Mathematical simplicity.

Mathematics isn't always simple.

But sometimes, with a little thought, we can find very simple shortcuts,
which are, however, surprisingly true.

We said that in quadratic functions f(x), for example, it was enough to
change the sign of the monomial with an even exponent to obtain the point-symmetric function $ (for those who follow) called g(x).

This function g(x) has real roots if f(x) doesn't, having only two complex roots.

Now, what does [-b±sqrt(b²-4ac)]/2a become if we change the sign of a?

It becomes [-b±sqrt(b²+4ac)]/(-2a)

It's mathematical.

But that's not all, you'll remember, if you remember anything from what I
said earlier: I said that the complex roots of a function are pure
imaginaries, and that they are found by rotating f(x) 180° about the
point $(0,y₀ ) to form g(x).

We then have here, directly, the complex roots of f(x), given in pure imaginaries, as should always be the case if we correctly understand what
we are doing. Notations like x'=2+3i or x"=-3-i are a mathematical joke.

Real roots of quadratic functions: x= [-b±sqrt(b²-4ac)]/2a

Complex roots of quadratic functions:
x= {-[b±sqrt(b²+4ac)]/(2a)}.i

Beware of sign errors (the big trap of complex roots).

Example, let's set f(x)=x²+4x+5

x'=i

x"=-5i

If you replace x with i or -5i, you will get f(x)=0.

If you can't do this, it's because you haven't understood how imaginary
numbers work, like 100% of the human beings on this earth.

Thank you for your attention.

R.H.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Le 06/04/2025 à 02:18, Ross Finlayson a écrit :

On 04/05/2025 03:35 PM, Richard Hachel wrote:

Mathematical simplicity.

Mathematics isn't always simple.

(BS cut)

R.H.

I image you're familiar with Schwarz functions.

Hachel's mathematical level is roughly equivalent to the US 9th grade
(maybe less) :)
Everything after Pythagore is difficult for him.

BTW, I guess you were talking about the Schwarz functions, that map a
complex curve into its conjugate, and not the Schwartz functions (from
Laurent Schwartz) that are elements of a Schwartz space (even more
difficult to understand for a 70 year old 9th grader :)


--
F.J.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Le 06/04/2025 à 10:49, efji a écrit :

Le 06/04/2025 à 02:18, Ross Finlayson a écrit :

On 04/05/2025 03:35 PM, Richard Hachel wrote:

Mathematical simplicity.

Mathematics isn't always simple.

(BS cut)

R.H.

I image you're familiar with Schwarz functions.

Hachel's mathematical level is roughly equivalent to the US 9th grade
(maybe less) :)
Everything after Pythagore is difficult for him.

Note that g(x)=-f(-x)+2y₀ in all cases.

Même Python est tombé d'accord là-dessus et n'a pas osé contredire.
:))

R.H.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Am 06.04.2025 um 10:49 schrieb efji:

On 04/05/2025 03:35 PM, Richard Hachel wrote:

Mathematics isn't always simple.

Actually, it's not really simple at all (in general).

That's why idiots (like RH, WM, JG, etc.) are't able to complehend
mathematics.

Hachel's mathematical level is roughly equivalent to the US 9th grade
(maybe less) :) Everything after Pythagore is difficult for him.

Yeah, obviously.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Le 08/04/2025 à 02:49, Moebius a écrit :

Am 06.04.2025 um 10:49 schrieb efji:

On 04/05/2025 03:35 PM, Richard Hachel wrote:

Mathematics isn't always simple.

Actually, it's not really simple at all (in general).

That's why idiots (like RH, WM, JG, etc.) are't able to complehend mathematics.

Hachel's mathematical level is roughly equivalent to the US 9th grade
(maybe less) :) Everything after Pythagore is difficult for him.

Yeah, obviously.

Not obviously.

If this were true, there would be no need to repeat it over and over
again.

R.H.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Le 08/04/2025 à 15:36, FromTheRafters a écrit :

Richard Hachel formulated the question :

Le 08/04/2025 à 02:49, Moebius a écrit :

Am 06.04.2025 um 10:49 schrieb efji:

On 04/05/2025 03:35 PM, Richard Hachel wrote:

Mathematics isn't always simple.

Actually, it's not really simple at all (in general).

That's why idiots (like RH, WM, JG, etc.) are't able to complehend
mathematics.

Hachel's mathematical level is roughly equivalent to the US 9th grade
(maybe less) :) Everything after Pythagore is difficult for him.

Yeah, obviously.

Not obviously.

If this were true, there would be no need to repeat it over and over again.

I've heard it over and over again that 1+1=2, so you're saying it must
not be true then?

Stupid and irrelevant remarks. During the Molotov-Ribbentrop Agreement,
the Russians spat on de Gaulle, saying he was a nobody, an imperialist,
and a careerist.
But when Hitler sent three army corps across the eastern plains, the song
was no longer the same, and all over Russian airwaves, people sang the greatness of Free France and their valiant general.
All this is futile and serves no purpose.

R.H.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)