[AntonioLao]

A friend of Socrates (450 B.C.) known only by the name of Hippias had taken to himself the task of solving the problem of measuring the area of a circle. 2 458 years later, his quadratrix arc can be argued to represent the existence of a quarter turn (p/2) around the circumference of a unit circle. This arc has a missing end point known as the indeterminate 0/0 where the numerator denotes zero ordinate and the denominator denotes zero angles. However, using arguments derived from theory of limits, the value of the limiting point is 2/p or (p/2)(2/p)=1 radian, that is a unit circle exists independent of any unit of measurement whether feet, meters, miles, or kilometers.

[Profpat]

Hi AntonioLao;

Wouldn't you still have a problem since pi is an approximation with no exact value?

Best to you,

Pat

[AntonioLao]

Originally Posted by Profpat still have a problem since pi is an approximation with no exact value

Pi is an irrational number. However, its approximation in terms of rational numbers as first noted by Archimedes is 22/7. For the above, it is simply canceled out of the expression.

[Profpat]

Thanks for your quick answer.

[AntonioLao]

Originally Posted by Profpat quick answer

But it took mathematicians more than 1000 years to make the distinction between rationals and irrationals otherwise known as Dedekind Cut see http://en.wikipedia.org/wiki/Dedekind_cut

[mkirkpatrick]

Surely if we put limits on our investigations into reality,we will fall short of our goal!


regards michael.

[AntonioLao]

Originally Posted by mkirkpatrick we will fall short of our goal

If we don't take the time to do it or simply run out of time to do it. In the upcoming Superbowl match between the Giants and the Patriots anybody can win but time will always runs out and decided at the last 2 minutes if tied then there is overtime and so on until somebody wins.

[Profpat]

I may be wrong but I'm putting my money on the Pats. Thanks for the link, as you are aware geometry is not my strong suit.

Best to both of you,

Pat

[AntonioLao]

Originally Posted by Profpat geometry is not my strong suit

You mean Euclidean geometry? But dont worry. Mathematicians dont. On the other hand, what they worry about now is non-Euclidean geometries: elliptic and hyperbolic and that abstract idea of analysis situs known as topology.

[mkirkpatrick]

Originally Posted by AntonioLao If we don't take the time to do it or simply run out of time to do it. In the upcoming Superbowl match between the Giants and the Patriots anybody can win but time will always runs out and decided at the last 2 minutes if tied then there is overtime and so on until somebody wins.

Can't say i have ever watched a match,the only bowl I have here is a breakfast bowl
for my cornflakes!


regards michael.