[math-fun] Math museum error?
Does anyone know anything about this? http://www.dailymail.co.uk/news/article-3152858/Teen-catches-math-error-gold... The press release (sounding more political than mathematical) asserts that the way the Museum presents the Golden Ratio in its exhibit "is in fact the less common - but no less accurate - way to present it". So, what was the "mistake" in the Eames exhibit, and was it in fact a mistake? The newspaper story doesn't give details. Jim Propp
It sounds like they said "the golden ratio is (1-sqrt(5))/2" instead of (1+sqrt(5))/2. On Wed, Jul 15, 2015 at 11:17 AM, James Propp <jamespropp@gmail.com> wrote:
Does anyone know anything about this?
http://www.dailymail.co.uk/news/article-3152858/Teen-catches-math-error-gold...
The press release (sounding more political than mathematical) asserts that the way the Museum presents the Golden Ratio in its exhibit "is in fact the less common - but no less accurate - way to present it".
So, what was the "mistake" in the Eames exhibit, and was it in fact a mistake?
The newspaper story doesn't give details.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
I’m guessing they are using the less popular “conjugate" definition tau = (1-sqrt(5))/2. Calling that an “error" is the same as taking issue with systematic replacement of i with -i in the equations of quantum mechanics. Curious that it was caught when the museum turned 34. -Veit
On Jul 15, 2015, at 2:17 PM, James Propp <jamespropp@gmail.com> wrote:
Does anyone know anything about this?
http://www.dailymail.co.uk/news/article-3152858/Teen-catches-math-error-gold...
The press release (sounding more political than mathematical) asserts that the way the Museum presents the Golden Ratio in its exhibit "is in fact the less common - but no less accurate - way to present it".
So, what was the "mistake" in the Eames exhibit, and was it in fact a mistake?
The newspaper story doesn't give details.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I don't agree. There is a real mathematical difference between positive and negative reals among complex numbers: Positive reals are the reals having their square roots among the reals; negatives don't. So tau is the positive root of 1/x = x-1. There is no mathematical difference between +i and -i. (They are distinct complex numbers, but they have the same properties.) —Dan
On Jul 15, 2015, at 11:29 AM, Veit Elser <ve10@cornell.edu> wrote:
I’m guessing they are using the less popular “conjugate" definition tau = (1-sqrt(5))/2. Calling that an “error" is the same as taking issue with systematic replacement of i with -i in the equations of quantum mechanics.
Curious that it was caught when the museum turned 34.
-Veit
On Jul 15, 2015, at 2:17 PM, James Propp <jamespropp@gmail.com> wrote:
Does anyone know anything about this?
http://www.dailymail.co.uk/news/article-3152858/Teen-catches-math-error-gold...
The press release (sounding more political than mathematical) asserts that the way the Museum presents the Golden Ratio in its exhibit "is in fact the less common - but no less accurate - way to present it".
So, what was the "mistake" in the Eames exhibit, and was it in fact a mistake?
The newspaper story doesn't give details.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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There is ambiguity in the mathematical literature as to whether the term "golden ratio" refers to 1.618... or 0.618... I think it's been suggested that one of these quantities be called tau and the other phi, but I can't remember which is which. Jim Propp On Wednesday, July 15, 2015, Dan Asimov <asimov@msri.org> wrote:
I don't agree. There is a real mathematical difference between positive and negative reals among complex numbers: Positive reals are the reals having their square roots among the reals; negatives don't. So tau is the positive root of 1/x = x-1.
There is no mathematical difference between +i and -i. (They are distinct complex numbers, but they have the same properties.)
—Dan
On Jul 15, 2015, at 11:29 AM, Veit Elser <ve10@cornell.edu <javascript:;>> wrote:
I’m guessing they are using the less popular “conjugate" definition tau = (1-sqrt(5))/2. Calling that an “error" is the same as taking issue with systematic replacement of i with -i in the equations of quantum mechanics.
Curious that it was caught when the museum turned 34.
-Veit
On Jul 15, 2015, at 2:17 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
Does anyone know anything about this?
http://www.dailymail.co.uk/news/article-3152858/Teen-catches-math-error-gold...
