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Topic: triangular numbers and dets
Replies: 32   Last Post: Apr 26, 2012 1:53 PM

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 Dan Cass Posts: 442 Registered: 12/6/04
Re: triangular numbers and dets
Posted: Apr 25, 2012 5:05 PM

By the way I just tried the e-mail you noted and it
immediately bounced back, saying "undeliverable".

Anyway some remarks...
===================================

If the angle between the 7 and 33 sides is 60 then the third side satisfies

c^2 = 7^2 +33^2 - 2*7*33*cos(60), which since cos(60) = 1/2 gives

c^2 = 7^2 - 7*33 + 33^2 so that c = 37.

[I didn't see the relevance of the equation to triangles...]

The area formula for a triangle of sides a,b with angle theta included is

A = (1/2)*a*b*sin(theta).

So here the triangle has area (1/2)*7*33*sin(60) = (231/4)*sqrt(3).

So it's really only a coincidence it comes out nearly an integer...

In fact with integer sides for a,b and integer c with angle 60 between

the shorter sides, the area will always be a rational multiple of sqrt(3).

I've heard of the topic of finding triangles with integer sides and area,

I think they're called "Heronian triangles"...

Date Subject Author
3/29/12 jm bergot
4/3/12 Dan Cass
4/3/12 jm bergot
4/4/12 Dan Cass
4/4/12 jm bergot
4/4/12 Dan Cass
4/5/12 jm bergot
4/7/12 Dan Cass
4/10/12 jm bergot
4/11/12 Dan Cass
4/11/12 Dan Cass
4/12/12 jm bergot
4/12/12 Dan Cass
4/12/12 jm bergot
4/16/12 Dan Cass
4/16/12 jm bergot
4/17/12 jm bergot
4/17/12 jm bergot
4/17/12 Dan Cass
4/18/12 jm bergot
4/19/12 Dan Cass
4/19/12 Dan Cass
4/19/12 jm bergot
4/19/12 jm bergot
4/19/12 Dan Cass
4/19/12 jm bergot
4/20/12 jm bergot
4/24/12 Dan Cass
4/21/12 jm bergot
4/25/12 jm bergot
4/25/12 jm bergot
4/25/12 Dan Cass
4/26/12 jm bergot