B Quadratic with simple meaningful intuitive constants

  • B
  • Thread starter Thread starter PaulDiddams
  • Start date Start date
  • Tags Tags
    Constants Quadratic
PaulDiddams
Messages
2
Reaction score
0
TL;DR Summary
A simple quadratic rearrangement that uses the intercept and the values of x and y that define the maxima or minima, in place of a, b and c, to drive a quadratic function. (demo Excel sheet attached).
Ever made a simple model that fits a quadratic function?

Tweaking the a, b and c constants to fit new observed data is a bit of a pain.

When I was a grad. student I came up with the following simple quadratic rearrangement that uses the intercept (Yo) and the values of x and y that define the maxima or minima (Xm, Ym) in place of non-intuitive a, b and c constants to drive the quadratic function. I also include rearrangements to calculate x from y, or Yo which I often find very useful too.

I would appreciate being credited "Diddams equation" if you choose to use my rearrangement. I think it's really neat and very powerful.

Enjoy.

1649843609412.png
 

Attachments

Mathematics news on Phys.org
That's a simple rearrangement exercise for high school, done millions of times before.
Naming things after yourself is frowned upon by the way. Even if it were something new.
 
mfb said:
That's a simple rearrangement exercise for high school, done millions of times before.
Naming things after yourself is frowned upon by the way. Even if it were something new.
I've been using this rearrangement for over 30 years now and neither I nor anyone I know has ever seen it done before, and my colleagues have been referring to it by that name for point of reference. If you have references where it's been done and shared before I'm interested to see them.
 
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
8
Views
3K
Replies
3
Views
4K
Replies
3
Views
2K
Replies
48
Views
34K
Replies
25
Views
3K
Replies
2
Views
1K
Replies
7
Views
4K
Back
Top