The press release (sounding more political than mathematical) asserts
that
the way the Museum presents the Golden Ratio in its exhibit "is in fact the less common - but no less accurate - way to present it".
So, what was the "mistake" in the Eames exhibit, and was it in fact a mistake?
The newspaper story doesn't give details.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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What Jim says is true, but a large majority of the literature agrees that the golden ratio is greater than 1: phi = (1+sqrt(5))/2) : 1. Namely the ratio of the sides of a rectangle such that if you cut off a square from it, what's left is the same ratio scaled and rotated 90 degrees. Which leads to phi = 1/(phi-1) and the same polynomial x^2 - x - 1 = 0. And it all agrees that phi s positive. —Dan
On Jul 15, 2015, at 11:53 AM, James Propp <jamespropp@gmail.com> wrote:
There is ambiguity in the mathematical literature as to whether the term "golden ratio" refers to 1.618... or 0.618...
I think it's been suggested that one of these quantities be called tau and the other phi, but I can't remember which is which.
Jim Propp
On Wednesday, July 15, 2015, Dan Asimov <asimov@msri.org> wrote:
I don't agree. There is a real mathematical difference between positive and negative reals among complex numbers: Positive reals are the reals having their square roots among the reals; negatives don't. So tau is the positive root of 1/x = x-1.
There is no mathematical difference between +i and -i. (They are distinct complex numbers, but they have the same properties.)
—Dan
On Jul 15, 2015, at 11:29 AM, Veit Elser <ve10@cornell.edu <javascript:;>> wrote:
I’m guessing they are using the less popular “conjugate" definition tau = (1-sqrt(5))/2. Calling that an “error" is the same as taking issue with systematic replacement of i with -i in the equations of quantum mechanics.
Curious that it was caught when the museum turned 34.
-Veit
On Jul 15, 2015, at 2:17 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
Does anyone know anything about this?
http://www.dailymail.co.uk/news/article-3152858/Teen-catches-math-error-gold...
The press release (sounding more political than mathematical) asserts
that
the way the Museum presents the Golden Ratio in its exhibit "is in fact the less common - but no less accurate - way to present it".
So, what was the "mistake" in the Eames exhibit, and was it in fact a mistake?
The newspaper story doesn't give details.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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There’s something to be said for having conventions, but you also lose sight of interesting things when you are rigid in your ways. The Galois automorphism sqrt(5) <-> -sqrt(5) has geometrical consequences. Perhaps you’ve encountered the construction of the 2D Penrose tiling starting from a lattice in 4D? Or its counterpart in 3D derived from a lattice in 6D? Basic to those constructions is an orthogonal decomposition of the 4D or 6D space by a pair of irrational subspaces. The automorphism has the effect of swapping those subspaces. So in addition to those obvious symmetries of the tiling, e.g. the pentagon (or icosahedron), there is the less obvious symmetry associated with changing the sign of sqrt(5). I’m actually surprised the term “Penrose involution” doesn’t bring up any hits. And there’s no better way of turning Conway’s “deflation” into “inflation”. In physics the Galois involution i <-> -i is also not exactly trivial, in the sense that it corresponds to “charge conjugation symmetry” (invariance upon changing the signs of all electrical charges). -Veit
On Jul 15, 2015, at 3:05 PM, Dan Asimov <dasimov@earthlink.net> wrote:
What Jim says is true, but a large majority of the literature agrees that the golden ratio is greater than 1:
phi = (1+sqrt(5))/2) : 1.
Namely the ratio of the sides of a rectangle such that if you cut off a square from it, what's left is the same ratio scaled and rotated 90 degrees. Which leads to
phi = 1/(phi-1)
and the same polynomial x^2 - x - 1 = 0.
And it all agrees that phi s positive.
—Dan
Of course the involution i <-> -i is nontrivial. But there is no distinction in field theory that distinguishes the two complex numbers +i and -i. With a field automorphism C -> C (or one of any subfield of C containing {i,-i}) you can interchange them or not, but they play entirely symmetrical roles. —Dan
On Jul 15, 2015, at 12:39 PM, Veit Elser <ve10@cornell.edu> wrote:
There’s something to be said for having conventions, but you also lose sight of interesting things when you are rigid in your ways.
