Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tessellations, fractals, anamorphic art, and more
 

Knots

We all know knots in every day life--in shoelaces, hair, and ropes--but mathematicians in the field of topology study mathematical knots, and create beautiful renditions both physical and digital.


Ashley Knot

This example illustrates the SE rendering mode in KnotPlot, which visualizes the symmetric energy distribution. KnotPlot is a program to visualize and manipulate mathematical knots in three and four dimensions, and the website includes a wealth of resources and pictures. This picture is a direct screen capture from KnotPlot, rendered entirely in OpenGL, an environment for portable, interactive graphics applications. - Rob Scharein

Symmetry 3

This example illustrates the SE rendering mode in KnotPlot, which visualizes the symmetric energy distribution. KnotPlot is a program to visualize and manipulate mathematical knots in three and four dimensions, and the website includes a wealth of resources and pictures. This picture is a direct screen capture from KnotPlot, rendered entirely in OpenGL, an environment for portable, interactive graphics applications. - Rob Scharein

Symmetry 2

This example illustrates the SE rendering mode in KnotPlot, which visualizes the symmetric energy distribution. KnotPlot is a program to visualize and manipulate mathematical knots in three and four dimensions, and the website includes a wealth of resources and pictures. This picture is a direct screen capture from KnotPlot, rendered entirely in OpenGL, an environment for portable, interactive graphics applications. - Rob Scharein

8 torus

This is an example of a torus knot. A torus is a surface best described as a doughnut. A torus knot can be thought of as looping around and through the torus. The symbol T(4,3) means that the string making the knot loops through the hole of the torus 4 times, making 3 revolutions. This knot is drawn with TubePlot. - Dror Bar-Natan (University of Toronto)

27 torus

This is an example of a torus knot. A torus is a surface best described as a doughnut. A torus knot can be thought of as looping around and through the torus. The symbol T(9,4) means that the string making the knot loops through the hole of the torus 9 times, making 4 revolutions. TubePlot. - Dror Bar-Natan (University of Toronto)


American Mathematical Society