spring-of-mathematics:

Herwig Hauser Classic(P1) - Authors | Herwig Hauser:
Zitrus (Citric): The equation x2+z2 = y3(1−y)3 of Citric appears as simple as the figure itself. Two cusps mirror-symmetrically arranged rotate around the traversing axis. The equation x2+z2 = y3 simplified by omitting (1−y)3 provides for exactly one cusp, and x2+z2 = (1−y)3 yields the mirror image. Both are infinitely extending surfaces. The product on the right side of the initial equation ensures that Citric remains bounded. You may consider the following: If the absolute value of y is getting larger than 1 the right side becomes negative and the equation does not admit real solutions of x and z.


Ding Dong: This surface described by the equation x²+y²+z³ = z² was one of the very first visualizations we tried. Equation and shape are simple: A vertical alpha-loop rotates around the z-axis. But there was the problem with the colouring. Green is generally rather tricky in three-dimensional visualization of surfaces and, in addition, tends to be matt or yellowish. The lights and reflexions must be well tested. Note the light blue hard shadow intensifying the spatial effect.
 Daisy: The equation (x2−y3)2 = (z2−y2)3 of Daisy implies by differentiation that the singular locus consists of two (plane) curves which transversally meet at their common singular point. In order to better understand singularities the geometrician constructs their resolution by means of blowups. In finitely many steps they provide a surface without singularities (a manifold) together with a projection map onto the original surface which interprets it as a shade of manifold.
 Diabolo:  The Diabolo equation x2 = (y2+z2)2 factorizes into the product (x−y2−z2)(x+y2+z2) = 0. Hence, the respective surface is the unification of the two single-shell rotating hyperboloids x = ±(y2+z2).  They touch each other tangentially at the origin. The contact can algebraically be gathered from the concurrent linear term x in the two factors. The tangent plane is the vertical plane x = 0.The stripes in the images are shades due to lighting. If you modify the Diabolo equation by adding a constant term such as in x2 = (y2+z2)2+1/1000, then the two halves are separated. The substitution of x by x+y, however, yields the variation (x+y)2 = (y2+z2)2 of the equation. The two shells are moved at an angle to each other.
 Dullo: If the audience in an oval stadium scream about a score (typically of the favoured team), the sound spreads like a quickly inflated floating tyre. After some split seconds the tyre meets itself at its centre – the opening has closed – and that is what exactly happens at the kick-off spot. At that point sound waves from all directions meet simultaneously and are boosted accordingly. This is why referees are advised to always stay level with the ball. Thus, when a goal is scored they do not stand in the middle circle and get a buzzing in their ears.
Seepferdchen (Seahorse):  If you want to find the equation of this surface it would take strong efforts. The soft tangential contact is not easy to achieve. It vanishes as you only slightly change the formula.  The elegance of the sea horse is an illusion: If you look at it from behind or from the side, it appears quite clumsy. Sea horses live worldwide in tropical and temperate climate zones. Its Latin name is Hippocampus, you can find the equation next to it.

Herwig Hauser’s classic algebraic surfaces are compiled for the original IMAGINARY exhibition. Herwig Hauser’s forms and formulas are chosen in such a way that equations are simple and beautiful. The figures are plain and natural and show interesting geometrical facts. Herwig Hauser is professor of mathematics at the University of Vienna and works in algebraic geometry and singularity theory. [Source]
Zoom Info
spring-of-mathematics:

Herwig Hauser Classic(P1) - Authors | Herwig Hauser:
Zitrus (Citric): The equation x2+z2 = y3(1−y)3 of Citric appears as simple as the figure itself. Two cusps mirror-symmetrically arranged rotate around the traversing axis. The equation x2+z2 = y3 simplified by omitting (1−y)3 provides for exactly one cusp, and x2+z2 = (1−y)3 yields the mirror image. Both are infinitely extending surfaces. The product on the right side of the initial equation ensures that Citric remains bounded. You may consider the following: If the absolute value of y is getting larger than 1 the right side becomes negative and the equation does not admit real solutions of x and z.