The Galois automorphism sqrt(5) <-> -sqrt(5) has geometrical consequences. Perhaps you’ve encountered the construction of the 2D Penrose tiling starting from a lattice in 4D? Or its counterpart in 3D derived from a lattice in 6D? Basic to those constructions is an orthogonal decomposition of the 4D or 6D space by a pair of irrational subspaces. The automorphism has the effect of swapping those subspaces. So in addition to those obvious symmetries of the tiling, e.g. the pentagon (or icosahedron), there is the less obvious symmetry associated with changing the sign of sqrt(5). I’m actually surprised the term “Penrose involution” doesn’t bring up any hits.
And there’s no better way of turning Conway’s “deflation” into “inflation”.
In physics the Galois involution i <-> -i is also not exactly trivial, in the sense that it corresponds to “charge conjugation symmetry” (invariance upon changing the signs of all electrical charges).
-Veit
On Jul 15, 2015, at 3:05 PM, Dan Asimov <dasimov@earthlink.net> wrote:
What Jim says is true, but a large majority of the literature agrees that the golden ratio is greater than 1:
phi = (1+sqrt(5))/2) : 1.
Namely the ratio of the sides of a rectangle such that if you cut off a square from it, what's left is the same ratio scaled and rotated 90 degrees. Which leads to
phi = 1/(phi-1)
and the same polynomial x^2 - x - 1 = 0.
And it all agrees that phi s positive.
—Dan
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The rotational symmetry group of a dodecahedron is well known to be A_5. One way to see this is by noticing that precisely five cubes can be formed by taking 8 of the 20 vertices of the dodecahedron; the rotations of the dodecahedron induce even permutations on those cubes: https://en.wikipedia.org/wiki/Compound_of_five_cubes Then the Penrose involution gives an odd permutation, upgrading the symmetry group to S_5. Sincerely, Adam P. Goucher
Sent: Wednesday, July 15, 2015 at 8:39 PM From: "Veit Elser" <ve10@cornell.edu> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Math museum error?
There’s something to be said for having conventions, but you also lose sight of interesting things when you are rigid in your ways.
The Galois automorphism sqrt(5) <-> -sqrt(5) has geometrical consequences. Perhaps you’ve encountered the construction of the 2D Penrose tiling starting from a lattice in 4D? Or its counterpart in 3D derived from a lattice in 6D? Basic to those constructions is an orthogonal decomposition of the 4D or 6D space by a pair of irrational subspaces. The automorphism has the effect of swapping those subspaces. So in addition to those obvious symmetries of the tiling, e.g. the pentagon (or icosahedron), there is the less obvious symmetry associated with changing the sign of sqrt(5). I’m actually surprised the term “Penrose involution” doesn’t bring up any hits.
And there’s no better way of turning Conway’s “deflation” into “inflation”.
In physics the Galois involution i <-> -i is also not exactly trivial, in the sense that it corresponds to “charge conjugation symmetry” (invariance upon changing the signs of all electrical charges).
-Veit
On Jul 15, 2015, at 3:05 PM, Dan Asimov <dasimov@earthlink.net> wrote:
What Jim says is true, but a large majority of the literature agrees that the golden ratio is greater than 1:
phi = (1+sqrt(5))/2) : 1.
Namely the ratio of the sides of a rectangle such that if you cut off a square from it, what's left is the same ratio scaled and rotated 90 degrees. Which leads to
phi = 1/(phi-1)
and the same polynomial x^2 - x - 1 = 0.
And it all agrees that phi s positive.
—Dan
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On Jul 15, 2015, at 9:17 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
The rotational symmetry group of a dodecahedron is well known to be A_5.
One way to see this is by noticing that precisely five cubes can be formed by taking 8 of the 20 vertices of the dodecahedron; the rotations of the dodecahedron induce even permutations on those cubes:
https://en.wikipedia.org/wiki/Compound_of_five_cubes
Then the Penrose involution gives an odd permutation, upgrading the symmetry group to S_5.
