sciman55 Posted January 25, 2006 Report Share Posted January 25, 2006 Is it possible to have a radius below zero; like 0.000002? Quote Link to comment Share on other sites More sharing options...
TheFaithfulStone Posted January 25, 2006 Report Share Posted January 25, 2006 Well, that radius is ABOVE zero. A radius of -2 or something? That doesn't make much sense. Your circle would be smaller than nothing. Mathematically, this may mean something, but radii smaller than zero are physically impossible. TFS Quote Link to comment Share on other sites More sharing options...
CraigD Posted January 25, 2006 Report Share Posted January 25, 2006 Is it possible to have a radius below zero; like 0.000002?0.000002 is a valid value to use as a radius in calculating anything about a circle, sphere, etc. In Math writing, the word “below” usually means “less than”. 0.000002 is not less than 0. I think sciman55 should have phrased the question “is it possible to have a radius less than 1?” to which the answer is “yes”. It’s not meaningful to consider a radius less than 0, such as -0.1 or -123. Allowing such a value result in circles with positive areas but negative circumferences, spheres with negative volume but positive surface areas, and other amusing but not very useful properties. Therefore, a sensible answer to “is it possible to have a radius less than 0?” is “no”. Quote Link to comment Share on other sites More sharing options...
Qfwfq Posted January 25, 2006 Report Share Posted January 25, 2006 Is it possible to have a radius below zero; like 0.000002?Apart from whether 0.0000002 is less than zero, geometry is concerned with positive values of length, area and volume. Only quantities such as a difference or variation might be negative. Quote Link to comment Share on other sites More sharing options...
sanctus Posted January 26, 2006 Report Share Posted January 26, 2006 And to complete Qfwfq any norm in any space (not forcefully a geometric one, but in a geometric one it is usual to speak about distances while it is just a norm for that space...not the only one) is defined to be definitely positive (that means that the norm is bigger or equal to zero and if it is equal to zero it implies that the quantity of which we take the norm is the zero element of that space). Quote Link to comment Share on other sites More sharing options...
Qfwfq Posted January 27, 2006 Report Share Posted January 27, 2006 any norm in any space (.....) is defined to be definitely positiveMinkowski's metric isn't positive definite! :( But Euclid's is and I was trying to be simple. Quote Link to comment Share on other sites More sharing options...
sanctus Posted January 28, 2006 Report Share Posted January 28, 2006 Complete black-out.... what is the relation between a metric and a norm? Quote Link to comment Share on other sites More sharing options...
Qfwfq Posted January 30, 2006 Report Share Posted January 30, 2006 :surprise: While a metric can be defined over any set and is an application from the cartesian square to R+, definition of a norm requires a vector space and its domain is the space "only once". However, a norm induces a metric canonically by norm of the vector difference. Quote Link to comment Share on other sites More sharing options...
sanctus Posted January 30, 2006 Report Share Posted January 30, 2006 therefore the minkowsky metric is only positive but definte positive. Yes it must be thing about simultaneity Quote Link to comment Share on other sites More sharing options...
Qfwfq Posted January 30, 2006 Report Share Posted January 30, 2006 Uh, :surprise: but.... Minkowski's metric ain't positive! The square of distance can be positive or negative! Quote Link to comment Share on other sites More sharing options...
sanctus Posted January 31, 2006 Report Share Posted January 31, 2006 yes now I remember time-like or space-likle distance accordingly. Quote Link to comment Share on other sites More sharing options...
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