Pentagons, Theorems and
Problems  Table of Content




Euclid's Elements
Book I, 23 Definitions. Onepage visual illustration.
Euclid's Elements Book.
Index 

Pentagon and Lissajous Art


Word
Cloud of Pentagon.
Visual Summary. 

Geometric Art: Isolines, Pentagon, Star, Parallel Lines, Symmetry, Kaleidoscope, Geometry for Kids, Software 

Euclid's
Elements, Book XIII, Proposition 10 Pentagon, Hexagon, and Decagon. One page
visual illustration. 

Proposition 15.
Circle and regular pentagon. 

iPad Apps: Springle by Bolasol Inc. Geometric Art: Squares and Pentagons 

Miquel's Pentagram Theorem
Interactive proof with animation and key theorems.


Miquel's
Pentagram with Dynamic Geometry. You can alter the pentagram
dynamically in order to test and prove (or disproved) conjectures and
gain mathematical insight that is less readily available with static
drawings by hand. Requires Java Plugin 1.3 or higher. Please
be patient while the applet loads on your computer. 

Pentagon
and Lissajous Art


iPad Apps: Shapes  3D Geometry Learning (Solids Elementary HD),
Regular Dodecahedron. 

iPad Apps: Shapes  3D Geometry Learning (Solids Elementary HD),
Unfolded Regular Dodecahedron. 

Optical Prism with
Regular Pentagonal Form.
Scene created using Prism HD for iPad. 

iPad Apps:
fractBG.
Fractal Image with Pentagons. 

Dynamic Geometry 1477.
Miquel's Pentagram Theorem, Pentagon, Triangle, Circumcircles, Concyclic Points, Stepbystep Illustration. GeoGebra,
iPad. 

Geometry Problem 1141.
Inscribed Pentagon, Circle, Triangle, Congruence, Midpoint, Concurrency. 

Geometry Problem 771
Area of a Parallelogram, Star, Pentagon, Triangles. 

Proposed Problem 430.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas. 

Proposed Problem 429.
Circumscribed and Inscribed Regular Pentagon, Perpendicular,
Measurement. 

Proposed Problem 410.
Two Regular Pentagons, Angle. 

Proposed Problem 342.
Pentagon, Inscribed circle, Tangent, Semiperimeter. 

Proposed Problem 261.
Regular Pentagon inscribed in a circle, sum of distances.


Video: Visualization of Solid Tessellations. 

Experiencing Geometry Poem. Taken from "Experiencing Geometry on
Plane and Sphere," a classic textbook on Euclidean and nonEuclidean
space. Used by permission of the author David W. Henderson.
Pentagons illustration. 

Proposed Problem 169.
Parallelogram, Interior and Exterior Points, Diagonals, Pentagon,
Triangles, Areas.


Proposed Problem 168.
Parallelogram, Diagonal, Triangles, Pentagon, Areas.


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

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

Index,
Platonic
Solids, Interactive animation,
Tetrahedron in the cube,
Archimedes and the Rhombicuboctahedron with animation,
In the
News,


Pentagons & Pentagrams. I found, exploring with dynamic geometry
software, new facts about pentagons and pentagrams. Key concept:
Menelaus Theorem.
