wolf and Rabbit Geometric Fallacies A Circle With Two Centers All Triangles Are Isosceles Curry's Paradox Delian Problem Solved A Faulty Dissection Hooper's Paradox John Sharp's Paradox Langman's Paradox Popping A Square Rouse Ball's Fallacy Sam Loyd's Son's Dissection Two Perpendiculars From a Point to a Line Social Science Adams' Apportionment Method Fair Division: Method of Lone Divider Fair Division: Method of Markers Fair Division: Method of Sealed Bids Fast Power Indices Hamilton's Apportionment Method Huntington-Hill Apportionment Method Jefferson's Apportionment Method Social Choice Webster's Apportionment Method Weighted Voting and Power Indices Elementary Geometry A Property of Equiangular Polygons Al-Nayrizi's Construction Angle: An Illustrated Classification Angle Bisector Angle Subtended by a Diameter Area of Median Triangle Area of the Union of Two Squares Arithmetic in Disguise Building a Bridge Carpet With a Hole Circles and Semicircles in Rectangle Circumcenter on Angle Bisector Classification of Quadrilaterals Common Chord and a Tangent Conic Sections as Loci of Points Construction of the Angle Bisector Construction of the Perpendicular Bisector Diagonal Count Dissection of Cyclic Quadrilateral Divide a Circle into N Parts of Equal Area E. W. Dijkstra's Proof of the Pythagorean Theorem Eight Equal Tangents Equidecomposition of a Rectangle and a Square Equidecomposition of Two Rectangles Equidecomposition of a Triangle and a Rectangle Equidecomposition of a Triangle and a Rectangle II Equidecomposition of Two Parallelograms Equilic Quadrilateral I Equilic Quadrilateral I, A Variation Equilic Quadrilateral II Euclid's Segment Division Existence of the Circumcenter Fibonacci Bamboozlement Famous Theorem Finding Circle Center By Ruler Alone Four Hinged Squares Geoboard Harmonic Mean Sangaku Hippocrates' Squaring of a Lune Huygens' proof of the Pythagorean Theorem Inscribed and Central Angles in a Circle Inscribed Angles Inscriptible Quadrilateral: An Illustration Maimed Cake Mathematics in Pizzeria Octagon in Parallelogram Octagon in Parallelogram: Overlapping Regions Olof Hanner's Jigsaw Puzzle Orthocenters of Two Triangles Sharing Circumcenter and Base Pappus' Generalization of Euclid I.47 Orthodiagonal and Cyclic Quadrilaterals Parallel Chords II Parallel Lines in a Quadrilateral Polygon Metamorphosis Property of Angle Bisectors Pythagorean Theorem By Dissection Pythagorean Theorem By Dissection II Pythagorean Theorem by Hinged Dissection Pythagorean Theorem by Hinged Dissection I Pythagorean Theorem by Hinged Dissection II Pythagorean Theorem: J. Adams' Proof by Dissection Pythagorean Theorem: Versluys' Proof by Dissection Pythagoras' Theorem By Sheer Shearing Pythagoras' Theorem By Similarity Pythagoras' Theorem Solely By Sliding Pythagorean Segment Division Quadrilateral With Equal Opposite Sides And Angles Secant Angles Secant Angles II Shearing a Polygon into a Triangle of Equal Area Simple Quadrilaterals Tessellate the Plane Shearing and Translation in Pythagorean Pants Square From Nowhere Square in Chair Squaring a Rectangle Three Touching Circles Translation Transform Triangle Areas in a Parallelogram Triangle Areas in a Parallelogram II Triangle Classification Trigonometric Functions Two Intersecting Circles Two Symmetric Triangles Are Directly Equidecomposable Two Symmetric Triangles Are Directly Equidecomposable II Two Symmetric Triangles Are Directly Equidecomposable III Two Symmetric Triangles Are Directly Equidecomposable IV Two Touching Circles Van Schooten's and Pompeiu's Theorems Viviani's Theorem Viviani's Theorem II   Geometry 120° Breeds 90° 2N-Wing Butterfly Theorem 3 Isosceles Trapezoids 5-Star and A Circle 6 to 9 Point