Ding Dong: This surface described by the equation x²+y²+z³ = z² was one of the very first visualizations we tried. Equation and shape are simple: A vertical alpha-loop rotates around the z-axis. But there was the problem with the colouring. Green is generally rather tricky in three-dimensional visualization of surfaces and, in addition, tends to be matt or yellowish. The lights and reflexions must be well tested. Note the light blue hard shadow intensifying the spatial effect.
 Daisy: The equation (x2−y3)2 = (z2−y2)3 of Daisy implies by differentiation that the singular locus consists of two (plane) curves which transversally meet at their common singular point. In order to better understand singularities the geometrician constructs their resolution by means of blowups. In finitely many steps they provide a surface without singularities (a manifold) together with a projection map onto the original surface which interprets it as a shade of manifold.
 Diabolo:  The Diabolo equation x2 = (y2+z2)2 factorizes into the product (x−y2−z2)(x+y2+z2) = 0. Hence, the respective surface is the unification of the two single-shell rotating hyperboloids x = ±(y2+z2).  They touch each other tangentially at the origin. The contact can algebraically be gathered from the concurrent linear term x in the two factors. The tangent plane is the vertical plane x = 0.The stripes in the images are shades due to lighting. If you modify the Diabolo equation by adding a constant term such as in x2 = (y2+z2)2+1/1000, then the two halves are separated. The substitution of x by x+y, however, yields the variation (x+y)2 = (y2+z2)2 of the equation. The two shells are moved at an angle to each other.
 Dullo: If the audience in an oval stadium scream about a score (typically of the favoured team), the sound spreads like a quickly inflated floating tyre. After some split seconds the tyre meets itself at its centre – the opening has closed – and that is what exactly happens at the kick-off spot. At that point sound waves from all directions meet simultaneously and are boosted accordingly. This is why referees are advised to always stay level with the ball. Thus, when a goal is scored they do not stand in the middle circle and get a buzzing in their ears.
Seepferdchen (Seahorse):  If you want to find the equation of this surface it would take strong efforts. The soft tangential contact is not easy to achieve. It vanishes as you only slightly change the formula.  The elegance of the sea horse is an illusion: If you look at it from behind or from the side, it appears quite clumsy. Sea horses live worldwide in tropical and temperate climate zones. Its Latin name is Hippocampus, you can find the equation next to it.

Herwig Hauser’s classic algebraic surfaces are compiled for the original IMAGINARY exhibition. Herwig Hauser’s forms and formulas are chosen in such a way that equations are simple and beautiful. The figures are plain and natural and show interesting geometrical facts. Herwig Hauser is professor of mathematics at the University of Vienna and works in algebraic geometry and singularity theory. [Source]
Zoom Info
spring-of-mathematics:

Herwig Hauser Classic(P1) - Authors | Herwig Hauser:
Zitrus (Citric): The equation x2+z2 = y3(1−y)3 of Citric appears as simple as the figure itself. Two cusps mirror-symmetrically arranged rotate around the traversing axis. The equation x2+z2 = y3 simplified by omitting (1−y)3 provides for exactly one cusp, and x2+z2 = (1−y)3 yields the mirror image. Both are infinitely extending surfaces. The product on the right side of the initial equation ensures that Citric remains bounded. You may consider the following: If the absolute value of y is getting larger than 1 the right side becomes negative and the equation does not admit real solutions of x and z.


