Chronology |
Current Month |
Current Thread |
Current Date |

[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |

*From*: David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>*Date*: Mon, 16 Aug 2004 21:35:56 -0400

Regarding Carl's latest attempt:

Okay, one last attempt. If I interchange the order of integration I

now find:

area = s - 2*integral from 0 to s/2 of {dY/sqrt(1+tan^2(A)*sin^2(Y)}

That integral almost looks like an elliptic integral, except for the

sign in front of the trig fn. It has the correct (trivial) limiting

values for A = 0 and 90 degrees. Carl

Sorry, but your formula *doesn't* have the correct limiting value for

small s. In the small s limit the expression above approaches

area = (s^3)/8

(which is dimensionally impossible). But the correct limiting

formula for the small s area is

area = (sqrt(3)/4)*s^2 .

Also, when the side length s is small A *does* not go to zero; it

goes to 60 deg (whose squared tangent is 3).

David Bowman

- Prev by Date:
**Re: spherical geometry** - Next by Date:
**Re: Stone skipping. Was: Re: bending of object thrown into pool** - Previous by thread:
**Re: spherical geometry** - Next by thread:
**Re: spherical geometry** - Index(es):