|
Field |
Author |
Description |
| Basis of Vector Spaces |
Algebra |
Mathematica |
The same object, here a circle, can be completely different when viewed in other vector spaces. |
| Boys Surface (Bryant and Kusner) |
Geometry |
3D Xplor Math |
The Boy surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. |
| Brunnian Links |
Algebra |
Rob Scharein |
These are Borromean Rings... |
| Chryzodes |
Number Theory |
J-F. Collonna &. J-P Bourguigno |
Chryzodes are visualizations of arithmetic using chords in a circle. |
| Complex Numbers |
Algebra |
Brendan |
We visualize complex numbers in the same way we visualize an ordered pair on a plane. |
| Dual Polyhedron |
Geometry |
MathWorld |
This image shows the five Platonic solids in the first row, their duals directly below them in the second row, and the compounds of the Platonic solids and their duals in the third row. |
| Ford Circles |
Geometry |
code.haskell.org |
This is an example of a fractal image called Ford Circles which is a subset of the Apollonian gasket |
| Frabjous |
Other |
George W. Hart |
Frabjous is a sculpture created by George W. Hart from laser cut aspen wood. The sculpture is constructed from elongated s-curve pieces that, when fitted together, create a swirling vortex. |
| Frozen Pages/Volume of Revolution |
Calculus |
Lizah Masis |
|
| Gaussian Pyramid |
|
|
A Gaussian pyramid is a set of images that are successively blured and subsampled that has many computer vision applications |
| Hyperboloid |
Calculus |
Paul Nylander |
A hyperboloid is a quadric, a type of surface in three dimensions. |
| Hypercube |
Geometry |
John Baez |
This is an example of a figure that exists in the 4th dimension. It is the dual to the tesseract. It is also the four dimensional figure that is analogous to the three dimensional octahedron. |
| Impossible Geometry |
Geometry |
Lizah Masis |
This image mirrors the depths of artistic creativity combined with mathematical abstractness. M.C. Escher(1898-1972)in this image depicted distorted geometry by presenting infinite planes on a two dimensional plane, making it an impossible reality. If you look closely at the image and imagine being in the house after it has been built, there are a few things you will notice that are not quite right. Imagine standing at one place in the house and watching people move about. At one time, they will be straight up on the floor, but as they climb to higher storeys, it will look like they are walking upside down or on the walls, which is a practical impossibility. Also, although the people climbing the stairs will seem to be ascending, they will actually always remain on the same storey. This image goes beyond the third dimension, showing three different worlds on a two dimensional plane as if they were continuously existing. |
| Inside the Flat (Euclidean) Dodecahedron |
Geometry |
Paul Nylander |
Here is a dodecahedron viewed from the inside with flat mirrored walls. |
| Inversion |
Geometry |
Xah Lee |
This image is an example of a fractal pattern that can be created with repeated inversion in circles. |
| Involute |
Geometry |
Xah Lee |
A colorful illustration of different involutes of a circle obtained by rolling a line around the circle. |
| Kleinian Quasifuchsian Limit Set |
Fractals |
Paul Nylander |
Here is a Sunset Moth “blown about” inside a Quasifuchsian limit set. Originally, Felix Klein described these fractals as “utterly unimaginable”, but today we can visualize these fractals with computers. |
| Lorenz Attractor |
Dynamic Systems |
Aaron A. Aaronson |
The Lorenz Attractor is a 3-dimensional fractal structure generated by a set of 3 ordinary differential equations. |
| Mobius Strip |
Topology |
Wikipedia |
A Mobius strip, also referred to as a Mobius band, is a surface with only one side and one edge. |
| Problem of Apollonius |
Geometry |
Paul Nylander |
This an example of a fractal that can be created by repeatedly solving the Problem of Apollonius. |
| Quaternion |
|
|
|
| Roulette |
Geometry |
Wolfram MathWorld |
Four different roulettes formed by rolling four different shapes and tracing a fixed point on each of these shapes. |
| Seven Bridges of Königsberg |
Graph Theory |
Bogdan Giuşcă |
The Seven Bridges of Königsberg is a historical problem that illustrates the foundations of Graph Theory |
| Sphere Inversion 1 |
Geometry |
Jos Leys |
A 3D inversion of a sphere. |
| Tesseract |
Geometry |
Robert Neil Boyd |
This is an image of the generalization of the cube to the fourth dimension. |
| Three Cottages Problem |
Other |
Unknown |
The three cottage problem is a problem in graph theory. |