Circle 60o Breeds 90o 9-point Circle as a Locus of Concurrency A Circle Related to Incenter and Circumcenter A Line in Triangle Through the Circumcenter A Sangaku Follow-Up on an Archimedes' Lemma A Sangaku: Two Unrelated Circles A Sangaku with an Egyptian Attachment A Sangaku with Many Circles and Some A Stronger Triangle Inequality Adams' Circle Addition of Radius-Vectors Altitudes and the Power of a Point An Isoperimetric Theorem Angle Bisector in Parallelogram Angle Bisector in Touching Circles Angle Bisectors and Perpendiculars in a Quadrilateral Angle Bisectors in a Quadrilateral Angle Bisectors On Circumcircle Angle Preservation Property Angle Trisection by Archimedes Angle Trisection by Hippocrates Angle Trisection by Paul Vjecsner Angle Trisectors on Circumcircle Angles in Triangle Add to 180o Another Pair of Twins in an Arbelos Anticomplementary Triangle Surprise Antiparallel Apollonian Circles Theorem Apollonius Problem Application of Ceva's Theorem Archimedes' Quadruplets Archimedes Triangle and Squaring of Parabola Archimedes' Twin Circles and a Brother Area of an Arbelos Area of Parallelogram Area of Triangle Areas and Centroid in a Triangle Areas in Triangle Areas in Triangle II Arithmetic Mean Sangaku Arithmetic Mean Sangaku II Around the Incircle Around the Incircle in a Polygon Asymmetric Propeller I Asymmetric Propeller II Asymmetric Propeller III Barycentric Coordinates: a Tool Bevan's Point and Theorem Bisectal Circle Book of Lemmas: Proposition 1 Book of Lemmas: Proposition 2 Book of Lemmas: Proposition 3 Book of Lemmas: Proposition 5 Book of Lemmas: Proposition 6 Book of Lemmas: Proposition 9 Book of Lemmas: Proposition 10 Book of Lemmas: Proposition 12 Book of Lemmas: Proposition 13 Böttcher's Proof of the Pythagorean Theorem Böttcher's Proof Variant Bottema Shatters Japan's Seclusion Bottema's Theorem Bottles in a Slanted Rack Bottles in a Wine Rack Bottles in a Wine Rack: Proofs and Generalizations Brahmagupta's Theorem Brianchon in Ellipse Brianchon's Theorem Bride's Chair Broken Chord Theorem Broken Chord Theorem by Paper Folding Broken Chord Theorem: G. Patruno's proof Broken Chord Theorem: S. Anderson's proof Butterfly in Ellipse Butterfly Problem Cantor's Theorem Cardioid As Envelope of Circles Cardioid As Epicycloid Carnot's Theorem Carpets in a Parallelogram Carpets in a Quadrilateral Carpets in a Quadrilateral II Carpets Theorem Carpets Theorem With Parallelograms Center Circles and Their Chains Centroids in a Polygon Ceva and Menelaus Theorems for Angle Bisectors Ceva's Theorem Ceva's Theorem (PWW) Cevian Nest Cevian Triangle Chain of Inscribed Circles Chasles' Theorem, a Proof Cherchez le quadrilatère cyclique Cherchez le quadrilatère cyclique II Chords, Concurrency and Orthic Triangle Chords in Cardioid Circle and Hyperbola as Lighthouse Curves Circle Chains and Inscribed Angles Circle Concurrency and Spiral Similarity Circle Crosses Triangle Circle Division by Euclid and Leonardo Circle Inscribed in a Circular Segment Circle of Similitude Circle-Stacking Theorem Circles And Parallels Circles and Reflections in a Triangle Circles in Morley's Triangles Circles Lined on the Legs of a Right Triangle Circles On Cevians Circles Tangent to Circumcircle Circles through the Orthocenter Circumcevian Triangle Cleavance Center Cleaver Clifford Chain Clifford's Lemma Coaxal Circles Theorem Colburn's Proof of the Pythagorean Theorem Common Tangents to Two Circles I Common Tangents to Two Circles II Complete Quadrilateral Concyclic Points in Equilateral Bumps Concurrency in Analytic Geometry Concurrency in Arbelos Concurrency in the Intouch Triangle Concyclic Circumcenters: A Dynamic View Concyclic Points in a Triangle Consecutive Isosceles