That’s not quite right. The Penrose involution (sqrt(5) <-> -sqrt(5)) does not have the effect of giving you a bigger group, rather, it gives a geometrical interpretation of the unique outer automorphism of the original symmetry group, A_5. Try mapping the “golden coordinates” of the regular icosahedron ([tau,1,0] , …) and you will see that the involution maps the icosahedron into the stellated icosahedron. In particular, pentagonal faces map to pentagrams. That in turn tells you that 2pi/5 rotations get mapped to 4pi/5 rotations about the same axis (this is also the outer automorphism of the 5-element cyclic group, the symmetry of the planar Penrose pattern). Little did we know that the only thing that separates the headquarters of the US Defense Department and ritual satanic worship is a minus sign. -Veit
[I don't know from the Penrose involution, but:] Isn't it a bit easier to see the equivalence of the rotational symmetry group of a dodecahedron with A_5 by embedding the compound of 5 tetrahedra in its 20 vertices? Then its 60 rotations correspond to the even permutations of the tetrahedra. —Dan
On Jul 15, 2015, at 6:17 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
The rotational symmetry group of a dodecahedron is well known to be A_5.
One way to see this is by noticing that precisely five cubes can be formed by taking 8 of the 20 vertices of the dodecahedron; the rotations of the dodecahedron induce even permutations on those cubes:
https://en.wikipedia.org/wiki/Compound_of_five_cubes <https://en.wikipedia.org/wiki/Compound_of_five_cubes>
Then the Penrose involution gives an odd permutation, upgrading the symmetry group to S_5.
Searching for images of "origami five tetrahedra" produces lots of nice results. Note also that the icosadodecahedron has 6 great-circle like paths on it, which get permuted by its rotations. This shows that A_5 can be embedded in S_6 in a nontrivial way --- which has to do with the outer automorphism of S_6 :-) - Cris On Jul 16, 2015, at 11:13 AM, Dan Asimov <dasimov@earthlink.net> wrote:
[I don't know from the Penrose involution, but:]
Isn't it a bit easier to see the equivalence of the rotational symmetry group of a dodecahedron with A_5 by embedding the compound of 5 tetrahedra in its 20 vertices? Then its 60 rotations correspond to the even permutations of the tetrahedra.
—Dan
On Jul 15, 2015, at 6:17 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
The rotational symmetry group of a dodecahedron is well known to be A_5.
One way to see this is by noticing that precisely five cubes can be formed by taking 8 of the 20 vertices of the dodecahedron; the rotations of the dodecahedron induce even permutations on those cubes:
https://en.wikipedia.org/wiki/Compound_of_five_cubes <https://en.wikipedia.org/wiki/Compound_of_five_cubes>
Then the Penrose involution gives an odd permutation, upgrading the symmetry group to S_5.
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Cristopher Moore Professor, Santa Fe Institute The Nature of Computation Cristopher Moore and Stephan Mertens Available now at all good bookstores, or through Oxford University Press http://www.nature-of-computation.org/
* Veit Elser <ve10@cornell.edu> [Jul 16. 2015 08:15]:
There’s something to be said for having conventions, but you also lose sight of interesting things when you are rigid in your ways.
The Galois automorphism sqrt(5) <-> -sqrt(5) has geometrical consequences. Perhaps you’ve encountered the construction of the 2D Penrose tiling starting from a lattice in 4D? Or its counterpart in 3D derived from a lattice in 6D? Basic to those constructions is an orthogonal decomposition of the 4D or 6D space by a pair of irrational subspaces. The automorphism has the effect of swapping those subspaces. So in addition to those obvious symmetries of the tiling, e.g. the pentagon (or icosahedron), there is the less obvious symmetry associated with changing the sign of sqrt(5). I’m actually surprised the term “Penrose involution” doesn’t bring up any hits.
Could you point me to any reference regarding this (especially 6D-->3D)?
[...]
On Jul 16, 2015, at 3:02 AM, Joerg Arndt <arndt@jjj.de> wrote:
* Veit Elser <ve10@cornell.edu> [Jul 16. 2015 08:15]:
There’s something to be said for having conventions, but you also lose sight of interesting things when you are rigid in your ways.
The Galois automorphism sqrt(5) <-> -sqrt(5) has geometrical consequences. Perhaps you’ve encountered the construction of the 2D Penrose tiling starting from a lattice in 4D? Or its counterpart in 3D derived from a lattice in 6D? Basic to those constructions is an orthogonal decomposition of the 4D or 6D space by a pair of irrational subspaces. The automorphism has the effect of swapping those subspaces. So in addition to those obvious symmetries of the tiling, e.g. the pentagon (or icosahedron), there is the less obvious symmetry associated with changing the sign of sqrt(5). I’m actually surprised the term “Penrose involution” doesn’t bring up any hits.
