
Isochronous Curves - anonu
https://en.wikipedia.org/wiki/Tautochrone_curve
======
davidmurdoch
Adam Savage builds a brachistochrone curve, which is the same curve as an
Isochronous, just with potentially different starting/ending points, with
Vsauce's Michael Stevens. It's a pretty bizarre phenomenon:
[https://youtu.be/skvnj67YGmw](https://youtu.be/skvnj67YGmw)

~~~
agumonkey
They should build tautochronous pendulums. Or just add a spring bouncer on the
end of the tracks so to enjoy multiple simultaneous bounces of different
heights.

~~~
monochromatic
For small displacements, pendulums are already approximately isochronous.

~~~
pantalaimon
One of the first definitions of the meter was a pendulum with a period of 1s
afaik

~~~
hexane360
Surely you mean 2 seconds?

    
    
      T = 2*pi*sqrt(L/g) = 2*pi*sqrt(1 m / 9.81 m/s^2) = 2.01 s

------
lifeisstillgood
Is this off the back of a video of a 1970s Open University style presenter
showing the properties of isochromus curves - i loved watching it and realised
that these are national treasures of programs - and also was quite stunned by
the assumption one would have a round empty tobacco tin lying around to do the
experiment with - times do chnage :-)

~~~
quietbritishjim
I suspect it is... It turned up in my YouTube suggestions yesterday. Here's a
link:

[https://youtu.be/eBc827pwKf0](https://youtu.be/eBc827pwKf0)

~~~
escapologybb
I think we three are in the same Google Bubble as I've just finished watching
that glorious Open University video. If the algorithm wills it, I think it
means we have to be best friends!

Seriously though, I would be weirdly fascinated to see what else you guys
subscribe to and if there are any correlations to my subscriptions. I find
this channelling people into little boxes fascinating, and those curves are
also very cool.

~~~
anonu
Engineer guy, slow mo guys, motherboard vice, primitive technology, smarter
everyday

~~~
escapologybb
We have a winner! I'm subscribed to all of those.

~~~
lifeisstillgood
It strikes me that, as YouTube puts its hand into the bag to pull out a
marble, there are probably just a lot less marbles than we think, and
certainly less marbles worth watching than we think, and far far less worth
watching that have been made in the past week?

Additionally, if youtube was forced to only play videos where copyright was
proven to belong to the owner of the channel, would it collapse completely.

Is that perhaps what is shrinking the bag of marbles ?

Which interestingly suggests that if we force youtube to actually respect IP,
it would reward new creators of quality work more proportionately

------
ur-whale
Variation calculus is a great lens through which to look at many physics and
CS problems. It is IMO under-taught and under-utilized, especially in the
machine learning discipline.

The framework is basically minimization in functional space (as opposed to R^n
or a subset thereof, the more common case).

The (to me) surprising thing is that finding an extremum in functional space
(i.e. infinite-dimensional space) can be reduced to solving a differential
equation, via Euler–Lagrange.

The first problem feels intractable, while the second is "just" numerical
integration.

~~~
montalbano
Feynman on Calculus of variations:

“When I was in high school, my physics teacher—whose name was Mr. Bader—called
me down one day after physics class and said, ‘You look bored; I want to tell
you something interesting.’ Then he told me something which I found absolutely
fascinating, and have, since then, always found fascinating. Every time the
subject comes up, I work on it. In fact, when I began to prepare this lecture
I found myself making more analyses on the thing. Instead of worrying about
the lecture, I got involved in a new problem. The subject is this—the
principle of least action."

The rest at:
[http://www.feynmanlectures.caltech.edu/II_19.html](http://www.feynmanlectures.caltech.edu/II_19.html)

~~~
ur-whale
If physics is your thing, and it certainly was Feynman's, it'd be hard not to
be fascinated by the calculus of variations, it shows up all over the place:

    
    
       - principle of least action (lagrangians)
       - adiabatic cycles in thermodynamics
       - quantum mechanics
       - etc..
    

and I'm probably missing another 100.

Looks like it's a fairly fundamental thing in the world.

------
tacon
The same term has been adopted in transportation planning, for the curves of
equal commute time to a job location, etc. Google has an incredible amount of
data about this, but I don't know that it has been made available in any
usable form.

~~~
neverhigh
Google offers it on a bilateral basis for cash. Resources of
[http://iso4app.net](http://iso4app.net) are great and prices are ok.

~~~
creato
This comment is pretty interesting, it's almost indistinguishable from the "I
work from home and make $10k a week!!" facebook posts plaguing comment
sections... but it might make legitimate sense in context!

The only way to find out is to click the link.

edit: And it's legit!

~~~
ehsankia
Aren't half the comments on HackerNews basically "I work on a similar project,
check out my project"? Although extra suspicious when it's a green user.

Which to be fair, I'm entirely fine with as long as the projects are
legitimate. In the world of programming, there are so many cool and useful
libraries, services and tools out there that you have little hope to find out
about them otherwise.

~~~
creato
I actually wasn't even thinking about whether the poster I replied to was the
owner of that project or not.

------
amai
An important related question you dared to ask:
[https://physics.stackexchange.com/questions/348242/can-a-
cyc...](https://physics.stackexchange.com/questions/348242/can-a-cycloidal-
pendulum-be-extended-to-make-a-full-swing)

------
foobarbecue
What is the relationship between involute and isochronus curves?

------
ryanmarr
hmmmm. I hadn't been here since Friday, and now I see this link shared after I
was randomly on this wikipedia entry 30 minutes ago... That's odd.

------
amelius
Applications?

~~~
enriquto
This is a toy application of the calculus of variations, which is the
mathematical theory behind the equilibrium of continuous structures and many
other things. How can you build the strongest bridge with a given amount of
material? A similar computation to that of isochronous curves gives you the
answer.

