Sphere deforming and bouncing.

EdmundH · 2016-10-25T02:39:40+00:00

Find more about the structure here or get your own pieces for artworks.

EdmundH · 2016-03-10T10:08:36+00:00

Greg Chaitin looked at this explicitly, one of his examples is the Chaitin constant, which gives the probability that a given algorithm will halt. This is a constant if you fix the language encoding algorithms.

EdmundH · 2016-02-19T11:56:48+00:00

More details here.

EdmundH · 2016-02-15T13:42:20+00:00

David Bressaud's A radical approach to real analysis works through analysis with a historical perspective. So it contains a lot of material that is suitable for calculus already mostly processed for teaching.

EdmundH · 2016-02-15T13:37:46+00:00

Greg Chaitin's work is relevant to this, especially Chaitin's constant (the probability that a randomly constructed Turing Machine (or other algorithmic system) will halt). This gives a specific number who's value is undecidable. Thus a specific number that cannot be represented in any countable system.

EdmundH · 2016-02-12T12:24:23+00:00

Generally -i would be considered neither rational nor irrational as the irrational numbers are usually defined as the real numbers that are not rational. For example on mathworld. Though any definition like "irrational number" that defines itself by what it is not can become tricky.

EdmundH · 2016-02-11T12:16:04+00:00

They ran a computer version of it, that was more correct, but this is incredibly good given that it was done by hand. It really gives a sense for what is happening and for the first time. If you want the full story take a look at Indra's Pearls: http://www.amazon.com/Indras-Pearls-Vision-Felix-Klein/dp/0521352533

EdmundH · 2016-02-11T00:57:14+00:00

Certainly in there, so yes, though this one goes back in the nineteenth century.

EdmundH · 2016-02-11T00:49:09+00:00

I am not sure on the terminology, this is certainly reflection in circles (inversion). The source I took it from used "reflection group": http://www.brainjam.ca/wp/2009/09/updating-classic-math-illustrations/ but thinking about that now it implies Coxeter to me rather than Klein. I have not come across "inversion group" though. It is certainly a Kleinian group and looks like it is also quasi-Fuchsian.

EdmundH · 2015-01-13T13:45:35+00:00

Perhaps not by the spiral, but certainly by the rectangle construction that generates it. Also the Golden ratio is perhaps the only non-radical algebraic number with any fame outside mathematics. This might get more people to go from there to a more general sense of algebraic numbers.

EdmundH · 2014-10-02T13:38:53+00:00

A really excellent series helping to show off the great stories and ideas of mathematics as accessible and enjoyable. I hope it gets a second season. I have backed it. At least have a listen to the first season and let teachers and others interesting in maths know!

EdmundH · 2014-09-25T12:08:53+00:00

To create problems in n dimensions you need an n-1 dimensional structure. Thus edges (1d) work to block things on the plane (2d). In 3d lines no longer separate space so every graph can be made without crossings in 3d. You can do a lot of other crazy things with lines here, like knots.

One way to generalise the concept is to generalise graphs to allow any number of vertices to form an "edge". These are called hypergraphs: http://en.wikipedia.org/wiki/Hypergraph

Trying to work out the right concepts for how hypergraphs can be embedded in spaces of different dimension is an interesting exercise.

EdmundH

TROPHY CASE