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What Does Pi Have To Do With Gravity?

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Re: What Does Pi Have To Do With Gravity?

#11

Post by claudius »

andrewflnr wrote: post #5
xonea wrote: post #4

Earlier quoted context omitted.

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.

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

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.

Re: What Does Pi Have To Do With Gravity?

#15

Post by shardling »

Camillo wrote: post #12

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

I guess I find that a weird comment -- the entire point of the article was the historical connection, so if that was the only thing that was interesting, how does that make it terrible?

It seems like most people on HN were expecting something very different, and so were disappointed when it was "just" a bit of history. As someone with a backbround in physics, but who had never heard this tidbit, I thought it was pretty neat.

Re: What Does Pi Have To Do With Gravity?

#17

Post by Someone »

claudius wrote: post #3
PankajGhosh wrote: post #2

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...

Yes, the definition of ‘1 metre’ s.t. a pendulum of this length has a period of 2 seconds (with some other, not length-related definition of seconds) only works in uniform gravity. But this wasn’t really a problem at the time these definitions were first made, as few people wanted to build metre sticks on the moon and the variations of g on the surface of Earth are likely to small to be measured given the usual exper…

You are underestimating early 19th century science, and even 17th century science. http://en.wikipedia.org/wiki/History_of_the_metre: "However, it was soon discovered that the length of a seconds pendulum varies from place to place: French astronomer Jean Richer had measured the 0.3% difference in length between Cayenne (in French Guiana) and Paris."

Richer discovered that while in French Guyana, between 1671 and 1673 (http://en.wikipedia.org/wiki/Jean_richer)

Re: What Does Pi Have To Do With Gravity?

#18

Post by 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

Re: What Does Pi Have To Do With Gravity?

#19

Post by madaxe »

shardling wrote: post #15
Camillo wrote: post #12

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

I guess I find that a weird comment -- the entire point of the article was the historical connection, so if that was the only thing that was interesting, how does that make it terrible? It seems like most people on HN were expecting something very different, and so were disappointed when it was "just" a bit of history. As someone with a backbround in physics, but who had never heard this tidbit, I thought it was pret…

Well, because his conclusion was basically "shit, I don't know, something to do with sine waves and SHM I guess".

I'd explain why here but it wouldn't fit in this margin.

Re: What Does Pi Have To Do With Gravity?

#20

Post by madaxe »

hmsimha wrote: post #8
andrewflnr wrote: post #5

Earlier quoted context omitted.

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

Exactly. I found this article sorely lacking of punch, however. It's like saying what does the meter have to do with the mass of the H2O molecule? Well 1 Kg is defined as the weight of 1 cubic meter of water at 1 atm.

1000 cubic centimetres - a cubic decimetre. Not a cubic meter. A cubic meter of water ways a ton.
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