Geometry

Andy's picture

Cayley graph 3D

Submitted by Andy on Sat, 13/07/2013 - 23:17
Cayley graph 3D

I was in the keynote session of AAMT conference. In the keynote, the mathematician Hanna Neumann was mentioned. I immediately googled and started reading about her on Wikipedia.

While reading, my thoughts are like the hyperlinks that go everywhere, then suddenly I saw and clicked into the Group theory, where I found the Cayley graph that caught my attention.

It is easily recognisable that this cayley graph is a fractal image, which can be produced with a simple recursive procedure in VRMath2's LOGO language.

Knoblauch's picture

Rhomicuboctahedron

Submitted by Knoblauch on Sat, 13/07/2013 - 14:54
Rhomicuboctahedron

So, at first glance, this seemed like it would be quite difficult....

turns out, it only took 10 minutes, very simple to construct, only angles involved are 45 degrees (would likely be more difficult if trying to show the faces, rather than just the edges.

Knoblauch's picture

My first Icosahedron

Submitted by Knoblauch on Fri, 12/07/2013 - 09:26
Icosahedron

Icosahedron is the last of the five Platonic solids. It consists of 20 regular triangular faces.

I am sure that there is a more efficient way to do this...

Andy's picture

Recursive 2D fern leaf procedure

Submitted by Andy on Sat, 06/07/2013 - 20:15
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In my previous blog, I explained about a recursive tree procedure. Here is another one borrowed from Joshua's Logo Interpreter example: fern leaf procedure. This fern leaf procedure creates a 2D fern leaf in VRMath2's 3D space. You can examine it below in the 3D space with the LOGO program.

Andy's picture

Recursive 2D tree

Submitted by Andy on Sat, 06/07/2013 - 16:12
Recursive 2D tree

One of the powerful abilities of LOGO programming language is its recursive execution of procedure. Recursive call of procedure means a procedure calls itself until an exiting condition is met. A recursive procedure can be very simple yet it can produce complex and beautiful mathematical graphics such as fractal images and naturally occurring objects.