Ding Dong: This surface described by the equation x²+y²+z³ = z² was one of the very first visualizations we tried. Equation and shape are simple: A vertical alpha-loop rotates around the z-axis. But there was the problem with the colouring. Green is generally rather tricky in three-dimensional visualization of surfaces and, in addition, tends to be matt or yellowish. The lights and reflexions must be well tested. Note the light blue hard shadow intensifying the spatial effect.
 Daisy: The equation (x2−y3)2 = (z2−y2)3 of Daisy implies by differentiation that the singular locus consists of two (plane) curves which transversally meet at their common singular point. In order to better understand singularities the geometrician constructs their resolution by means of blowups. In finitely many steps they provide a surface without singularities (a manifold) together with a projection map onto the original surface which interprets it as a shade of manifold.
 Diabolo:  The Diabolo equation x2 = (y2+z2)2 factorizes into the product (x−y2−z2)(x+y2+z2) = 0. Hence, the respective surface is the unification of the two single-shell rotating hyperboloids x = ±(y2+z2).  They touch each other tangentially at the origin. The contact can algebraically be gathered from the concurrent linear term x in the two factors. The tangent plane is the vertical plane x = 0.The stripes in the images are shades due to lighting. If you modify the Diabolo equation by adding a constant term such as in x2 = (y2+z2)2+1/1000, then the two halves are separated. The substitution of x by x+y, however, yields the variation (x+y)2 = (y2+z2)2 of the equation. The two shells are moved at an angle to each other.
 Dullo: If the audience in an oval stadium scream about a score (typically of the favoured team), the sound spreads like a quickly inflated floating tyre. After some split seconds the tyre meets itself at its centre – the opening has closed – and that is what exactly happens at the kick-off spot. At that point sound waves from all directions meet simultaneously and are boosted accordingly. This is why referees are advised to always stay level with the ball. Thus, when a goal is scored they do not stand in the middle circle and get a buzzing in their ears.
Seepferdchen (Seahorse):  If you want to find the equation of this surface it would take strong efforts. The soft tangential contact is not easy to achieve. It vanishes as you only slightly change the formula.  The elegance of the sea horse is an illusion: If you look at it from behind or from the side, it appears quite clumsy. Sea horses live worldwide in tropical and temperate climate zones. Its Latin name is Hippocampus, you can find the equation next to it.

Herwig Hauser’s classic algebraic surfaces are compiled for the original IMAGINARY exhibition. Herwig Hauser’s forms and formulas are chosen in such a way that equations are simple and beautiful. The figures are plain and natural and show interesting geometrical facts. Herwig Hauser is professor of mathematics at the University of Vienna and works in algebraic geometry and singularity theory. [Source]
Zoom Info
spring-of-mathematics:

Herwig Hauser Classic(P1) - Authors | Herwig Hauser:
Zitrus (Citric): The equation x2+z2 = y3(1−y)3 of Citric appears as simple as the figure itself. Two cusps mirror-symmetrically arranged rotate around the traversing axis. The equation x2+z2 = y3 simplified by omitting (1−y)3 provides for exactly one cusp, and x2+z2 = (1−y)3 yields the mirror image. Both are infinitely extending surfaces. The product on the right side of the initial equation ensures that Citric remains bounded. You may consider the following: If the absolute value of y is getting larger than 1 the right side becomes negative and the equation does not admit real solutions of x and z.


Ding Dong: This surface described by the equation x²+y²+z³ = z² was one of the very first visualizations we tried. Equation and shape are simple: A vertical alpha-loop rotates around the z-axis. But there was the problem with the colouring. Green is generally rather tricky in three-dimensional visualization of surfaces and, in addition, tends to be matt or yellowish. The lights and reflexions must be well tested. Note the light blue hard shadow intensifying the spatial effect.
 Daisy: The equation (x2−y3)2 = (z2−y2)3 of Daisy implies by differentiation that the singular locus consists of two (plane) curves which transversally meet at their common singular point. In order to better understand singularities the geometrician constructs their resolution by means of blowups. In finitely many steps they provide a surface without singularities (a manifold) together with a projection map onto the original surface which interprets it as a shade of manifold.
 Diabolo:  The Diabolo equation x2 = (y2+z2)2 factorizes into the product (x−y2−z2)(x+y2+z2) = 0. Hence, the respective surface is the unification of the two single-shell rotating hyperboloids x = ±(y2+z2).  They touch each other tangentially at the origin. The contact can algebraically be gathered from the concurrent linear term x in the two factors. The tangent plane is the vertical plane x = 0.The stripes in the images are shades due to lighting. If you modify the Diabolo equation by adding a constant term such as in x2 = (y2+z2)2+1/1000, then the two halves are separated. The substitution of x by x+y, however, yields the variation (x+y)2 = (y2+z2)2 of the equation. The two shells are moved at an angle to each other.
 Dullo: If the audience in an oval stadium scream about a score (typically of the favoured team), the sound spreads like a quickly inflated floating tyre. After some split seconds the tyre meets itself at its centre – the opening has closed – and that is what exactly happens at the kick-off spot. At that point sound waves from all directions meet simultaneously and are boosted accordingly. This is why referees are advised to always stay level with the ball. Thus, when a goal is scored they do not stand in the middle circle and get a buzzing in their ears.
Seepferdchen (Seahorse):  If you want to find the equation of this surface it would take strong efforts. The soft tangential contact is not easy to achieve. It vanishes as you only slightly change the formula.  The elegance of the sea horse is an illusion: If you look at it from behind or from the side, it appears quite clumsy. Sea horses live worldwide in tropical and temperate climate zones. Its Latin name is Hippocampus, you can find the equation next to it.

