

What Does Pi Have To Do With Gravity? - mitmads
http://www.wired.com/wiredscience/2013/03/what-does-pi-have-to-do-with-gravity/

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Camillo
This is a terrible article in both content and form. Pretty much the only
interesting thing in it is the historical connection between the seconds
pendulum and the metre, but then you could just read this instead:
<http://en.wikipedia.org/wiki/History_of_the_metre>

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Aardwolf
Why is meter spelled "metre" in English? English is a Germanic language, and
Germanic languages like Dutch and German happen to have the perfectly
reasonable word "meter" for this. But for some reason English chose the
romance French spelling "metre", that looks really odd outside of French. Why?

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Camillo
Because the word has its origin in the Greek _metron_ , and has nothing to do
with Germanic languages whatsoever.

Besides, there are countless precedents of English words with a mute final "e"
and a schwa inserted between two consonants, e.g. "little".

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shardling
For anyone hoping for some deeper fundamental connection, you should read
about natural units[1] to understand why that couldn't happen.

Given a dimensional constant, it can only be related to some more fundamental
mathematical constant in a particular set of units. So the connection will be
entirely due to how the units are defined, as is the case here.

1\. <http://en.wikipedia.org/wiki/Natural_units>

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PankajGhosh
Wouldn't this relationship only exist on earth (to be exact on surface of
earth)? Unless we redefine 1 meter of length depending on gravitational field
on every surface of planet/star...

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xonea
Yup. So - the answer to the question "What Does Pi Have To Do With Gravity" is
pretty much - nothing.

The article also notes that it does not work it you use feet instead of
meters, hence basically already answering the question.

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andrewflnr
No, the answer is that our units were constructed so that pi has something to
do with gravity.

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claudius
If you think of π as the relation between the circumference of a circle and
its diameter, then it does have _something_ to do with gravity (and
dimensions) - in a one-dimensional world, for example, the force of gravity
would not fall of with distance, as it is the gravitational flux that is
conserved. If there is only one dimension, there's no way for it to disperse
away from a body, hence it is constant.

If you then add another dimension (a flat world of two spatial dimensions),
you suddenly get a 1/r relation for the force (log(r) for the potential) as
the gravitational flux can now disperse in two dimensions. Naturally, a
constant comes in here, which is a function of π. The argument naturally
extends to three dimensions to give you 1/r² and a more complicated
coefficient.

Naturally, this also applies to other classical forces, viz. electromagnetism.

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Retric
That depends on how you pick the gravitational constant. It's trivial to make
e show up in gravitational equations but with the right g you can avoid pi in
a our world. At which point you can play around with a different number of
dimensions, but that's just math and has nothing to do with physics.

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prof_hobart
>Does it look like the local gravitational field on the surface of the Earth,
g? Well, no – it doesn’t because it doesn’t have any units.

Well, no - because it's a different number. Given that, the rest of the
article just seems rather odd.

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georgecmu
_In 1668, Wilkins proposed using Christopher Wren's suggestion of a pendulum
with a half-period of one second to measure a standard length that Christiaan
Huygens had observed to be 38 Rijnland inches or 39 1⁄4 English inches (997
mm) in length.[3] In the 18th century, there were two favoured approaches to
the definition of the standard unit of length. One approach followed Wilkins
in defining the metre as the length of a pendulum with a half-period of one
second, a 'seconds pendulum'._

 _In 1791, the French Academy of Sciences selected the meridional definition
over the pendular definition because the force of gravity varies slightly over
the surface of the Earth, which affects the period of a pendulum._

<http://en.wikipedia.org/wiki/Metre#Meridional_definition>

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calhoun137
This is what i was hoping to read in this article:

If pi is defined as the ratio of the circumference of a circle to its
diameter, then a gravitational field indeed changes pi, and by measuring this
change, its possible to measure the strength of gravity.

A quick way to understand this is to realize that "straight lines" (geodesics)
are defined as the path taken by a beam of light, and gravity causes the path
of light to bend. Measuring the difference is the same as measuring the
curvature of space time, which when multiplied by a constant IS the strength
of the gravitational field according to general relativity.

Another way to see it: take a sphere and draw a circle on it, then measure pi.
You can determine the curvature of the sphere once you measure the difference
with pi on a flat piece of paper.

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pardner
I spent $3.14 (USD) on a latte this morning.

~~~
cleaver
And if you drink a whole lotta lattes, you will start to feel stronger
gravitational attraction to nearby masses such as the earth.

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madiator
Was hoping to see some relation with the big G, but the author instead used
small g, which depends on all kinds of things and cannot be treated as a
constant.

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shardling
It wasn't up to the author! He's just relaying a historical point.