Decomposition Conway's Circle Copernicus' Theorem Crossed-Lines Construction of Shapes of Constant Width Cyclic Hexagon Cyclic Incenters Cycloids Diameters and Chords Directly Similar Figures Desargues' Theorem Discovery of Duane DeTemple Dividing a Segment into N parts: Besteman's Construction Dividing a Segment into N parts: Besteman's Construction II Dividing a Segment into N parts: GLaD Construction Dividing a Segment into N parts: SaRD Construction Dividing Evenly a Quadrilateral Dividing Evenly a Quadrilateral II Double Generation Theorem Douglas' Theorem (complex variables, linear algebra) Droz-Farny Circles Droz-Farny Line Theorem Dual to Pappus' Theorem Dynamic Construction of Ellipse and Other Curves Easy Construction of Bicentric Quadrilateral Easy Construction of Bicentric Quadrilateral II Eight Point Circle Ellipse, how to draw Ellipse in Arbelos Equal Angles in Two Circles Equal Angles in Two Circles II Equal Areas In Parallelogram à la Pythagoras Equal Incircles Theorem Equichordal Curves Equilateral Triangle, Straight Line and Tangent Circles Equilateral Triangles on Diagonals of Antiequilic Quadrilateral Equilateral Triangles on Segments of Equilic Quadrilateral Equilateral Triangles On Sides of a Parallelogram Equilateral Triangles On Sides of a Parallelogram II Equilateral Triangles on Sides of a Quadrilateral Euler Line Cuts Off Equilateral Triangle Euclid I.43 Euclid I.43 Extended Extouch Triangle in Poncelet Porism Eyeball Theorem External Angle Bisector Fagnano's problem Fagnano's problem II Fagnano's Problem, Third Solution Fagnano's Problem, Fourth Solution Fagnano's Problem in Reverse Fermat point and 9-point Centers Fermat's Point Feuerbach's theorem Feuerbach's Theorem: A Proof First Vecten Point Five Cardioids Five Concyclic Points Five Incircles in a Square Five Incircles Theorem Fixed Point of Circles Orthogonal to the Given One Fixed point on a rod rotating around a triangle Focal Properties of Parabola Foot of Altitude and Minimum Distance Four Centroids and Parallels Four 9-Point Circles in a Quadrilateral Four Circles In a Triangle Four Concurrent Lines in a Cyclic Quadrilateral Four Incident Circles Four Incircles in Equilateral Triangle Four Pedal Circles Four Touching Circles Four Triangles, One Circle Four Turtles (or Bugs, or Dogs, etc.) Friendly Kiepert's Perspectors From Foci to a Tangent in Ellipse Fundamental Theorem of 3-Bar Motion Fuss' Theorem Generalizing a Romanian Olympiad Problem Gergonne and Medial Triangles Are Orthologic Gergonne and Soddy Lines Are Perpendicular Gergonne in Ellipse Glide Reflection Golden Ratio in an Irregular Pentagon, Construction I Golden Ratio in an Irregular Pentagon, Construction II Golomb's inductive proof of a tromino theorem Gothic Arc Grebe's Theorem Greg Markowsky's Problem for Parabola Griffiths Points in Cyclic Quadrilateral Harmonic Ratio Hart Circle Hart's Inversor Haruki's Lemma Heron's Problem Hexagon Parallel to Medial Triangle Hexagon Parallel to Orthic Triangle Hinged Squares Hjelmslev Theorem Hofstadter Triangles and Points Homothety Hypocycloid Families Ian McGee's Observation Illustration of Pascal's Theorem Incenters in Cyclic Quadrilateral Incidence in Feuerbach's Theorem Incident Center Circles and Cardioid Incircles, Circumcircles and Inscribed Angles Inscriptible and Exscriptible Quadrilaterals Internal Tangents to Three Circles Intouch Triangle in Poncelet Porism Inversion: Reflection in a Circle Inversion in the Incircle Inversion Tool Inversion with Negative Power Isogonal and Isotomic Conjugalities Isogonal Concurrency Isogonal image of the circumcircle Isosceles on the Sides of a Triangle Isotomy and Isogonality Hand-in-Hand Iterations in Geometry, an example