Online Geometry: Equilateral Triangles, Theorems and Problems

Equilateral Triangles - Table of Content

Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book. Index

Euclid's Elements Book I, Proposition 3: Given two unequal straight lines, to cut off from the greater a straight line equal to the less

Euclid's Elements Book I, Proposition 2: To place at a given point (as an extremity) a straight line equal to a given straight line

Euclid's Elements Book I, Proposition 1: On a given finite line to construct an equilateral triangle

Euclid's Elements, Book XIII, Proposition 10 One page visual illustration.

Napoleon's theorems and problems, Index.

Proposed Problem 404.
External Equilateral triangles, Congruent and Concurrent Lines.

Da Vinci Tetrahedron and Jenn 3D tool for visualizing Coxeter polytopes.
Jenn 3D is a free software license program for visualizing regular polytopes in stereographic projection.

Da Vinci Octahedron and Jenn 3D tool for visualizing Coxeter polytopes.
Jenn 3D is a free software license program for visualizing regular polytopes in stereographic projection.

Da Vinci Icosahedron and Jenn 3D tool for visualizing Coxeter polytopes.
Jenn 3D is a free software license program for visualizing regular polytopes in stereographic projection.

Geometry Problem 700.
Equilateral Triangle, Circle, Circular Segment, Midpoint of a side, Metric Relations.

Geometry Problem 699.
Equilateral Triangle, Circle, Circular Segment, Midpoint, Metric Relations.

Proposed Problem 396.
Square, Angle Trisectors, Congruence, Area.

Proposed Problem 395.
Square, 15 Degree, Equilateral triangle.

Proposed Problem 366.
Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle.

Proposed Problem 365.
Circular Sector of 60 degrees, Midpoints, Perpendicular, Congruence.

Proposed Problem 326.
Equilateral triangle, Semicircle, Equal arcs.

Proposed Problem 248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.

Proposed Problem 247.
Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon triangle.

Proposed Problem 246.
Napoleon's Theorem I. External Equilateral triangles.

Morley's Triangle & Center: with interactive animation and manipulation.

Proposed Problem 262.
Regular Hexagon inscribed in a circle, sum of distances.

Proposed Problem 260.
Equilateral Triangle, Incircle, Tangency Points, Vertices, Distances, Squares.

Proposed Problem 259.
Equilateral Triangle, Incircle, Tangency Points, Side, Distances, Squares.

Proposed Problem 258.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares.

Proposed Problem 257.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares.

Proposed Problem 256.
Equilateral Triangle, Circumcircle, Point, Vertices, Distances.

Proposed Problem 245. Parallelogram with Equilateral triangles

Proposed Problem 243. Triangle with Equilateral triangles, Parallelogram.

Proposed Problem 242. Triangle with Equilateral triangles, Parallelogram.

Proposed Problem 241. Triangle with Equilateral triangles, Congruence.

Proposed Problem 240. Triangle with Equilateral triangles, Parallelogram.

Proposed Problem 225. Viviani's Theorem Extension, Regular Polygon, Apothem, Distance.  

Proposed Problem 222. Viviani's theorem, Equilateral triangle, Exterior point, Distances.  

Proposed Problem 221. Viviani's theorem, Equilateral triangle, Interior point, Distances.  

Proposed Problem 212. 120 Degree Triangle, Equilateral triangles, Areas.

Proposed Problem 211. 60 Degree Triangle, Equilateral triangles, Areas.

Geometry in Action. Reuleaux's rotor: How Round is your Circle? The Reuleaux triangle is a constant width curve based on an equilateral triangle.

Proposed Problem 132.
Triangle, 60 degree, Orthocenter, Congruence, Midpoint.
 

Proposed Problem 103.Equilateral Triangle Area, Interior Point, Heron's Formula.

Proposed Problem 102.Equilateral Triangle Area, Interior Point.

Proposed Problem 101.Equilateral Triangle, Pythagorean Theorem, Angles.

Machu Picchu and Sierpinski Triangle. The canonical Sierpinski triangle uses an equilateral triangle with a base parallel to the horizontal axis.

Machu Picchu and Sierpinski Tunel Effect.

Crop Circles and Complexity
Crop Circles and Sacred Geometry
 

Tessellations Index.

Symmetry (1966). Greatest film, a fantasy of dancing images breaking apart, spinning, and converging. Produced by the University of Washington, the Commission on College Physics, and the Polytechnic Institute of Brooklyn.

Sacred Geometry: Introduction by Charles Gilchrist. 

Interactive Mind Map of the Van Hiele Model of Geometric Thought
Level 0. (Basic Level) Visualization.

Machu Picchu and the Flower of Life

The Flower of Life Index:
 Christ Redeemer, Taj Mahal,
 Machu Picchu, Chichen Itza
 Roman Colosseum, Petra, Jordan
 Great Wall of China

Proposed Problem 59: Right and Equilateral Triangles, Midpoints.

Proposed Problem 50. Triangle with Equilateral triangles.
Seventeen conclusions.

Geometry of Circles "Sesame Street" by Philip Glass, 1979.

Proposed Problem 42. Angles and triangles.

Problem 40. Triangle, Incenter, Excenter, Angles 80, 40, Distances.
Problem 40. Geometry Help. Suggestions.

Problem 4. Quadrilateral, equal sides and angles.

Problem 1. Triangle, median and angles.

Hexagon and Lissajous Art  

Index, Platonic Solids, Interactive animation, Tetrahedron in the cube, Archimedes and the Rhombicuboctahedron with animation, In the News, Video: How to make platonic solids with gum drops and tooth picks

Geometry Online Glossary .
Geometry Glossary based on the new New York State mathematics standards initiative.

Geometry and Cultures Gold Tumi.

Triangles and Lissajous Art  

Equilic Quadrilateral.
 

Napoleon's Theorem. A purely geometric proof. It uses the Fermat point to prove Napoleon without transformations.
 

Morley's Theorem. Introduction with animation. Triangle + Trisectors = Equilateral triangle.

Morley's Theorem Puzzle: 22 pieces of polygons.

Langley's Problem Adventitious angles. 20° isosceles triangle with animation.
 

Kurschak's Tile and Theorem. Jozsef Kurschak (Hungary, 1864-1933) A square, with equilateral triangles. An elegant and a purely geometric way of finding the area of a regular dodecagon.