Angle trisection using a Cardioid
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How does one proceed to trisect an angle using the cardioid?
It is known that Etienne Pascal, father of Blaise Pascal, has devised a way to do it. I haven´t found the method in my search on the literature.
Best Regards.
euclidean-geometry
asked Nov 27 at 5:41
Petruchio de São Zeno
63
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up vote
1
down vote
favorite
How does one proceed to trisect an angle using the cardioid?
It is known that Etienne Pascal, father of Blaise Pascal, has devised a way to do it. I haven´t found the method in my search on the literature.
Best Regards.
euclidean-geometry
asked Nov 27 at 5:41
Petruchio de São Zeno
63
Do you have reason to believe that a cardioid is suited to trisection? Is your motivation to find a novel way to use the cardioid? or a novel way to trisect an angle?
– Blue
Nov 27 at 6:20
1
A trisectrix is a curve that can be used to trisect an arbitrary angle. Cardioid isn't listed on above wiki entry. The Limaçon trisectrix seems to be the trisectrix closest to a cardioid.
– achille hui
Nov 27 at 6:35
2
The Limaçon trisectrix is listed in deed. There is an observation in the book The Budget of Trisections (Underwood Dudley) at pages 9-10 that goes like this: "Although the trisection is no longer the obsession it was to Greek mathematicians, new methods have been devised in modern times. Etienne Pascalthe father of Blaise (1623-1662) the mathematician, philosopher, and writer, trisected with a cardioid."
– Petruchio de São Zeno
Nov 27 at 7:17
@PetruchiodeSãoZeno: Ah. Well, then ... You already have it on good authority that it is indeed possible to trisect an angle with a cardioid. So, your question really is: What method did Pascal, Sr, (and/or others) devise? Interestingly, a 1907 American Mathematical Monthly article "The Trisection Problem" (JSTOR link) opens with a casual mention that "The solution of this problem by means of the quadratrix, conchoid, and the cardioid are well known [...]".
– Blue
Nov 27 at 9:48
1
Thank you, Blue. I have edited the question now so that the initial answers keep sounding useful. I realized that I was in fact interested in the method itself. I am not putting in doubt what these authors have said.
– Petruchio de São Zeno
Nov 27 at 16:25
|
show 2 more comments
up vote
1
down vote
favorite
up vote
1
down vote
favorite
How does one proceed to trisect an angle using the cardioid?
It is known that Etienne Pascal, father of Blaise Pascal, has devised a way to do it. I haven´t found the method in my search on the literature.
Best Regards.
euclidean-geometry
asked Nov 27 at 5:41
Petruchio de São Zeno
63
How does one proceed to trisect an angle using the cardioid?
It is known that Etienne Pascal, father of Blaise Pascal, has devised a way to do it. I haven´t found the method in my search on the literature.
Best Regards.
euclidean-geometry
euclidean-geometry
asked Nov 27 at 5:41
Petruchio de São Zeno
63
asked Nov 27 at 5:41
Petruchio de São Zeno
63
edited Dec 6 at 3:00
asked Nov 27 at 5:41
Petruchio de São Zeno
63
asked Nov 27 at 5:41
Petruchio de São Zeno
63
asked Nov 27 at 5:41
Petruchio de São Zeno
63
63
Do you have reason to believe that a cardioid is suited to trisection? Is your motivation to find a novel way to use the cardioid? or a novel way to trisect an angle?
– Blue
Nov 27 at 6:20
1
A trisectrix is a curve that can be used to trisect an arbitrary angle. Cardioid isn't listed on above wiki entry. The Limaçon trisectrix seems to be the trisectrix closest to a cardioid.
– achille hui
Nov 27 at 6:35
2
The Limaçon trisectrix is listed in deed. There is an observation in the book The Budget of Trisections (Underwood Dudley) at pages 9-10 that goes like this: "Although the trisection is no longer the obsession it was to Greek mathematicians, new methods have been devised in modern times. Etienne Pascalthe father of Blaise (1623-1662) the mathematician, philosopher, and writer, trisected with a cardioid."
– Petruchio de São Zeno
Nov 27 at 7:17
@PetruchiodeSãoZeno: Ah. Well, then ... You already have it on good authority that it is indeed possible to trisect an angle with a cardioid. So, your question really is: What method did Pascal, Sr, (and/or others) devise? Interestingly, a 1907 American Mathematical Monthly article "The Trisection Problem" (JSTOR link) opens with a casual mention that "The solution of this problem by means of the quadratrix, conchoid, and the cardioid are well known [...]".
– Blue
Nov 27 at 9:48
1
Thank you, Blue. I have edited the question now so that the initial answers keep sounding useful. I realized that I was in fact interested in the method itself. I am not putting in doubt what these authors have said.
– Petruchio de São Zeno
Nov 27 at 16:25
|
show 2 more comments
Do you have reason to believe that a cardioid is suited to trisection? Is your motivation to find a novel way to use the cardioid? or a novel way to trisect an angle?
– Blue
Nov 27 at 6:20
1
A trisectrix is a curve that can be used to trisect an arbitrary angle. Cardioid isn't listed on above wiki entry. The Limaçon trisectrix seems to be the trisectrix closest to a cardioid.
– achille hui
Nov 27 at 6:35
2
The Limaçon trisectrix is listed in deed. There is an observation in the book The Budget of Trisections (Underwood Dudley) at pages 9-10 that goes like this: "Although the trisection is no longer the obsession it was to Greek mathematicians, new methods have been devised in modern times. Etienne Pascalthe father of Blaise (1623-1662) the mathematician, philosopher, and writer, trisected with a cardioid."
