MHB Can an Ellipse Help Solve the Scalene Triangle Problem?

  • Thread starter Thread starter Samwise-zambeezi
  • Start date Start date
  • Tags Tags
    Triangle
Samwise-zambeezi
Messages
6
Reaction score
0
Hi guys!

I've got a problem with a triangle, and I'm frazzled my brain trying to work it out (not even sure if what I'm looking for is possible with the info I have!).

Pic of the offending triangle attached.

Basically, I know the length of C and the sum of lengths A and B.

Now, if C was static and remained unchanged, but if the point c was to move, lengths A and B would change. I'm trying to find the individual lengths of A and B at the point at which, C is split with a vertical into two equal angles (f and g).

Is this possible? Hope this is clear enough, any tips would be a massive help.

Best regards

Swise
 

Attachments

  • 20220221_185236.jpg
    20220221_185236.jpg
    1.2 MB · Views: 115
Mathematics news on Phys.org
Screenshot 2022-02-21 at 21.21.41.png


If the point $c$ moves so that the sum of its lengths to $a$ and $b$ is constant, then its locus will be an ellipse (the red curve in the diagram) with one focus at $a$ and the other one at $b$. The vertical line through $c$ will bisect the angle between the blue lines through $c$ at the point where the tangent to the ellipse is horizontal, as in the diagram. In other words, this happens at the lowest point of the ellipse. As far as I know, there is no purely geometric way of constructing this point.

In physics, if there is a light source at one focus of an ellipse then the light rays from it will all be focused at the other focus. (That is the reason for using the term focus for these points.) This means that the two blue lines from $c$, to $a$ and $b$, make equal angles with the tangent at $c$. Therefore the line perpendicular to the tangent (in this case, the vertical line) bisects the angle between the blue lines.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top