What Does Pi Have To Do With Gravity?
wired.com
wired.com
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.
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.
I'd explain why here but it wouldn't fit in this margin.
Besides, there are countless precedents of English words with a mute final "e" and a schwa inserted between two consonants, e.g. "little".
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.
Nervertheless, the correct constant should be τ[0] anyways.
Richer discovered that while in French Guyana, between 1671 and 1673 (http://en.wikipedia.org/wiki/Jean_richer)
The article also notes that it does not work it you use feet instead of meters, hence basically already answering the question.
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.
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.
Well, no - because it's a different number. Given that, the rest of the article just seems rather odd.
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.
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.
COINCIDENCE???