Things you don't need to know...

[Redglyph]

Here's a real and imaginary (stipled) plot of the function using Mathematica. The imaginary part passes 0 for x=2 and 3, where the real part is 1.
[..]

Actually, there's an easy way to see it, a real value can be expressed in polar form as r * (cos α + i sin α), where α happens to be a multiple of pi (180°). Exponentiating that by y yields r^y * (cos αy + i sin αy), so there is no reason why it shouldn't be continuous as long as y is continuous. It is real when αy is a multiple of pi, so when y is an integer.
It's probably not easy for most programs to check that, since they approach the solutions from a numerical point of view and not an analytical. I'm a bit disappointed that Mathematica didn't find it though.

 

[Corwin]

Impressing.

I solved it in less than a minute with nothing but a pen and paper. Who needs all these complex programs!!

 

[Taluntain]

What are you guys, a bunch of maths professors or something? I've forgotten everything maths above primary school level by now...

 

[Corwin]

I taught high school maths for many years!!

 

[HiddenX]

I have a university diploma (nowadays called master) in business mathematics.
A combination of informatics, mathematics and operations research

 

[pibbuR]

And I have a master in informatics and mathematics is one of my hobbies.

pibbuR who as far as he can remember (and to some degree repressed) also at some time dabbled in medicine

 

[Redglyph]

I'm an engineer (microelectronics - nothing to do with bridges), so I ate differential equations for breakfast at uni. It was a few years ago, though, and it shows, those complex subdomains confused me at first. It saddens me that most of that knowledge is gone for not using it...

What? There was no need for pen & paper here, extracting those integer roots can easily be done mentally. But I did check the graph with this, which seems pretty fast (but it failed to plot the discrete values).

 

[Corwin]

While doing it mentally is obviously not overly difficult, I always taught my students to do all work on paper as good technique and as evidence of their thought processes. Old habits die hard!!

 

[Couchpotato]

I was a simple blue collar warehouse manager. Math is not my major. My job was logistics and getting China made crap to every store in ten states. So yeah does not compute.

 

[pibbuR]

I was a simple blue collar warehouse manager. Math is not my major. My job was logistics and getting China made crap to every store in ten states. So yeah does not compute.

That's ok, no disrespect. Honestly, I would do a terrible job at handling logistics.

This is a thread where everybody is free to post things that they find interesting, but many others do not. That being said, I sometimes wonder if things like math is too ... whattocallit ... much of special interest to very few watchers.

dpibbu(R)/dR

 

[Redglyph]

To be honest, now that there's always a calculator nearby in our lives, I tend to be lazy and not often calculate mentally. Smartphones and Internet are the most tempting tools that diminish our personal abilities if not checked. But then they can amplify them too.

I wonder where interest for maths is coming from. I suppose it's a good teach in young age or a parent who said just the right things, like for any other domain. But otherwise maths seems to be the less liked course overall. Even worse is the stats and probability branches (which I really liked, something must be wrong with me).

But yeah, maths has its uses but it's not everything. Logistics must be quite challenging, I had to work with a logistic department in another life (installing cancer treatment systems into hospitals) and they did miracles to find all the pieces, send them to manufacturers, get them back and so on. Never understood how they could keep track of it all. (or cope up with off-putting software like SAP)

I sometimes wonder if things like math is too ... whattocallit ... much of special interest to very few watchers.

Geeky, nerdy?

 

[pibbuR]

According to my sources (https://www.theregister.com/2022/09/19/jupiter_70_years_closest_approach/?td=rt-3a) next Monday (26.09.2022) Jupiter will make closest approach to Earth in 70 years. 587 million kilometres.

Now, a question: Which planet is the closest to earth?

pibbuR

 

[pibbuR]

So, nobody knows?

Answer depends on how you interprete the question: At it's closest, nothing beats Venus. But on the average: It's Mercury, due to it's distance from us compared to the other planets from behind the sun, and it's short circulation period. Actually, Mercury is the closest to any planet in the solar system.

 

[bkrueger]

So, nobody knows?

Answer depends on how you interprete the question: At it's closest, nothing beats Venus. But on the average: It's Mercury, due to it's distance from us compared to the other planets from behind the sun, and it's short circulation period. Actually, Mercury is the closest to any planet in the solar system.

Interesting information!

As a mathematician, however, I would claim that earth itself is the planet next to earth, with a distance of zero.

 

[pibbuR]

Interesting information!

As a mathematician, however, I would claim that earth itself is the planet next to earth, with a distance of zero.

Of cource.

Rephrasing the question: Which planet, excluding earth is the closest to earth? Answer: Mercury.

Or in general: Which planet is the closest to any planet in the solar system, excluding the planet itself (apart from Mercury)? Answer: Mercury.

pibbuR who bows to the mathematician.

 

[bkrueger]

Related question: Which is the fixed star nearest to earth?

 

[pibbuR]

1. The sun.
2. Proxima centauri.

pibbuR who for 5 seconds was fooled.

 

[HiddenX]

The sun is not a fixed star by definition.

 

[bkrueger]

1. The sun.
2. Proxima centauri.

pibbuR who for 5 seconds was fooled.

Correct. And a reward of merit for the second place.

The sun is not a fixed star by definition.

What?

 

[HiddenX]

Correct. And a reward of merit for the second place.

What?

Fixed stars
From Wikipedia, the free encyclopedia

This article may be confusing or unclear to readers. Please help clarify the article. There might be a discussion about this on the talk page. (August 2020) (Learn how and when to remove this template message)
Kepler, Johannes. Mysterium Cosmographicum, 1596. Kepler's heliocentric rendition of the cosmos, containing an outermost “sphaera stellar fixar,” or sphere of fixed stars.

The fixed stars (Latin: stellae fixae) compose the background of astronomical objects that appear not to move relative to one another in the night sky, unlike the foreground of Solar System objects, which appear to move. Generally, the fixed stars are taken to include all stars other than the Sun. Nebulae and other deep-sky objects may also be counted among the fixed stars.

Exact delimitation of the term is complicated by the fact that celestial objects are in fact not fixed with respect to one another. Nonetheless, extrasolar objects move so slowly in the sky that the change in their relative positions is nearly imperceptible on typical human timescales, except to careful examination, and so can be considered to be "fixed" for many purposes. Furthermore, distant stars and galaxies move even more slowly in the sky than comparatively closer ones.

People in many cultures have imagined that the stars form constellations, which are apparent pictures in the sky. In Ancient Greek astronomy, the fixed stars were believed to exist on a giant celestial sphere, or firmament, which revolves daily around the Earth.