Thursday, 22 June 2017

Irrational ^ Irrational

I came upon this very clever but simple proof recently ...

It is not known which irrational numbers x and y would make xy rational.  But it can be easily proved that such rational xy exists.  We know that 2 is irrational.  Take, for instance, the number


which must either be rational or irrational.  If it is rational, then we're done.  If it is not, then the number


must be rational.  So either case proves the existence of rational xy where both x and y are irrational.

Monday, 19 June 2017

Architectural compositions 2

More abstract compositions of architectural fragments ... all pictures were taken in London, 2016:





Sunday, 18 June 2017

Architectural compositions

I like using architectural fragments to create abstract compositions.  All pictures were taken in Toronto, 2017:





Saturday, 17 June 2017

Monday Night

Goto80's Monday Night from his latest album Floptrik just released yesterday:


Video from CPU Records' youtube channel

Friday, 16 June 2017