What Does Pi Have To Do With Gravity?

http://www.wired.com/wiredscience/2013/03/what-does-pi-have-to-do-with-gravity/

by mitmads • 13 years ago

34 28 13 years ago

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...

claudius2• 13 years ago

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 experimental errors in the 19th century.

Nervertheless, the correct constant should be τ[0] anyways.

[0] http://tauday.com/

Someone• 13 years ago

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)

xonea• 13 years ago

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.

andrewflnr• 13 years ago

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

madaxe4• 13 years ago

Pi relates to SI units, but not gravity.

Unless you wanna be esoteric and go herp derp g=(GMm)/((orbital circumference)/2pi)^2 at which point tada QED!

Also tidal forces, lots of pi when your cranking those out. And keplers laws of planetary motion, which last I checked are all about gravity.

pardner• 13 years ago

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

notdrunkatall• 13 years ago

I spent 3.14 seconds deciding that this was a funny comment.

COINCIDENCE???

cleaver• 13 years ago

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

madiator• 13 years ago

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.

shardling4• 13 years ago

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

shardling4• 13 years ago

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

Camillo3• 13 years ago

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

shardling4• 13 years ago

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.

madaxe4• 13 years ago

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.

Camillo3• 13 years ago

Because it was horribly written, even for a random blog post; and because the time spent reading it could have been better spent reading the Wikipedia article, which would have been both more informative and more pleasant.

Basically, the author wrote a rehash that is worse than its source in every possible way. The only reason to do that is when you're forced to do it, as with an essay in school, or, in this author's case, an arbitrary requirement to write something for Pi day. But that's still no reason to post it on HN.

Aardwolf• 13 years ago

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?

madaxe4• 13 years ago

We formalised spelling in the 18th c., independently of one another. No particular reason beyond that, afaik.

opminion• 13 years ago

It's consistent with "centre" vs American "center"

Camillo3• 13 years ago

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".

prof_hobart• 13 years ago

>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.

georgecmu• 13 years ago

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

calhoun137• 13 years ago

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.

What Does Pi Have To Do With Gravity?

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