For those that don't feel like reading an article, it's essentially questioning the premise of how we defined pi. When they say "pi is wrong," they aren't questioning that pi is the ratio of a circle's circumference to its diameter -- because it is. They're questioning why we defined pi that way when using the ratio of circumference to radius is more elegant. I'd imagine that pi was defined that way since diameter is easier to measure, but mathematics shouldn't be constrained by something superficial like that.
Rather than trying to change the definition of pi (which would cause huge problems), they propose a new constant, tau, which is the new ratio (circumference:radius). Look at some of their examples and I think you'll agree that this tidies up mathematics regarding trig, as well as Euler's identity, quantum mechanics, statistics, and more.
If you prefer a video to an article (the video is a bit more entertaining and less mathy if that's a concern of yours), check this out (and if you enjoy, she has several other videos that are interesting):
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No amount of planning will ever replace dumb luck.
I think the main argument is between people for whom pi is easier with people for whom tau is easier. It doesn't matter at all, but for some things one is better than the other, not across the board.
From: Leebo86 | #002 I think the main argument is between people for whom pi is easier with people for whom tau is easier. It doesn't matter at all, but for some things one is better than the other, not across the board.
The mathematics is the same regardless of which you use, yes. I think section 4.4 of the opening article address this.
From: _Regaro_ | #003 so basically they want to define 2*pi
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Yup. See section 4.4. Pi is an important number, but only because it's half of a number that's the true fundamental constant of interest. That's why "2*pi" shows up in so many equations.
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No amount of planning will ever replace dumb luck.
The article isn't necessarily calling for change. If you read this paper on the subject... http://www.math.utah.edu/~palais/pi.pdf the second paragraph states that he's not really expecting any change, but it's more of a "oops" moment, that we defined a constant poorly. It's like if e was defined as 1/e for whatever reason. All of the math would still work, we'd just have negative signs all over the place, because we were using a modified form of the truly significant number.
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No amount of planning will ever replace dumb luck.
From: Ness26 | #007 The article isn't necessarily calling for change. If you read this paper on the subject... http://www.math.utah.edu/~palais/pi.pdf the second paragraph states that he's not really expecting any change, but it's more of a "oops" moment, that we defined a constant poorly. It's like if e was defined as 1/e for whatever reason. All of the math would still work, we'd just have negative signs all over the place, because we were using a modified form of the truly significant number.
So, kinda like how Ben Franklin defined electrons as the negative charge so we have to deal with that whenever we do electromagnetic calculations?
From: AlecTrevelyan006 | #009 So, kinda like how Ben Franklin defined electrons as the negative charge so we have to deal with that whenever we do electromagnetic calculations?
Yup. Except you can't really change that easily -- if we changed the sign convention we would have to rewrite all of the textbooks and it'd be a constant effort to make sure you've defined which convention you're using (... sort of like Thermo's sign convention). With this it's just an additional constant. Nothing is being undone.
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No amount of planning will ever replace dumb luck.
For the same reason people cared about Pluto not being a planet even though there are legitimate reasons to not call it one
Back when that was happening I remember something about "if Pluto isn't a planet, neither is Jupiter." I don't remember the specifics but someone was saying that Jupiter hasn't actually cleared the neighborhood of it's orbit either. Am I recalling this correctly? Does anyone know anything about it?
The first thing that comes to mind is that you'd have to use 0.5 tau r^2 for the area of a circle, but maybe that's less significant to science and math.
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"God Hand is the ultimate expression of the joy of humanity, specifically the punching part of the joy of humanity."-Shigeru Miyamoto
In August of 2006, the International Astronomical Union came up with a definition of the word “Planet”. According to this new definition, Pluto is no longer a planet. It is a “Dwarf Planet”. However, this has created controversy around the world among Astronomers.
The IAU members gathered at the 2006 General Assembly agreed that a "planet" is defined as a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.
A "dwarf planet" is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, (c) has not cleared the neighbourhood around its orbit, and (d) is not a satellite.
The definition is flawed, relating to “cleared the neighborhood”. Every 228 years Pluto crosses inside of the orbit of Neptune, so technically speaking, it does not clear its neighborhood. But that also means that Neptune does not clear its own neighborhood. Mars and Jupiter don’t clear their neighborhoods as they “interfere” with the Asteroids, and the Earth actually orbits the Sun with thousands of Asteroids. So the Earth doesn’t clear its own neighborhood either.
So if we use the definition set forth by the IAU, Pluto, Neptune, Jupiter, Mars, and the Earth, are NOT planets! Also, why aren’t “Dwarf Planets” known as planets? Dwarf Stars are still stars, and Dwarf Galaxies are still galaxies.
These new definitions ONLY apply to objects in OUR Solar System, making the definition even more un-scientific.
Along with the definition being both linguistically and scientifically flawed, so was the voting process. Although there are over 10,000 Astronomers in the IAU, only 237 of them voted and approved this definition. Therefore, there was NOT a majority consensus of what a planet is. Hundreds of Astronomers around the world (and this planetarium) have signed petitions to ignore the new definition and still refer to Pluto as the ninth planet in our Solar System.
Discovered in 1930, Pluto orbits the Sun, has three moons, has an atmosphere, has weather, and even polar caps. It is not that much different than any of the other planets. It has been known as a planet for more than 75 years, and to change its status with a poor definition and process, is bad science.
The Suits-Bueche Planetarium recognizes the fact that Astronomy changes as our knowledge grows, but we do not go along with the IAU’s flawed voting process and flawed definition.
Therefore, our official policy is that Pluto is STILL the ninth planet in the Solar System!
the problem is that there are like...scores of pluto sized masses in the kuiper belt and calling them all planets would be pretty damn silly. clearly we can classify things to make life easier for everyone.
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There is no shame in not knowing; the shame lies in not finding out
From: paperwarior | #019 The first thing that comes to mind is that you'd have to use 0.5 tau r^2 for the area of a circle, but maybe that's less significant to science and math.
Section 3 of the opening article. You can argue that form is actually more appropriate since it parallels equations of a similar form (1/2 * constant * squared term) that result from integrations analogous to that which gives you the circle area formula.
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No amount of planning will ever replace dumb luck.
From: BoshStrikesBack | #027 Topic title: "Pi is wrong." OP content: "Pi isn't wrong, per se; it just might've been cleaner if we multiplied it by two."
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You're messing with me! You're messing with me, aren't you!? You're making fun of me, aren't you!? Aren't you!? You definitely are! I'll murder you!