Could you point me to any reference regarding this (especially 6D-->3D)?
The book by Marjorie Senechal is pretty good: http://www.amazon.com/Quasicrystals-Geometry-Marjorie-Senechal/dp/0521575419 But it might be quicker if you follow these steps: 1) Label half the vertices of the regular icosahedron 1,…,6 in some arbitrary way, just so no two labels are opposite the origin. 2) Construct a 6x6 “golden matrix” G by these rules: a) all the elements are -1/2 or +/12 b) diagonal elements are + c) off-diagonal elements are + if the corresponding icosahedron vertices form an acute angle at the origin, - otherwise 3) Check that G^2 = G+1. 4) Check that det G = -1. Together with 3) this implies that G has eigenvalues {tau,tau,tau,-1/tau,-1/tau,-1/tau}. You may therefore write G = tau P + (-/tau) P’, where P and P’ are projections into orthogonal 3-spaces. 5) Using P+P’=1 and the G you constructed in 2), use G = tau P + (-/tau) P’ to solve for P. 6) Now you can project things from 6D into 3D using P. The “checkerboard lattice" in 6D (points with integer coordinates that have even sum), called D_6, is a natural place to start because G acts as a bijection on D_6. Example: applying P to the 12 points {[2,0,0,0,0,0], … , [0,0,0,0,0,-2]} gives you the icosahedron. You can also try things like selecting points of D_6 that are close to the origin of one of the 3-spaces, by using P’, and project those into the other 3-space using P. That’ll give you something like a 3D Penrose tiling. -Veit
[...]
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Coxeter called (1+sqrt(5))/2 tau. On Wed, Jul 15, 2015 at 1:53 PM, James Propp <jamespropp@gmail.com> wrote:
There is ambiguity in the mathematical literature as to whether the term "golden ratio" refers to 1.618... or 0.618...
I think it's been suggested that one of these quantities be called tau and the other phi, but I can't remember which is which.
Jim Propp
On Wednesday, July 15, 2015, Dan Asimov <asimov@msri.org> wrote:
I don't agree. There is a real mathematical difference between positive and negative reals among complex numbers: Positive reals are the reals having their square roots among the reals; negatives don't. So tau is the positive root of 1/x = x-1.
There is no mathematical difference between +i and -i. (They are distinct complex numbers, but they have the same properties.)
—Dan
On Jul 15, 2015, at 11:29 AM, Veit Elser <ve10@cornell.edu <javascript:;>> wrote:
I’m guessing they are using the less popular “conjugate" definition tau = (1-sqrt(5))/2. Calling that an “error" is the same as taking issue with systematic replacement of i with -i in the equations of quantum mechanics.
Curious that it was caught when the museum turned 34.
-Veit
On Jul 15, 2015, at 2:17 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
Does anyone know anything about this?
http://www.dailymail.co.uk/news/article-3152858/Teen-catches-math-error-gold...
The press release (sounding more political than mathematical) asserts
that
the way the Museum presents the Golden Ratio in its exhibit "is in fact the less common - but no less accurate - way to present it".
So, what was the "mistake" in the Eames exhibit, and was it in fact a mistake?
The newspaper story doesn't give details.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Wolfram Math World has a few things to add: http://mathworld.wolfram.com/GoldenRatio.html I personally like my ratios to be in the range (0,1]. In fact I once wrote some code that made extensive use of "phi", where I was treating it as the smaller ratio. When I realized I was using the opposite of the more common convention, I was annoyed, but just replaced the name "phi" with "rphi" (reciprocal of phi) and called it a day. Tom James Buddenhagen writes:
Coxeter called (1+sqrt(5))/2 tau.
On Wed, Jul 15, 2015 at 1:53 PM, James Propp <jamespropp@gmail.com> wrote:
There is ambiguity in the mathematical literature as to whether the term "golden ratio" refers to 1.618... or 0.618...
I think it's been suggested that one of these quantities be called tau and the other phi, but I can't remember which is which.
