[math-fun] Irrational constants
Hi all, I don’t normally start a conversation on here basically due to my lack of formal higher math education and a very specific limited math-related skill set, however this is a question that is really just about mathematical preference rather than math itself. I'm writing with the holiday spirit in mind, posing the following question just for pure fun and hoping it won’t cause too much divisive argument ! What is the most important strictly irrational constant ? #pi or #e or sqrt(2) or maybe something else ? (Not including infinity) As a programmer I find it very hard to choose :D (Apologies to those who prefer the term software engineer)
Hello, the 3 most important constants are the golden ratio, 1.6180339887... or 1/2*sqrt(5)/2. the number Pi, 3.141592... the e constant (exp of 1). 2.71828182845904523536... which one is the most important may vary according to who is saying it. Golden ratio : most plants have pattern in their shape and count of leaves, petal or form, it has been said that 95 % of plants have this pattern. just type <golden ratio and plants > on youtube, you will see a couple of films explaining this phenomena. Pi : because the number appear in so many mathematical and physical formulas. There are a lot of them. Open a math book, any math book, a large proportion of math books have always one to many formulas linked to that number. It also appears in important formulas : - the general relativity Einstein formula contains Pi. - see wikipedia page on Pi for that. Exp(1) : because the number e is THE constant that gives the solution to all differential equations with constant coefficients. Since ln(e) = 1, also because many of those solutions can be expressed by a linear combination of exp(1) terms. In all of these 3 cases, you can find a large literature covering it. So it is perhaps a matter of opinion. For me : Pi is the most important. Best regards, Simon Plouffe Le 2018-12-28 à 11:36, D J Makin via math-fun a écrit :
Hi all, I don’t normally start a conversation on here basically due to my lack of formal higher math education and a very specific limited math-related skill set, however this is a question that is really just about mathematical preference rather than math itself. I'm writing with the holiday spirit in mind, posing the following question just for pure fun and hoping it won’t cause too much divisive argument !
What is the most important strictly irrational constant ? #pi or #e or sqrt(2) or maybe something else ? (Not including infinity)
As a programmer I find it very hard to choose :D (Apologies to those who prefer the term software engineer)
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Nobody ever lists 0 or 1 as candidates in these discussions! On Dec 28, 2018 6:22 AM, "Simon Plouffe" <simon.plouffe@gmail.com> wrote: Hello, the 3 most important constants are the golden ratio, 1.6180339887... or 1/2*sqrt(5)/2. the number Pi, 3.141592... the e constant (exp of 1). 2.71828182845904523536... which one is the most important may vary according to who is saying it. Golden ratio : most plants have pattern in their shape and count of leaves, petal or form, it has been said that 95 % of plants have this pattern. just type <golden ratio and plants > on youtube, you will see a couple of films explaining this phenomena. Pi : because the number appear in so many mathematical and physical formulas. There are a lot of them. Open a math book, any math book, a large proportion of math books have always one to many formulas linked to that number. It also appears in important formulas : - the general relativity Einstein formula contains Pi. - see wikipedia page on Pi for that. Exp(1) : because the number e is THE constant that gives the solution to all differential equations with constant coefficients. Since ln(e) = 1, also because many of those solutions can be expressed by a linear combination of exp(1) terms. In all of these 3 cases, you can find a large literature covering it. So it is perhaps a matter of opinion. For me : Pi is the most important. Best regards, Simon Plouffe Le 2018-12-28 à 11:36, D J Makin via math-fun a écrit :
Hi all, I don’t normally start a conversation on here basically due to my lack of formal higher math education and a very specific limited math-related skill set, however this is a question that is really just about mathematical preference rather than math itself. I'm writing with the holiday spirit in mind, posing the following question just for pure fun and hoping it won’t cause too much divisive argument !
What is the most important strictly irrational constant ? #pi or #e or sqrt(2) or maybe something else ? (Not including infinity)
As a programmer I find it very hard to choose :D (Apologies to those who prefer the term software engineer)
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They're not exactly irrational. On 28-Dec-18 08:19, Allan Wechsler wrote:
Nobody ever lists 0 or 1 as candidates in these discussions!
On Dec 28, 2018 6:22 AM, "Simon Plouffe" <simon.plouffe@gmail.com> wrote:
Hello, the 3 most important constants are
the golden ratio, 1.6180339887... or 1/2*sqrt(5)/2. the number Pi, 3.141592... the e constant (exp of 1). 2.71828182845904523536...
which one is the most important may vary according to who is saying it.
Golden ratio : most plants have pattern in their shape and count of leaves, petal or form, it has been said that 95 % of plants have this pattern. just type <golden ratio and plants > on youtube, you will see a couple of films explaining this phenomena.
Pi : because the number appear in so many mathematical and physical formulas. There are a lot of them. Open a math book, any math book, a large proportion of math books have always one to many formulas linked to that number. It also appears in important formulas : - the general relativity Einstein formula contains Pi. - see wikipedia page on Pi for that.