Herwig Hauser’s classic algebraic surfaces are compiled for the original IMAGINARY exhibition. Herwig Hauser’s forms and formulas are chosen in such a way that equations are simple and beautiful. The figures are plain and natural and show interesting geometrical facts. Herwig Hauser is professor of mathematics at the University of Vienna and works in algebraic geometry and singularity theory. [Source]
Zoom Info
spring-of-mathematics:

Herwig Hauser Classic(P1) - Authors | Herwig Hauser:
Zitrus (Citric): The equation x2+z2 = y3(1−y)3 of Citric appears as simple as the figure itself. Two cusps mirror-symmetrically arranged rotate around the traversing axis. The equation x2+z2 = y3 simplified by omitting (1−y)3 provides for exactly one cusp, and x2+z2 = (1−y)3 yields the mirror image. Both are infinitely extending surfaces. The product on the right side of the initial equation ensures that Citric remains bounded. You may consider the following: If the absolute value of y is getting larger than 1 the right side becomes negative and the equation does not admit real solutions of x and z.


Ding Dong: This surface described by the equation x²+y²+z³ = z² was one of the very first visualizations we tried. Equation and shape are simple: A vertical alpha-loop rotates around the z-axis. But there was the problem with the colouring. Green is generally rather tricky in three-dimensional visualization of surfaces and, in addition, tends to be matt or yellowish. The lights and reflexions must be well tested. Note the light blue hard shadow intensifying the spatial effect.
 Daisy: The equation (x2−y3)2 = (z2−y2)3 of Daisy implies by differentiation that the singular locus consists of two (plane) curves which transversally meet at their common singular point. In order to better understand singularities the geometrician constructs their resolution by means of blowups. In finitely many steps they provide a surface without singularities (a manifold) together with a projection map onto the original surface which interprets it as a shade of manifold.
 Diabolo:  The Diabolo equation x2 = (y2+z2)2 factorizes into the product (x−y2−z2)(x+y2+z2) = 0. Hence, the respective surface is the unification of the two single-shell rotating hyperboloids x = ±(y2+z2).  They touch each other tangentially at the origin. The contact can algebraically be gathered from the concurrent linear term x in the two factors. The tangent plane is the vertical plane x = 0.The stripes in the images are shades due to lighting. If you modify the Diabolo equation by adding a constant term such as in x2 = (y2+z2)2+1/1000, then the two halves are separated. The substitution of x by x+y, however, yields the variation (x+y)2 = (y2+z2)2 of the equation. The two shells are moved at an angle to each other.
 Dullo: If the audience in an oval stadium scream about a score (typically of the favoured team), the sound spreads like a quickly inflated floating tyre. After some split seconds the tyre meets itself at its centre – the opening has closed – and that is what exactly happens at the kick-off spot. At that point sound waves from all directions meet simultaneously and are boosted accordingly. This is why referees are advised to always stay level with the ball. Thus, when a goal is scored they do not stand in the middle circle and get a buzzing in their ears.
Seepferdchen (Seahorse):  If you want to find the equation of this surface it would take strong efforts. The soft tangential contact is not easy to achieve. It vanishes as you only slightly change the formula.  The elegance of the sea horse is an illusion: If you look at it from behind or from the side, it appears quite clumsy. Sea horses live worldwide in tropical and temperate climate zones. Its Latin name is Hippocampus, you can find the equation next to it.

