Stream of approximations of ϕ

Nice. Are you doing the exercises in SICP or something?

Nope! I just remembered that ϕ=1+1/ϕ and made a stream of that with more and more terms.

Cool. Nice having a mathematician around. :~)

A mathematician that likes math.

$$\phi=\sqrt{1+\phi}$$

Is there another kind?

Mathematicians that don't like math, but rather are forced to use it?

Will it converge to the golden ratio no matter what starting value you give it?

If I'm not mistaken, yes it does.

Such a person is not a mathematician. They might be an engineer, or an accountant, or a student. To be a mathematician, you have to consider ei𝜋+1=0 the most beautiful thing in the world.

Do you mean $$e^{i\tau}=1$$?

No, 𝑒𝑖𝜋 = −1, but with the −1 moved to the left side. Euler's identity.

Grr, you made me spend two hours in a rabbit hole. Interesting argument. (Except for the puns.) But today is 𝜋 Day; maybe on 6/28 I'll be more receptive. :~)

I think of it as $$e^{\pi i}=-1$$

I don't like $$\tau$$, I prefer $$c=2\pi r$$.

In fact, I had a $$\pi$$ pie and stayed up the whole night watching videos.

Why?

IDK, I just don't like tau.

Your way is fine, but people usually present it the other way so as to have the five fundamental mathematical constants (including additive and multiplicative identity elements) in one equation.

The shape, or the value itself?

Neither. It's a nice letter, and I have nothing against it being $$2\pi$$; I just don't like it being used as the main circle constant.