Exp(1) : because the number e is THE constant that gives the solution to all differential equations with constant coefficients. Since ln(e) = 1, also because many of those solutions can be expressed by a linear combination of exp(1) terms.
In all of these 3 cases, you can find a large literature covering it.
So it is perhaps a matter of opinion.
For me : Pi is the most important.
Best regards, Simon Plouffe
Le 2018-12-28 à 11:36, D J Makin via math-fun a écrit :
Hi all, I don’t normally start a conversation on here basically due to my lack of formal higher math education and a very specific limited math-related skill set, however this is a question that is really just about mathematical preference rather than math itself. I'm writing with the holiday spirit in mind, posing the following question just for pure fun and hoping it won’t cause too much divisive argument ! What is the most important strictly irrational constant ? #pi or #e or sqrt(2) or maybe something else ? (Not including infinity)
As a programmer I find it very hard to choose :D (Apologies to those who prefer the term software engineer)
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I just woke up and my bleary brain completely slid over the irrational constraint. Apologies. On Fri, Dec 28, 2018, 8:29 AM Mike Speciner <ms@alum.mit.edu wrote:
They're not exactly irrational.
On 28-Dec-18 08:19, Allan Wechsler wrote:
Nobody ever lists 0 or 1 as candidates in these discussions!
On Dec 28, 2018 6:22 AM, "Simon Plouffe" <simon.plouffe@gmail.com> wrote:
Hello, the 3 most important constants are
the golden ratio, 1.6180339887... or 1/2*sqrt(5)/2. the number Pi, 3.141592... the e constant (exp of 1). 2.71828182845904523536...
which one is the most important may vary according to who is saying it.
Golden ratio : most plants have pattern in their shape and count of leaves, petal or form, it has been said that 95 % of plants have this pattern. just type <golden ratio and plants > on youtube, you will see a couple of films explaining this phenomena.
Pi : because the number appear in so many mathematical and physical formulas. There are a lot of them. Open a math book, any math book, a large proportion of math books have always one to many formulas linked to that number. It also appears in important formulas : - the general relativity Einstein formula contains Pi. - see wikipedia page on Pi for that.
Exp(1) : because the number e is THE constant that gives the solution to all differential equations with constant coefficients. Since ln(e) = 1, also because many of those solutions can be expressed by a linear combination of exp(1) terms.
In all of these 3 cases, you can find a large literature covering it.
So it is perhaps a matter of opinion.
For me : Pi is the most important.
Best regards, Simon Plouffe
Le 2018-12-28 à 11:36, D J Makin via math-fun a écrit :
Hi all, I don’t normally start a conversation on here basically due to my lack of formal higher math education and a very specific limited math-related skill set, however this is a question that is really just about mathematical preference rather than math itself. I'm writing with the holiday spirit in mind, posing the following question just for pure fun and hoping it won’t cause too much divisive argument ! What is the most important strictly irrational constant ? #pi or #e or sqrt(2) or maybe something else ? (Not including infinity)
As a programmer I find it very hard to choose :D (Apologies to those who prefer the term software engineer)
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Eons before Euler, somebody took "^", "*", "+", "=", and with these operators he glued e, i, pi, 1 and 0 together to form: <math>e^{i \pi} + 1 = 0</math> (cf. <https://en.wikipedia.org/wiki/Euler%27s_identity> <https://en.wikipedia.org/wiki/Euler%27s_identity>)
Am 28.12.2018 um 12:21 schrieb Simon Plouffe:
Hello, the 3 most important constants are the golden ratio, 1.6180339887... or 1/2*sqrt(5)/2. the number Pi, 3.141592... the e constant (exp of 1). 2.71828182845904523536... which one is the most important may vary according to who is saying it. ... Am Fr., 28. Dez. 2018 um 12:22 Uhr schrieb Simon Plouffe < simon.plouffe@gmail.com>:
Hello, the 3 most important constants are
the golden ratio, 1.6180339887... or 1/2*sqrt(5)/2. the number Pi, 3.141592... the e constant (exp of 1). 2.71828182845904523536...
which one is the most important may vary according to who is saying it.
Golden ratio : most plants have pattern in their shape and count of leaves, petal or form, it has been said that 95 % of plants have this pattern. just type <golden ratio and plants > on youtube, you will see a couple of films explaining this phenomena.
Pi : because the number appear in so many mathematical and physical formulas. There are a lot of them. Open a math book, any math book, a large proportion of math books have always one to many formulas linked to that number. It also appears in important formulas : - the general relativity Einstein formula contains Pi. - see wikipedia page on Pi for that.
Exp(1) : because the number e is THE constant that gives the solution to all differential equations with constant coefficients. Since ln(e) = 1, also because many of those solutions can be expressed by a linear combination of exp(1) terms.
In all of these 3 cases, you can find a large literature covering it.
So it is perhaps a matter of opinion.
For me : Pi is the most important.