Iterations in Geometry, Generalization Iterations on Euler Lines Kiepert's Theorem Kürschak's Tile and Theorem Law of Cosines Law of Cosines: PWW Law of Cosines: An Unfolded Variant La Hire's Theorem La Hire's Theorem, a Variant La Hire's Theorem in Ellipse Lean Napoleon's Triangles Lighthouse Curves Locus of Points in a Given Ratio to Two Points Malfatti's Problem Malfatti's Problem, Hart's Solution Maxwell's Theorem Median in Touching Circles Medians in a Quadrilateral Menelaus and Ceva Theorems Menelaus From Ceva Midline in Similar Triangles Midpoints from Gergonne Triangle Midpoints of the Lines Joining In- and Excenters Minkowski's addition of convex shapes Miquel's Point Miquel's Point of a 4-line Via Spiral Similarity Mirror on the Wall Mirror property of the altitudes Mirror Property of Altitudes via Pascal's Hexagram Mixtilinear Circles and Concurrence Monge via Desargues Monge via Desargues II More Bottles in a Wine Rack Morley Constellation Morley's Theorem Morley's Theorem, Cardioids and Such Morley's Theorem, G. Zsolt Kiss' proof Nagel Line Nagel point Nagel Point of Medial Triangle Nagel's Theorem Napoleon Theorem by Plane Tessellation Napoleon's Theorem by Transformation Neuberg Sangaku Newton's Construction of Conics Newton's Theorem Nine Point Circle No Equilateral Triangles, Please Nobbs' Points, Gergonne Line Non-classic Way To Draw Cardioid On Bottema's Shoulders On Bottema's Shoulders II One Sided Surface in 4D Optical Property of Ellipse Optimization Problem in Acute Angle Orthocentric System From Rectangle Orthogonality in Isosceles Triangles Orthologic Triangles in a Quadrilateral Orthopole Pairs of Incircles in a Quadrilateral Pappus' Theorem Parabola As Envelope of Straight Lines Parabola As Envelope II Parabolic Mirror Paragon Parahexagon Parallel Chords Parallel Lines and Similar Triangles Parallelogram and Similar Triangles Parallelogram Law Parallelogram Law: A PWW Parallelogram Law: A Tessellation Pascal in a Cyclic Quadrilateral Pascal Lines: Steiner and Kirkman Theorems Pascal Lines: Steiner and Kirkman Theorems II Pascal's Theorem Peaucellier Linkage Pedal Polygons Pedal Triangle and Isogonal Conjugacy Pedoe's Theorem Perigal's Proof of the Pythagorean Proposition Perpendicular Bisectors in an Inscriptible Quadrilateral Perpendicular Bisectors in an Inscriptible Quadrilateral II Pinning Butterfly on Radical Axes Pivot Theorem Point common to two similar rectangles Polar Circle Pole and Polar with respect to a Triangle Poles and Polars Poles, Polars and Quadrilaterals Polygon from midpoints of its sides Polygons Formed by Perpendicular Bisectors Poncelet's Porism Poncelet's Porism in Ellipses Poncelet's Theorem Problem in an Equilateral Triangle Problem in an Equilateral Triangle II Problem In an Isosceles Right Triangle Problem in Three Squares Problem of Equal Steps Problem of Equal Steps II Problem of polygon construction Problem with Equilateral Triangles Product of Rotations Projections on Internal and External Angle Bisectors Projective Collinearity in a Quadrilateral Projective Generalization of Maxwell's Theorem Projective Proof of Pascal's Theorem Proof Without Words for the Pythagorean Theorem Properties of the Circle of Similitude Property of 6-Parpolygon Property of Angle Bisectors II Property of Circumscribed Quadrilaterals Property of Points Where In- and Excircles Touch a Triangle Property of Rhombi Property of the Line IO Property of the Line IO II Property of the Line IO: a proof from the Book Pythagoras and Vecten Break Japan's Isolation Pythagorean Condition in An Isosceles Right Triangle Pythagorean Theorem: Subtle Dangers of Visual Proof Pythagorean Theorem By Euclid Pythagorean Theorem By Plane Tessellation