## Gallery of Algebraic Surfaces

Here’s a very sexy gallery of algebraic surfaces. One of my favorite surfaces is the one defined by equation $x^2 + y^3 + z^5 = 0$, which is named the “sofa“:

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### 2 Responses to “Gallery of Algebraic Surfaces”

1. jose Says:

Algebraic superficial dialogue

5×2 + 2xz2 + 5y6 + 15y4 + 5z2 = 15y5 + 5y3, my x2yz + x2z2 = y3z + y3, every time I see you my (x2+9/4y2+z2-1)3 – x2z3-9/80y2z3=0 does x2 +y2 +z3 = z2! It’s a kind o x2-x3+y2+y4+z3-10z4=0; I’m your x3z + 10x2y + xy2 + yz2 = z3, your x2y2z2+3×2+3y2+z2=1, and you’re my x3 + x2z2 – y2… Let’s seat on the x2+y3+z5 = 0 at (z3-2)2 +(x2+y2-3)3 =0, eating a ‘(x2+y2+z2+R2-r2)2 = R2(x2+y2)’, facing x2yz +xy2+y3+y3z=x2z2 (x2-x3+y2+y4+z3-z4=0) and looking for z2-x2-y2 = 1 in the sky. x2yz + x2z2 + 2 y3z + 3 y3 = 0!

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(Eve, my geisha, every time I see you my süss does dingdong! It’s a kind of flirt; I’m your Harlekin, your Leopold, and you’re my Kolibri… Let’s seat on the sofa at twilight, eating a ‘croissant’, facing solitude (vis a vis) and looking for ufo in the sky. Miau!)

2. Rod Carvalho Says:

Let me convert it to $\LaTeX$ to see how it looks:

$5 x^2 + 2 xz^2 + 5y^6 + 15 y^4 + 5 z^2 = 15 y^5 + 5 y^3$, my $x^2 yz + x^2 z^2 = y^3 z + y^3$, every time I see you my $(x^2+9/4 y^2+z^2 - 1)^3 - x^2 z^3 - 9/80 y^2 z^3=0$ does $x^2 +y^2 +z^3 = z^2$! It’s a kind o $x^2 - x^3 + y^2 + y^4 + z^3 - 10 z^4 = 0$; I’m your $x^3 z + 10 x^2 y + x y^2 + y z^2 = z^3$, your $x^2 y^2 z^2 + 3 x^2 + 3 y^2 + z^2 = 1$, and you’re my $x^3 + x^2 z^2 - y^2$… Let’s seat on the $x^2 + y^3 +z^5 = 0$ at $(z^3 - 2)^2 +(x^2 + y^2 - 3)^3 =0$, eating a ‘$(x^2 + y^2 + z^2 + R^2 - r^2)^2 = R^2 (x^2 + y^2)$’, facing $x^2 y z + x y^2 + y^3 + y^3 z = x^2 z^2$ $(x^2 - x^3 + y^2 + y^4 + z^3 - z^4 = 0)$ and looking for $z^2 - x^2 - y^2 = 1$ in the sky. $x^2 y z + x^2 z^2 + 2 y^3 z + 3 y^3 = 0!$