Origamis

I made every model presented here, and if it is possible I put the tutorial link so you can do them too.

• Some mathematical origamis

• Others origamis

Some beautiful surfaces

All pictures were made with the software Surfer that is downloadable on imaginary.org.

• The Barth Sextic

This surface of degree 6 (sextic) was constructed by Wolf Barth in 1996. The Barth Sextic has 65 singularities altogether. This is the maximum possible number of singularities on a sextic as shown shortly after Barth's construction by Jaffe and Ruberman...so Barth's worls record is unbeatable!

Barth's construction was a big surprise because for a long time people thought that surfaces of degree 6 can only have 64 singularities.

A striking feature of the construction is its icosahedral symmetry.

(Presentation text by Surfer)

I made these images of the Barth Sextic:

• Saturn

From a mathematical point of view, Saturn is not much more than a sphere with a plane crossing it in the middle. Then to see this planet appear, we need a sphere (x^2+y^2+z^2-30=0 for example), and a plane (y=0 for example). Thus the points of the space that satisfy y(x^2+y^2+z^2-30)=0 are not on Earth, are not on Mars, but are on Saturn!

One can say "But a planet is not a "perfect sphere"!" and this person would be right. Well, in fact it's more an ellipsoid than a sphere. So we just have to adjust the equation of the sphere x^2+y^2+z^2-30=0 to make it an ellipsoid 0,6*x^2+0,8*y^2+z^2-30=0. Then if you draw y(0,6*x^2+0,8*y^2+z^2-30)=0, you will see the following image.

Ok, now, one can say "but the rings of Saturn are not a plane, they are not touching the ellipsoid!", and this person would be right. Again. Well now it's a bit more complicated, but if you draw ((0.2*x^2+0.4*y^2+z^2+0.12)^2-0.5*(0.2*x^2+0.4*y^2))*(0.4*x^2+0.6*y^2+0.6*z^2-0.1)=0 you will see the following image.

Now one can say "We can do better!", and this person would be right. Again. But this time I let you play with Surfer and do a better Saturn! If you do it, please let me know. :)

• The little prince became mathematician!

The little prince is one of the best-selling and most translated books ever published. Every one remembers the snake which has eaten an elephant, the crate/sheep, the rose...So I wanted to illustrate this story by the images (and the equations) of these essential symbols of The little prince. I hope one day I'll find the equation of the little prince himself, but if you find it or find the equation of another symbol of this famous book, please let me know!

The snake which has eaten an elephant (this is not a hat).

(x^2+y^3+z^3)(y+z)=0

The crate (the sheep is inside).

The rose.

Some funny surfaces

All pictures were made with the software Surfer.