Pythagorean Theorem By Hexagonal Tessellation Pythagorean Theorem By Rearrangement Pythagorean Theorem By Shearing and Rotations I Pythagorean Theorem By Shearing and Rotations II Pythagorean Theorem in an Orthodiagonal Quadrilateral Quadrilaterals Formed by Perpendicular Bisectors Quest for Paragon MathPro Logo Radical Axis and Center, an Application Radical Axis of Circles Inscribed in a Circular Segment Radical Center Radius and Construction of a Mixtilinear Circle Radius of a Circle by Paper Folding Rectangle in Arbelos Reflection In Line Reflections in Ellipse Reflections of a Line Through the Orthocenter Reflections of a Point on the Circumcircle Reflections of the Orthocenter Remarkable Line in a Quadrilateral Remarkable Line in Cyclic Quadrilateral Rendezvous Right Isosceles Triangles on Sides of a Quadrilateral Rotation Transform Rotations in Disguise Rusty Compass Construction of Equilateral Triangle Salinon: from Archimedes Book of Lemmas Sangaku Iterations, Is it Wasan? Sangakus with a Mixtilinear Circle Sangaku with Three Mixtilinear Circles Seven Circles Theorem Squares in Arbelos Secant, Tangents and Orthogonality See-Saw Lemma Segment Trisection Shape of Constant Width Shearing Butterflies in Quadrilaterals Siamese Triangles Siamese Triangles II Similar Triangles on Sides of a Quadrilateral Similar Triangles on Sides and Diagonals of a Quadrilateral Simson Line Simson Line From Isogonal Perspective Simson Lines Of Diametrically Opposite Points Simsons and 9-Point Circles in Cyclic Quadrilateral sin(N) Six Circles Theorem (Elkies) Six Circles Theorem (Evelyn) Six Concyclic Points Six Incircles in an Equilateral Triangle Six Point Circle Soddy Circles and David Eppstein's Centers Sperner's Lemma Spira Mirabilis - Wonderful Spiral Square in a Right Triangle Square Inscribed in a Triangle Square Inscribed in a Triangle II Squares Inscribed In a Triangle III Squares on Sides of a Quadrilateral Squinting Eyes Theorem Star Construction of Shapes of Constant Width Steiner's Chain Steiner's porism Straight Edge Construction of Polar Symmedian and Antiparallel Symmedian and 2 Antiparallels Symmedian and the Tangents Symmedian in a Right Triangle Tangency Point of Two Circles Tangent and Secant Tangent Circles and an Isosceles Triangle Tangent Circles in a Parallelogram Tangent in Concurrency Tangents and Diagonals in Cyclic Quadrilateral Tangents, Perpendiculars and Geometric Mean Tesseract Thébault's Problem I Thébault's Problem II Thébault's Problem III Thébault's Problem III, Proof Theorem of Complete Quadrilateral Three Concurrent Circles Three Congruent Circles by Reflection Three Congruent Circles by Reflection II Three Congruent Circles by Reflection III Three Incircles In a Right Triangle Three Incircles in a Triangle Three Isosceles Triangles Three Parabola Tangents Three Parallels in a Triangle Three Points on a Parabola Three Roads, Three Travelers Three Similar Polygons Three Similar Triangles Three Similar Triangles (but differently oriented) Three Similar Triangles (but differently oriented) II Three Squares and Two Ellipses Three Tangent Circles Three Tangents Theorem Three Tangents Theorem II Three Tangents, Three Secants Toothpick Construction of a Square Touching Circles Touching Circles and Concurrency Triangle and Segment Count in a Polygon Triangle Geometry Triangle Sliding on Two Straight Lines Triangles, Squares and Areas from Temple Geometry Triangles with Equal Area Triangular Billiard Trigonometric Form of Ceva's Theorem (a tool for discovery of trigonometric identities and other problems) Tromino as a Rep-tile Tucker Circles Tucker Circles Through Homothety Twin Segments in Arbelos Two Butterflies Theorem Two Butterflies Theorem II