NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Finding The Symmedian
From: Peter Fogg
Date: 2010 Dec 28, 14:07 +1100
From: Peter Fogg
Date: 2010 Dec 28, 14:07 +1100
Herbert Prinz wrote:
A spurious blank in my previous message makes it difficult to read. It should have said:
Proof: AA' bisects angle A <-> x = y <-> x : y = 1 <-> b : c = 1 <-> b = c
............................................................................................................................
I did find that extra blank, although it didn't make a lot of difference as to how easy it was to read. I take it the notation reads: A is greater or lesser or the same as x which equals y, which is greater or lesser or the same as x : (what does the colon signify?)
Thanks for this, Herbert. Can you, or ayone else with an idea, explain why this Symmedian point should be preferred as defining the centre of a triangle over any other centre of a triangle?
In particular, what advantage does the Symmedian offer in comparison to a triangle centre which this site calls the Incenter:
On 2010-12-24 13:56, Peter Fogg wrote:Correct.
OK, I think I can answer my own question; the distances b and c are the lengths of the sides b and c of the triangle, which leads to another question:
if and only if b = c.
Does the line connecting A' and A bisect the angle A?
Proof: AA' bisects angle A <-> x = y < -> x : y = 1 <-> b : c = 1 <-> b = c
Herbert Prinz then amended the above with:
A spurious blank in my previous message makes it difficult to read. It should have said:
Proof: AA' bisects angle A <-> x = y <-> x : y = 1 <-> b : c = 1 <-> b = c
............................................................................................................................
I did find that extra blank, although it didn't make a lot of difference as to how easy it was to read. I take it the notation reads: A is greater or lesser or the same as x which equals y, which is greater or lesser or the same as x : (what does the colon signify?)
Thanks for this, Herbert. Can you, or ayone else with an idea, explain why this Symmedian point should be preferred as defining the centre of a triangle over any other centre of a triangle?
In particular, what advantage does the Symmedian offer in comparison to a triangle centre which this site calls the Incenter:
