Net of a Sphere, Different Map Projections, anda library in Milan, Italy
Veneranda Biblioteca Ambrosiana
I have discovered a library while I was making my research about the lesson on spheres. We know that it is not possible to draw the net of a sphere like cylinders, cones or polyhedra.
That's why it is not easy to map our our spherical world on a 2D paper. There are many different projections to map the world. You can try the interactive of Mathigon to see a few of these projections and how they distort the real size and places of the continents.
Many Mathematicians tried to converge the sphere as different polyhedra so that by using their nets, they could draw the maps. For instance, Buckminster Fuller designed his map by using triangles since he uses an icosahedron ( A Platonic Solid with 20 triangular faces) as the main shape of our world.
This projection style is called Dymaxion (Fuller) projection - For the image and related article:
One of the most famous polymath of the human history, Leonardo Da Vinci, used eight congruent Reuleaux Triangles* as the net of the sphere.
Octant projection (1514), Leonardo da Vinci
- For the image and related article:
*A Reuleaux triangle is a shape formed from the intersection of three circular disks, each having its center on the boundary of the other two. Its boundary is a curve of constant width, the simplest and best known such curve other than the circle itself
Codex Atlanticus is the name of the Da Vinci's notebook that includes this and many other drawings.
To see the collection of all his notebooks, please visit https://www.discoveringdavinci.com/codexes
According to the newsi Bill Gates purchased one of these books "Codex Leicester" for 30 million dollars.
The notebook that we are looking for is “Codex Atlanticus” and it is original pages are in this little library in Milano
The official website of the library and the art gallery: https://www.ambrosiana.it/en/
You may visit the Ambrosiana Library virtually with the help of Google Arts and Culture.
The better news is that we can find this 1119 page - notebook online and categorized as algebra, geometry, physics, natural sciences and etc ...
The online platform where you can find Codex Atlanticus is;
Another reason that this library is a sacred place for the mathematicians is it also has the original copy of “Divina proportione” by Luca Pacioli.
Leonardo's drawings are probably the first illustrations of skeletonic solids which allowed an easy distinction between front and back.
For the Platonic solids, Da Vinci supplied two views: a plane view and a “vacua” or empty view where he removed the sides to better reveal the complete structure of the polyhedron. These “nets” of vertices and edges illustrate the artist’s graphic genius.