Herwig Hauser’s classic algebraic surfaces are compiled for the original IMAGINARY exhibition. Herwig Hauser’s forms and formulas are chosen in such a way that equations are simple and beautiful. The figures are plain and natural and show interesting geometrical facts. Herwig Hauser is professor of mathematics at the University of Vienna and works in algebraic geometry and singularity theory. [Source]
Zoom Info
spring-of-mathematics:

Herwig Hauser Classic(P1) - Authors | Herwig Hauser:
Zitrus (Citric): The equation x2+z2 = y3(1−y)3 of Citric appears as simple as the figure itself. Two cusps mirror-symmetrically arranged rotate around the traversing axis. The equation x2+z2 = y3 simplified by omitting (1−y)3 provides for exactly one cusp, and x2+z2 = (1−y)3 yields the mirror image. Both are infinitely extending surfaces. The product on the right side of the initial equation ensures that Citric remains bounded. You may consider the following: If the absolute value of y is getting larger than 1 the right side becomes negative and the equation does not admit real solutions of x and z.


Ding Dong: This surface described by the equation x²+y²+z³ = z² was one of the very first visualizations we tried. Equation and shape are simple: A vertical alpha-loop rotates around the z-axis. But there was the problem with the colouring. Green is generally rather tricky in three-dimensional visualization of surfaces and, in addition, tends to be matt or yellowish. The lights and reflexions must be well tested. Note the light blue hard shadow intensifying the spatial effect.
 Daisy: The equation (x2−y3)2 = (z2−y2)3 of Daisy implies by differentiation that the singular locus consists of two (plane) curves which transversally meet at their common singular point. In order to better understand singularities the geometrician constructs their resolution by means of blowups. In finitely many steps they provide a surface without singularities (a manifold) together with a projection map onto the original surface which interprets it as a shade of manifold.
 Diabolo:  The Diabolo equation x2 = (y2+z2)2 factorizes into the product (x−y2−z2)(x+y2+z2) = 0. Hence, the respective surface is the unification of the two single-shell rotating hyperboloids x = ±(y2+z2).  They touch each other tangentially at the origin. The contact can algebraically be gathered from the concurrent linear term x in the two factors. The tangent plane is the vertical plane x = 0.The stripes in the images are shades due to lighting. If you modify the Diabolo equation by adding a constant term such as in x2 = (y2+z2)2+1/1000, then the two halves are separated. The substitution of x by x+y, however, yields the variation (x+y)2 = (y2+z2)2 of the equation. The two shells are moved at an angle to each other.
 Dullo: If the audience in an oval stadium scream about a score (typically of the favoured team), the sound spreads like a quickly inflated floating tyre. After some split seconds the tyre meets itself at its centre – the opening has closed – and that is what exactly happens at the kick-off spot. At that point sound waves from all directions meet simultaneously and are boosted accordingly. This is why referees are advised to always stay level with the ball. Thus, when a goal is scored they do not stand in the middle circle and get a buzzing in their ears.
Seepferdchen (Seahorse):  If you want to find the equation of this surface it would take strong efforts. The soft tangential contact is not easy to achieve. It vanishes as you only slightly change the formula.  The elegance of the sea horse is an illusion: If you look at it from behind or from the side, it appears quite clumsy. Sea horses live worldwide in tropical and temperate climate zones. Its Latin name is Hippocampus, you can find the equation next to it.

Herwig Hauser’s classic algebraic surfaces are compiled for the original IMAGINARY exhibition. Herwig Hauser’s forms and formulas are chosen in such a way that equations are simple and beautiful. The figures are plain and natural and show interesting geometrical facts. Herwig Hauser is professor of mathematics at the University of Vienna and works in algebraic geometry and singularity theory. [Source]
Zoom Info

spring-of-mathematics:

