MHB Calculating Ratio of $\overline{BP}$ to $\overline {PN}$ in Hexagon $ABCDEF$

  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Hexagon Ratio
Albert1
Messages
1,221
Reaction score
0
Regular hexagon $ABCDEF$,points $M$ and $N$ are midpoints of $\overline{CD}$
and $\overline {DE}$ respectively, point $P$ is the intersection of $\overline {AM}$ and $\overline{BN}$
Find $\dfrac {\overline{BP}}{\overline {PN}}$
 
Mathematics news on Phys.org
Albert said:
Regular hexagon $ABCDEF$,points $M$ and $N$ are midpoints of $\overline{CD}$
and $\overline {DE}$ respectively, point $P$ is the intersection of $\overline {AM}$ and $\overline{BN}$
Find $\dfrac {\overline{BP}}{\overline {PN}}$

 

Attachments

  • BP over  PN.jpg
    BP over PN.jpg
    25.4 KB · Views: 106
Last edited by a moderator:
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.

Similar threads

Replies
1
Views
1K
Replies
3
Views
2K
2
Replies
93
Views
11K
3
Replies
104
Views
16K
Replies
4
Views
3K
Replies
3
Views
2K
Back
Top