MHB Can a Philologist Crack Complex Math in Plato's Music Theory?

  • Thread starter Thread starter Kobzar
  • Start date Start date
Kobzar
Messages
11
Reaction score
0
Hello, everybody:

I am a philologist who is fond of mathematics, but who unfortunately has just an elementary high school knowledge of them. I am translating La leçon de Platon, by Dom Néroman (La Bégude de Mazenc, Arma Artis, 2002), which deals with music theory and mathematics in the works of Plato. The problem which brings me here is not about translation, but about mathematics. Please see attached document.

Any help will be welcome. Thank you very much in advance!

Best regards.

Kobzar.
 

Attachments

Mathematics news on Phys.org
Rewrite the first equation as $y=\dfrac{M-x^2}{2x}$ and then substitute into the second equation. After quite a bit of multiplying, you will get $5x^4-(2M+4N)x^2+m^2=0$. Use the quadratic formula to solve for $x^2$ and you will get the value for $x^2$ given in the statement. The value for $y^2$ is incorrect. In addition to the error in the denominator that you pointed out, there is another error in the numerator.
 
mrtwhs said:
Rewrite the first equation as $y=\dfrac{M-x^2}{2x}$ and then substitute into the second equation. After quite a bit of multiplying, you will get $5x^4-(2M+4N)x^2+m^2=0$. Use the quadratic formula to solve for $x^2$ and you will get the value for $x^2$ given in the statement. The value for $y^2$ is incorrect. In addition to the error in the denominator that you pointed out, there is another error in the numerator.
Thank you very much for your useful and quick answer!
 
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

Back
Top