– Petruchio de São Zeno
Nov 27 at 7:17
@PetruchiodeSãoZeno: Ah. Well, then ... You already have it on good authority that it is indeed possible to trisect an angle with a cardioid. So, your question really is: What method did Pascal, Sr, (and/or others) devise? Interestingly, a 1907 American Mathematical Monthly article "The Trisection Problem" (JSTOR link) opens with a casual mention that "The solution of this problem by means of the quadratrix, conchoid, and the cardioid are well known [...]".
– Blue
Nov 27 at 9:48
1
Thank you, Blue. I have edited the question now so that the initial answers keep sounding useful. I realized that I was in fact interested in the method itself. I am not putting in doubt what these authors have said.
– Petruchio de São Zeno
Nov 27 at 16:25
Do you have reason to believe that a cardioid is suited to trisection? Is your motivation to find a novel way to use the cardioid? or a novel way to trisect an angle?
– Blue
Nov 27 at 6:20
Do you have reason to believe that a cardioid is suited to trisection? Is your motivation to find a novel way to use the cardioid? or a novel way to trisect an angle?
– Blue
Nov 27 at 6:20
1
1
A trisectrix is a curve that can be used to trisect an arbitrary angle. Cardioid isn't listed on above wiki entry. The Limaçon trisectrix seems to be the trisectrix closest to a cardioid.
– achille hui
Nov 27 at 6:35
A trisectrix is a curve that can be used to trisect an arbitrary angle. Cardioid isn't listed on above wiki entry. The Limaçon trisectrix seems to be the trisectrix closest to a cardioid.
– achille hui
Nov 27 at 6:35
2
2
The Limaçon trisectrix is listed in deed. There is an observation in the book The Budget of Trisections (Underwood Dudley) at pages 9-10 that goes like this: "Although the trisection is no longer the obsession it was to Greek mathematicians, new methods have been devised in modern times. Etienne Pascalthe father of Blaise (1623-1662) the mathematician, philosopher, and writer, trisected with a cardioid."
– Petruchio de São Zeno
Nov 27 at 7:17
The Limaçon trisectrix is listed in deed. There is an observation in the book The Budget of Trisections (Underwood Dudley) at pages 9-10 that goes like this: "Although the trisection is no longer the obsession it was to Greek mathematicians, new methods have been devised in modern times. Etienne Pascalthe father of Blaise (1623-1662) the mathematician, philosopher, and writer, trisected with a cardioid."
– Petruchio de São Zeno
Nov 27 at 7:17
@PetruchiodeSãoZeno: Ah. Well, then ... You already have it on good authority that it is indeed possible to trisect an angle with a cardioid. So, your question really is: What method did Pascal, Sr, (and/or others) devise? Interestingly, a 1907 American Mathematical Monthly article "The Trisection Problem" (JSTOR link) opens with a casual mention that "The solution of this problem by means of the quadratrix, conchoid, and the cardioid are well known [...]".
– Blue
Nov 27 at 9:48
@PetruchiodeSãoZeno: Ah. Well, then ... You already have it on good authority that it is indeed possible to trisect an angle with a cardioid. So, your question really is: What method did Pascal, Sr, (and/or others) devise? Interestingly, a 1907 American Mathematical Monthly article "The Trisection Problem" (JSTOR link) opens with a casual mention that "The solution of this problem by means of the quadratrix, conchoid, and the cardioid are well known [...]".
– Blue
Nov 27 at 9:48
1
1
Thank you, Blue. I have edited the question now so that the initial answers keep sounding useful. I realized that I was in fact interested in the method itself. I am not putting in doubt what these authors have said.
– Petruchio de São Zeno
Nov 27 at 16:25
Thank you, Blue. I have edited the question now so that the initial answers keep sounding useful. I realized that I was in fact interested in the method itself. I am not putting in doubt what these authors have said.
– Petruchio de São Zeno
Nov 27 at 16:25
|
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Do you have reason to believe that a cardioid is suited to trisection? Is your motivation to find a novel way to use the cardioid? or a novel way to trisect an angle?
– Blue
Nov 27 at 6:20
1
A trisectrix is a curve that can be used to trisect an arbitrary angle. Cardioid isn't listed on above wiki entry. The Limaçon trisectrix seems to be the trisectrix closest to a cardioid.
– achille hui
Nov 27 at 6:35
2
The Limaçon trisectrix is listed in deed. There is an observation in the book The Budget of Trisections (Underwood Dudley) at pages 9-10 that goes like this: "Although the trisection is no longer the obsession it was to Greek mathematicians, new methods have been devised in modern times. Etienne Pascalthe father of Blaise (1623-1662) the mathematician, philosopher, and writer, trisected with a cardioid."
– Petruchio de São Zeno
Nov 27 at 7:17
@PetruchiodeSãoZeno: Ah. Well, then ... You already have it on good authority that it is indeed possible to trisect an angle with a cardioid. So, your question really is: What method did Pascal, Sr, (and/or others) devise? Interestingly, a 1907 American Mathematical Monthly article "The Trisection Problem" (JSTOR link) opens with a casual mention that "The solution of this problem by means of the quadratrix, conchoid, and the cardioid are well known [...]".
– Blue
Nov 27 at 9:48
1
Thank you, Blue. I have edited the question now so that the initial answers keep sounding useful. I realized that I was in fact interested in the method itself. I am not putting in doubt what these authors have said.
– Petruchio de São Zeno
Nov 27 at 16:25