project . 2011 - 2015 . Closed

Real Geometry and Connectedness via Triangular Description

UK Research and Innovation
  • Funder: UK Research and InnovationProject code: EP/J003247/1
  • Funded under: EPSRC Funder Contribution: 359,554 GBP
  • Status: Closed
  • Start Date
    30 Sep 2011
    End Date
    31 Dec 2015
Description
Connectedness, as in "can we get there from here", is a fundamental concept, both in actual space and in various abstract spaces. Consider a long ladder in a right-angled corridor: can it get round the corner? Calling it a corridor implies that it is connected in actual three-dimensional space. But if we consider the space of configurations of the ladder, this is determined by the position and orientation of the ladder, and the `corridor' is now the requirement that no part of the ladder run into the walls - it is not sufficient that the ends of the ladder be clear of the walls. If the ladder is too long, it may have two feasible positions, one in each...
Description
Connectedness, as in "can we get there from here", is a fundamental concept, both in actual space and in various abstract spaces. Consider a long ladder in a right-angled corridor: can it get round the corner? Calling it a corridor implies that it is connected in actual three-dimensional space. But if we consider the space of configurations of the ladder, this is determined by the position and orientation of the ladder, and the `corridor' is now the requirement that no part of the ladder run into the walls - it is not sufficient that the ends of the ladder be clear of the walls. If the ladder is too long, it may have two feasible positions, one in each...
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