Herwig Hauser Classic(P1) - Authors | Herwig Hauser:
Zitrus (Citric): The equation x2+z2 = y3(1−y)3 of Citric appears as simple as the figure itself. Two cusps mirror-symmetrically arranged rotate around the traversing axis. The equation x2+z2 = y3 simplified by omitting (1−y)3 provides for exactly one cusp, and x2+z2 = (1−y)3 yields the mirror image. Both are infinitely extending surfaces. The product on the right side of the initial equation ensures that Citric remains bounded. You may consider the following: If the absolute value of y is getting larger than 1 the right side becomes negative and the equation does not admit real solutions of x and z.
Ding Dong: This surface described by the equation x²+y²+z³ = z² was one of the very first visualizations we tried. Equation and shape are simple: A vertical alpha-loop rotates around the z-axis. But there was the problem with the colouring. Green is generally rather tricky in three-dimensional visualization of surfaces and, in addition, tends to be matt or yellowish. The lights and reflexions must be well tested. Note the light blue hard shadow intensifying the spatial effect.
 Daisy: The equation (x2−y3)2 = (z2−y2)3 of Daisy implies by differentiation that the singular locus consists of two (plane) curves which transversally meet at their common singular point. In order to better understand singularities the geometrician constructs their resolution by means of blowups. In finitely many steps they provide a surface without singularities (a manifold) together with a projection map onto the original surface which interprets it as a shade of manifold.
 Diabolo:  The Diabolo equation x2 = (y2+z2)2 factorizes into the product (x−y2−z2)(x+y2+z2) = 0. Hence, the respective surface is the unification of the two single-shell rotating hyperboloids x = ±(y2+z2).  They touch each other tangentially at the origin. The contact can algebraically be gathered from the concurrent linear term x in the two factors. The tangent plane is the vertical plane x = 0.The stripes in the images are shades due to lighting. If you modify the Diabolo equation by adding a constant term such as in x2 = (y2+z2)2+1/1000, then the two halves are separated. The substitution of x by x+y, however, yields the variation (x+y)2 = (y2+z2)2 of the equation. The two shells are moved at an angle to each other.
 Dullo: If the audience in an oval stadium scream about a score (typically of the favoured team), the sound spreads like a quickly inflated floating tyre. After some split seconds the tyre meets itself at its centre – the opening has closed – and that is what exactly happens at the kick-off spot. At that point sound waves from all directions meet simultaneously and are boosted accordingly. This is why referees are advised to always stay level with the ball. Thus, when a goal is scored they do not stand in the middle circle and get a buzzing in their ears.
Seepferdchen (Seahorse):  If you want to find the equation of this surface it would take strong efforts. The soft tangential contact is not easy to achieve. It vanishes as you only slightly change the formula.  The elegance of the sea horse is an illusion: If you look at it from behind or from the side, it appears quite clumsy. Sea horses live worldwide in tropical and temperate climate zones. Its Latin name is Hippocampus, you can find the equation next to it.
  • Herwig Hauser’s classic algebraic surfaces are compiled for the original IMAGINARY exhibition. Herwig Hauser’s forms and formulas are chosen in such a way that equations are simple and beautiful. The figures are plain and natural and show interesting geometrical facts. Herwig Hauser is professor of mathematics at the University of Vienna and works in algebraic geometry and singularity theory. [Source]
You may have heard that a proton is made from three quarks. Indeed here are several pages that say so. This is a lie — a white lie, but a big one. In fact there are zillions of gluons, antiquarks, and quarks in a proton. The standard shorthand, “the proton is made from two up quarks and one down quark”, is really a statement that the proton has two more up quarks than up antiquarks, and one more down quark than down antiquarks. To make the glib shorthand correct you need to add the phrase “plus zillions of gluons and zillions of quark-antiquark pairs.” Without this phrase, one’s view of the proton is so simplistic that it is not possible to understand the LHC at all.

Matt Strassler, What’s a Proton, Anyway? (via thesummerofmark)

That’s why I like the term valence quarks, protons have three valence quarks along with all the other quark-antiquark pairs that arise from random fluctuation. This is a concept I feel is never taught well.

Talk Like a Physicist

scienceisbeauty:

It’s very easy, just rehearse these phrases… and try use them with confidence in every conversation.

  • Use “canonical” when you mean “usual” or “standard.” As in, “the canonical example of talking like a physicist is to use the word ‘canonical’.
  • Use “orthogonal” to refer to things that…

javeliner:

think about the concept of a library. that’s one thing that humanity didn’t fuck up. we did a good thing when we made libraries