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What Does Pi Have To Do With Gravity?
- PankajGhosh 14y agoWouldn'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...
- claudius 14y agoYes, 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/ http://tauday.com/
- Someone 14y agoYou are underestimating early 19th century science, and even 17th century science. http://en.wikipedia.org/wiki/History_of_the_metre 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 http://en.wikipedia.org/wiki/Jean_richer)
- xonea 14y agoYup. 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 14y agoNo, the answer is that our units were constructed so that pi has something to do with gravity.
- hmsimha 14y agoExactly. 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.
- madaxe 14y ago1000 cubic centimetres - a cubic decimetre. Not a cubic meter. A cubic meter of water ways a ton.
- claudius 14y agoIf 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.
- Retric 14y agoThat 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.
- pardner 14y agoI spent $3.14 (USD) on a latte this morning.
- notdrunkatall 14y agoI spent 3.14 seconds deciding that this was a funny comment. COINCIDENCE???
- cleaver 14y agoAnd if you drink a whole lotta lattes, you will start to feel stronger gravitational attraction to nearby masses such as the earth.
- madiator 14y agoWas 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.
- shardling 14y agoIt wasn't up to the author! He's just relaying a historical point.
- shardling 14y agoFor 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 http://en.wikipedia.org/wiki/Natural_units
- Camillo 14y agoThis 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 http://en.wikipedia.org/wiki/History_of_the_metre
- shardling 14y agoI 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.
- madaxe 14y agoWell, 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.
- shardling 14y agoHeh, I guess since I already know how that works out, I'm glad it was glossed over.
- Camillo 14y agoBecause 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 14y ago
- prof_hobart 14y 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 14y agoIn 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 http://en.wikipedia.org/wiki/Metre#Meridional_definition
- calhoun137 14y agoThis 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.