N dimensional Simplex

Zero D

Nothing inside 0D Point

1 D

0D Point inside 1D line

2 D

1D line inside 2D triangle

3D

2D triangle inside
3D pyramid

4D

Task

Table the numbers of dimensions, vertices, and faces to find patterns.

Make rules to find the number of vertices and faces for a 4D, 5D and 10D simplex.

Repeat the process for right-angular (square) shapes,
such as the 4D hypercube.

Graham Partis

For my students at Marsden High

11IPT

Links:

NS Diagrams http://users.evtek.fi/~jaanah/IntroC/DBeech/3gl_nassi.htm#what-is

2GL, 3GL, 4GL Definition
http://coding.derkeiler.com/pdf/Archive/Delphi/borland.public.delphi.non-technical/2004-05/1633.pdf

Shuffling Arrays http://delphi.about.com/cs/adptips2003/a/bltip1003_4.htm

Software Development Life Cycle
http://www.stylusinc.com/Common/Concerns/SoftwareDevtPhilosophy.php

My Interests

	Benji Bear	The mascot of Benji Bear and Friends.
	Game Theory	A math of competitive decision making. "I know that you know that I know that..." Its key concept is the prisoner’s dilemma.
	Cognitive Science Mind Body Problem	How information is processed in a thinker's mind or brain. Do we only dream we have brains? The seemingly digital and incomplete nature of our existence seems more in line with a computer simulation than a real universe.
	Personal Identity Cybernetics	What would I need to lose for me to no longer be me? Math of self maintaining systems and personalities. Who is more intelligent Einstein the man or Sol the star?
	Modal Logic Godel's Proof	Languages and logics are always: self defining, incomplete, and/or inconsistent. i.e. Logic can never completely make sense. Possible Worlds Semantics implies that individual thinking perspectives all have illuminations and blind spots unique to themselves.
	Cosmology	Latest findings suggest that that our universe is a living being still in its childhood, and we are merely a small part like a single nerve within a cosmic brain.
	Big and Small	I recently heard that there are about 100 billion stars in our galaxy and as many galaxies in our Universe. I would have guessed the universe would be bigger but it is likely that our physical universe (or the parts of it we can know) is finite in size. Modern Multi-Dimensional Theoretical Physics such as M-Theory and Loop Gravity suggest the universe is made up of plank length loops as tiny as a human inside a universe that is squashed inside an atom.
	Quantum Chaos	Quantum Mechanics and the laws of chaotic systems suggest that the stability of our physical universe is achieved by unpredictable digital foundations. Digital building blocks hold our universe together, like square bricks of a brick house. Likewise the messiness at the bottom (Quantum or Plank level) allows the leeway for our macroscopic world to seem rigidly ordered, and stable.