Best regards, Simon Plouffe
Le 2018-12-28 à 11:36, D J Makin via math-fun a écrit :
Hi all, I don’t normally start a conversation on here basically due to my lack of formal higher math education and a very specific limited math-related skill set, however this is a question that is really just about mathematical preference rather than math itself. I'm writing with the holiday spirit in mind, posing the following question just for pure fun and hoping it won’t cause too much divisive argument !
What is the most important strictly irrational constant ? #pi or #e or sqrt(2) or maybe something else ? (Not including infinity)
As a programmer I find it very hard to choose :D (Apologies to those who prefer the term software engineer)
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Thanks all - esp. Georg.
On 28 Dec 2018, at 15:40, Georg Dr. Fischer <dr.georg.fischer@gmail.com> wrote:
Eons before Euler, somebody took "^", "*", "+", "=", and with these operators he glued e, i, pi, 1 and 0 together to form:
<math>e^{i \pi} + 1 = 0</math>
(cf. <https://en.wikipedia.org/wiki/Euler%27s_identity> <https://en.wikipedia.org/wiki/Euler%27s_identity>)
Inspired by the irrational relations…. From the Mandelbrot for z^(6/(#i*#pi))+c: https://fractalforums.org/index.php?action=gallery;sa=view;id=2005 <https://fractalforums.org/index.php?action=gallery;sa=view;id=2005>
On 30 Dec 2018, at 10:52, D J Makin via math-fun <math-fun@mailman.xmission.com> wrote:
Thanks all - esp. Georg.
On 28 Dec 2018, at 15:40, Georg Dr. Fischer <dr.georg.fischer@gmail.com> wrote:
Eons before Euler, somebody took "^", "*", "+", "=", and with these operators he glued e, i, pi, 1 and 0 together to form:
<math>e^{i \pi} + 1 = 0</math>
(cf. <https://en.wikipedia.org/wiki/Euler%27s_identity> <https://en.wikipedia.org/wiki/Euler%27s_identity>)
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I couldn't decode what fractal you were exploring in "The Elven Palace", but had the impression of an intriguing 3-space structure, though the rendering does not quite succeed in resolving any ambiguity. Have you investigated the practicality of a fly-through movie? WFL On 12/31/18, D J Makin via math-fun <math-fun@mailman.xmission.com> wrote:
Inspired by the irrational relations….
From the Mandelbrot for z^(6/(#i*#pi))+c:
https://fractalforums.org/index.php?action=gallery;sa=view;id=2005 <https://fractalforums.org/index.php?action=gallery;sa=view;id=2005>
On 30 Dec 2018, at 10:52, D J Makin via math-fun <math-fun@mailman.xmission.com> wrote:
Thanks all - esp. Georg.
On 28 Dec 2018, at 15:40, Georg Dr. Fischer <dr.georg.fischer@gmail.com> wrote:
Eons before Euler, somebody took "^", "*", "+", "=", and with these operators he glued e, i, pi, 1 and 0 together to form:
<math>e^{i \pi} + 1 = 0</math>
(cf. <https://en.wikipedia.org/wiki/Euler%27s_identity> <https://en.wikipedia.org/wiki/Euler%27s_identity>)
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Hi Fred, “The Elven Palace” is indeed a 2D perspective view of a 3D ray-step render using a slightly brute force distance estimation method. It’s actually part of the standard quaternionic Mandelbrot for q^7+c but with an extra twist, if you take the quaternionic form is (x,y,z,w) then prior to calculating q^7 the (y,z) part is treated as a complex and rotated to 7* its original angle i.e. no change of magnitude. I was surprised when such a simple idea produced results very similar to the White/Nylander Mandelbulbs. Although similar to those Triplex Mandelbulbs (especially since here the 4th dimension, w, is zero throughout) it is not the same and seems to have less “whipped cream”, be more hollow and have fewer of the difficult tapering to infinitely thin sections found in the centre of the star shapes on the original Mandelbulbs of the same degree. Given that numeric adjustment (the extra twist) can someone more mathematically aware then myself possibly tell me how to calculate the derivative ? e.g. I’m guessing just use 7*q^6 where q^6 is quaternionic but with the twist first at *6 and the multiplication 7*(q^6) is purely quaternionic since both the y and z terms are zero for a simple real…...
On 1 Jan 2019, at 01:43, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I couldn't decode what fractal you were exploring in "The Elven Palace", but had the impression of an intriguing 3-space structure, though the rendering does not quite succeed in resolving any ambiguity. Have you investigated the practicality of a fly-through movie? WFL
Hi all, @Fred, sorry for the duplicate… re. fly-throughs, I only start those when I’m sure I’ve got rendering times down to a minimum and really that needs analytical distance estimation which requires the calculation of the running derivative and so far I’ve just been investigating the other possibilities similar forms presents e.g. and/or twisting x,y and/or z,w and/or x,z and/or x,w and/or y,w and even doing full complex powers instead including where the power change for the magnitude and the scaling for the angle don’t match ;)
participants (6)
-
Allan Wechsler -
D J Makin -
Fred Lunnon -
Georg Dr. Fischer -
Mike Speciner -
Simon Plouffe