This license lets others remix, tweak, and build upon your work non-commercially, as long as they credit you and license their new creations under the identical terms.
More information (license deed): http://creativecommons.org/licenses/by-nc-sa/3.0/
Submitted by IMAGINARY on
In quantum mechanics, unlike in classical mechanics, one cannot make precise predictions about how a system will behave. Instead, one is concerned with mere probabilities. Consequently, it is a very important task to determine the basic probabilities associated with a given system. In this snapshot we will present a recent uniqueness result concerning these probabilities.
Submitted by IMAGINARY on
Platonic solids, Felix Klein, H. S. M. Coxeter and a flap of a swallowtail: The five Platonic solids tetrahedron, cube, octahedron, icosahedron and dodecahedron have always attracted much curiosity from mathematicians, not only for their sheer beauty but also because of their many symmetry properties. In this snapshot we will start from these symmetries, move on to groups, singularities, and finally find the connection between a tetrahedron and a “swallowtail”.
Submitted by IMAGINARY on
A friend of mine, an expert in statistical genomics, told me the following story: At a dinner party, an attractive lady asked him, “What do you do for a living?” He replied, “I model.” As my friend is a handsome man, the lady did not question his statement and continued, “What do you model?” “Genes.” She then looked at him up and down and said, “Mh, you must be very much in demand.” “Yes, very much so, especially after I helped discover a new culprit gene for a common childhood disease.” The lady looked puzzled.
Submitted by IMAGINARY on
What is the most efficient way to fence land when you’ve only got so many metres of fence? Or, to put it differently, what is the largest area bounded by a simple closed planar curve of fixed length?
We consider the answer to this question and others like it, making note of recent results in the same spirit.
Submitted by IMAGINARY on
We discuss certain open problems in the context of arrangements of lines in the plane.
Submitted by Renate Quehenberger on
Analogous to Henri Poincaré’s concept of dodecahedral space the epita_dodecahedron allows to visualize the principle of the counter-movements of the opposite polyhedra E+ instead of the pentagonal spaces in his description of the homology sphere in the fifth “Complément” : Thus it clearly shows the different evolving symmetries,- crystallizing in steps of 36 degrees, just as Poincaré anticipated the shape of the universe in 1904.
Submitted by Hua-lun Li on
With computer technology we can visualize mathematics idea and this will explode people’s imagination.
Submitted by Francesco de Comité on
Some examples of polyhedra construction using modular origami.
Submitted by Diana Davis on
Using color and movement, this video rigorously explains what a translation surface is, and the theorem about translation surfaces that I proved in my Ph. D. thesis.
Submitted by Frank Sottile on
Build a hyperbolic football and explore hyperbolic geometry