Jim Propp
On Wednesday, July 15, 2015, Dan Asimov <asimov@msri.org> wrote:
I don't agree. There is a real mathematical difference between positive and negative reals among complex numbers: Positive reals are the reals having their square roots among the reals; negatives don't. So tau is the positive root of 1/x = x-1.
There is no mathematical difference between +i and -i. (They are distinct complex numbers, but they have the same properties.)
—Dan
On Jul 15, 2015, at 11:29 AM, Veit Elser <ve10@cornell.edu <javascript:;>> wrote:
I’m guessing they are using the less popular “conjugate" definition tau = (1-sqrt(5))/2. Calling that an “error" is the same as taking issue with systematic replacement of i with -i in the equations of quantum mechanics.
Curious that it was caught when the museum turned 34.
-Veit
On Jul 15, 2015, at 2:17 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
Does anyone know anything about this?
http://www.dailymail.co.uk/news/article-3152858/Teen-catches-math-error-gold...
The press release (sounding more political than mathematical) asserts
that
the way the Museum presents the Golden Ratio in its exhibit "is in fact the less common - but no less accurate - way to present it".
So, what was the "mistake" in the Eames exhibit, and was it in fact a mistake?
The newspaper story doesn't give details.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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--
I can certainly understand the confusion. The concept of the Golden Ratio is easy enough to understand, but remembering whether phi is the larger ratio or its reciprocal seems more a matter of convention than anything else. Introducing tau for the reciprocal may not be a bad idea, but then there's always the risk that people will mix the two up, leading to even more confusion. Here's a question: Which value is more "fundamental", pi or 2*pi? Arguably the smaller number is better since it's notationally easier to double a smaller number than to halve a larger one, and pi does often stand alone in things like pi*r^2. Are there any good arguments for viewing 2*pi the more fundamental value? Perhaps 2*pi could be called "cake". Tom James Propp writes:
There is ambiguity in the mathematical literature as to whether the term "golden ratio" refers to 1.618... or 0.618...
I think it's been suggested that one of these quantities be called tau and the other phi, but I can't remember which is which.
Jim Propp
On Wednesday, July 15, 2015, Dan Asimov <asimov@msri.org> wrote:
I don't agree. There is a real mathematical difference between positive and negative reals among complex numbers: Positive reals are the reals having their square roots among the reals; negatives don't. So tau is the positive root of 1/x = x-1.
There is no mathematical difference between +i and -i. (They are distinct complex numbers, but they have the same properties.)
—Dan
On Jul 15, 2015, at 11:29 AM, Veit Elser <ve10@cornell.edu <javascript:;>> wrote:
I’m guessing they are using the less popular “conjugate" definition tau = (1-sqrt(5))/2. Calling that an “error" is the same as taking issue with systematic replacement of i with -i in the equations of quantum mechanics.
Curious that it was caught when the museum turned 34.
-Veit
On Jul 15, 2015, at 2:17 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
Does anyone know anything about this?
http://www.dailymail.co.uk/news/article-3152858/Teen-catches-math-error-gold...
The press release (sounding more political than mathematical) asserts
that
the way the Museum presents the Golden Ratio in its exhibit "is in fact the less common - but no less accurate - way to present it".
So, what was the "mistake" in the Eames exhibit, and was it in fact a mistake?
The newspaper story doesn't give details.
Jim Propp
https://www.bostonglobe.com/lifestyle/2015/07/07/math-error-museum-science-n... I was somewhat annoyed that the Globe had to resort to authority ("Arthur Mattuck, an emeritus professor of mathematics at MIT") rather than simply demonstrating that 2/(sqrt(5)+1) = (sqrt(5)-1)/2 using the very skills in high school algebra that were being celebrated earlier in the article, but that's a battle lost long ago. On 07/15/2015 02:17 PM, James Propp wrote:
Does anyone know anything about this?
http://www.dailymail.co.uk/news/article-3152858/Teen-catches-math-error-gold...
The press release (sounding more political than mathematical) asserts that the way the Museum presents the Golden Ratio in its exhibit "is in fact the less common - but no less accurate - way to present it".
So, what was the "mistake" in the Eames exhibit, and was it in fact a mistake?
The newspaper story doesn't give details.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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