Profile

Scrapbook photo 1
Scrapbook photo 2
Scrapbook photo 3
Scrapbook photo 4
Scrapbook photo 5
Paul Ancka
297 followers|39,694 views
AboutPosts

Stream

Paul Ancka

Shared publicly  - 
 
 
This one is a bit long: it is constructed starting with no less than 92 regular dodecahedra glued face-to-face between themselves: 12 of those are in blue, 20 further in red and the remaining 60 in orange. Pay attention now: the centers of the blue (12) and red (20) dodecahedra are the 32 vertices of a rhombic triacontahedron (a Catalan solid dual to the Archimedean icosidodecahedron), the side of the rhombic triacontahedron is 4 times the radius of the sphere inscribed in a regular dodecahedron, that is sqrt(10 + 22/sqrt(5)). In all, the complex you are seeing is itself a great polyhedron of face vector [V= 1240, F= 864, E= 2160; genus: g= 29] (one hole per face of the said rhombic triacontahedron, that is 30 in all).
The overall symmetry of the 'animal' is Ih, that is, icosahedral complete w. horiz. reflection, the same of the regular dodecahedron & icosahedron.
6 comments on original post
2
Evelyn Loren's profile photo
 
Could be that Nassim Haramein constructed the original hypothesis such universal geometry figure?

Is your icon kinda of Arwing?
Cannt recognise it good.
Add a comment...

Paul Ancka

commented on a video on YouTube.
Shared publicly  - 
 
Why isn't SKR the secretary of education ! Obama, where were you thinking ?

Paul Ancka

Shared publicly  - 
1
Add a comment...

Paul Ancka

Shared publicly  - 
 
2030 Teen ?
1
Add a comment...

Paul Ancka

Shared publicly  - 
 
I won candy on the #googlebirthday doodle! Score: 131
1
Add a comment...

Paul Ancka

Shared publicly  - 
 
How did you get the link to the "Creative Style Estimation Exercise" ??? thx 
Thinking about Creativity My great-grandfather was a master craftsman. He was a general contractor who built numerous structures in and around Long Beach, CA in the 1920’s-’50’s. One bit of family lore- “Pop” (as he was kn...
1
Rick Bartlett's profile photoPaul Ancka's profile photo
2 comments
 
Found it ! Thx !
Add a comment...

Paul Ancka

commented on a video on YouTube.
Shared publicly  - 
 
Hi Ally, good presentation but there are quite a few misleading threads ... . See prof. Keith Devlin lecture on Phi - 2. The Golden Ratio & Fibonacci Numbers: Fact versus Fiction

Paul Ancka

commented on a video on YouTube.
Shared publicly  - 
 
Anat, where is Dan ... he should be in the clip too ... :) 

Paul Ancka

Shared publicly  - 
 
 
Atom Builder

Assemble your own atoms from buckets of Protons, Neutrons and Electrons and see where they are on the periodic table, their charge and atomic mass.

Fun, interactive, research-based simulations of physical phenomena from the PhET™ project at the University of Colorado.

Here (expects HTML5): http://goo.gl/RykXMV

More Science simulations (HTML5): http://goo.gl/MQKpAk
Older sims (inc. non HTML5): http://phet.colorado.edu/
PhET @ Wikipedia: http://goo.gl/Pyw4Bm


Podcast on Teaching with Interactive Simulations, featuring Katherine Perkins, Director of Physics Education Technology (PhET): http://goo.gl/aNF5hA
7 comments on original post
2
Add a comment...

Paul Ancka

Shared publicly  - 
 
 
The Penrose triangle is often called an impossible object.  But that depends on your perspective!

The Penrose triangle was actually first created by the Swedish artist Oscar Reutersvärd in 1934. The mathematician Roger Penrose independently devised it in the 1950s, describing it as "impossibility in its purest form".

However, you can actually build a 3-dimensional object that looks like a Penrose triangle from the right perspective.  You can see how that works here.  But it's even more fun in real life! 

For example: Brian MacKay & Ahmad Abas put a sculpture called Impossible Triangle in the Claisebrook Roundabout in East Perth, in Australia. Seen from the right angle, it looks like a Penrose triangle!  Check it out:

http://en.wikipedia.org/wiki/File:Perth_Impossible_Triangle.jpg

Penrose actually wrote about the Penrose triangle with his father, the psychiatrist Lionel Penrose, in a short article in the British Journal of Psychology called "Impossible Objects: A Special Type of Visual Illusion".

This article also included a related impossible object, the Penrose stairs.   Both these were later used by the artist M. C. Escher.  If you don't know what I mean, look at Escher's famous lithograph, Waterfall:

http://en.wikipedia.org/wiki/Waterfall_%28M._C._Escher%29

Both the Penrose triangle and Penrose stairs make sense 'locally' but not 'globally': if you look at a small region they look okay, but if you follow them around a loop you don't get back where you should.  So, mathematically we say they are examples of 'cocycles' that aren't 'coboundaries'.  Perhaps it's no coincidence that Penrose is an expert on cocycles and their role in physics - that's one of the ideas behind a theory he invented, called twistor theory.

For more impossible objects, see:

http://en.wikipedia.org/wiki/Impossible_object

Thanks to W Aden for pointing out the image here.

#illusions  
36 comments on original post
2
Add a comment...

Paul Ancka

Shared publicly  - 
 
I won candy on the #googlebirthday doodle! Score: 155
1
Add a comment...
Story
Introduction
Wish I was there !
Links
YouTube
Work
Occupation
Math