
Field 
Author 
Description 
Arbitrage 
Other 
psdGraphics 
Arbitrage is the possibility of making a riskfree profit without investing capital or, alternatively, as riskless instantaneous profit. For example, if one investor could purchase 10 dollars for 9 euros at one bank and then go to a different bank and sell the 10 dollars for 10 euros, he or she would have made a riskless profit of 1 euro and arbitrage would have been achieved. One can see the benefits of arbitrage; it is essentially the process of making free money! However, this reminds one of the adage, “There is no free lunch.” [1] Alas, arbitrage is no exception because, in reality, it does not exist. 
Basis of Vector Spaces 
Algebra 
Mathematica 
The same object, here a circle, can be completely different when viewed in other vector spaces. 
Boy's Surface 
Geometry 
Paul Nylander 
Boy's Surface was discovered in 1901 by German mathematician Werner Boy when he was asked by his advisor, David Hilbert, to prove that an immersion of the projective plane in 3space was impossible. Today, a large model of Boy's Surface is displayed outside of the Mathematical Research Institute of Oberwolfach in Oberwolfach, Germany. The model was constructed as well as donated by MercedesBenz. 
Boy's Surface Vocabulary 
Geometry 
Paul Nylander 
While trying to prove that an immersion (a special representation) of the projective plane did not exist, German mathematician Werner Boy discovered Boy’s Surface in 1901. Boy’s Surface is an immersion of the projective plane in threedimensional space. This object is a singlesided surface with no edges. 
Bridge of Peace 
Algebra 

The bridge of peace in Tbilisi ,Georgia, possesses a glass and steel covering frame which possesses a unique tiling structure, conic sections in its roof. Mapping a complicated pattern onto an uneven surface. 
Brunnian Links 
Algebra 
Rob Scharein 
These are Borromean Rings... 
Chryzodes 
Number Theory 
JF. Collonna &. JP Bourguigno 
Chryzodes are visualizations of arithmetic using chords in a circle. 
Coefficients 
Algebra 

Just a quadratic function. 
Cornu Spiral 
Algebra 

The Ponce de Leon Inlet Lighthouse is the tallest lighthouse in Florida. Its grand spiral staircase depicts the Cornu Spiral which is also commonly referred to the <b>Euler Spiral</b>. 
Dandelin Sphere Theory 
Geometry 
Hollister (Hop) David 
This image shows a cone floating on the ocean. a ball floats in the cone with a touch of the ocean surface. A round fish is kissing the ocean surface in the cone. The cone cuts the ocean surface with a "Conic Section", which in the image is an ellipse. 
Different Strokes 
Fractals 
Linda Allison 
Different Strokes is generated with Ultra Fractal, a program designed by Frederik Slijkerman. It consists of 10 layers and uses both Julia and Mandelbrot fractal formulas and other formulas for coloring. 
Dragons 1 
Geometry 
Jos Leys 
A tessellation created in the style of M.C. Escher. 
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. 
Fractal Bog 
Fractals 
JeanFrancois Colonna 
This image was obtained by means of a selftransformation of a fractal process. 
Gaussian Pyramid 


A Gaussian pyramid is a set of images that are successively blured and subsampled repeatedly. The recursive operation is applied on each step so many levels can be created. Gaussian Pyramids have many computer vision applications, and are used in many places. 
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 was created by the artist M. C. Escher 
Indra 432 
Other 
Jos Leys 
A Kleinian group floating on the water. 
Inside the Flat (Euclidean) Dodecahedron 
Geometry 
Paul Nylander 
Here is a dodecahedron viewed from the inside with flat mirrored walls. 
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. 
MILS 04B 
Number Theory 

The spiral curve of the Nautilus sea shell follows the pattern of a spiral drawn in a Fibonacci rectangle, a collection of squares with sides that have the length of Fibonacci numbers.

MILS 04B hlv1 
Number Theory 

The spiral curve of the Nautilus sea shell follows the pattern of a spiral drawn in a Fibonacci rectangle, a collection of squares with sides that have the length of Fibonacci numbers.

MILS 04B hlv2 
Number Theory 

The spiral curve of the Nautilus sea shell follows the pattern of a spiral drawn in a Fibonacci rectangle, a collection of squares with sides that have the length of Fibonacci numbers.

MILS 04B hlv3 
Number Theory 

The spiral curve of the Nautilus sea shell follows the pattern of a spiral drawn in a Fibonacci rectangle, a collection of squares with sides that have the length of Fibonacci numbers.

MILS 04B hlv4 
Number Theory 

The spiral curve of the Nautilus sea shell follows the pattern of a spiral drawn in a Fibonacci rectangle, a collection of squares with sides that have the length of Fibonacci numbers.

MILS 04B hlv5 
Number Theory 

The spiral curve of the Nautilus sea shell follows the pattern of a spiral drawn in a Fibonacci rectangle, a collection of squares with sides that have the length of Fibonacci numbers.

MILS 05 
Number Theory 

The spiral curve of the Nautilus sea shell follows the pattern of a spiral drawn in a Fibonacci rectangle, a collection of squares with sides that have the length of Fibonacci numbers.

Mateko 
Fractals 
Dan Kuzmenka 
Mateko uses different color palettes than image designer Dan Kuzmenka's usual earth tones. He uses fractals to express a spiral without showing the same shape over again. 
Mathematics of Gothic and Baroque Architecture 
Geometry 
Blog 
La Sagrada Família (Holy Family) is a Gothic cathedral in Barcelona, Spain designed by Spanish architect Antoni Gaudí. 
Pascal's triangle 
Algebra 
Chengying Wang and the Math Forum at Drexel 

Quadratic Functions in Landmarks 
Algebra 
Teacher's Network 
The Harbour Bridge in Sydney, Australia. The bridge is in the shape of a parabola. 
Regular Hexagon to Rectangle 
Geometry 

You can use the apothem and perimeter of a regular polygon to find its area. 
Regular Octagon to Rectangle 
Geometry 
Emma F. 
A regular polygon can be "unrolled" to form a rectangle with twice the area of the original polygon. 
Resonance 
Dynamic Systems 
Jeffrey Disharoon 
A picture of a clarinet, an instrument that utilizes a vibrating reed and a resonating chamber to produce sounds. 
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 Giu?c? 
The Seven Bridges of Königsberg is a historical problem that illustrates the foundations of Graph Theory 
Siefert surface I 
Algebra 
Jos Leys 
A Seifert surface, a subset of dynamic systems. 
Skull 
Fractals 
Jos Leys 
An abstract skull created by a variation on a fractal colored to achieve the desired image. 
Sphere Inversion 1 
Geometry 
Jos Leys 
A 3D inversion of a sphere. 
Straight Line and its construction 
Geometry 
Cornell University Libraries and the Cornell College of Engineering 

Strange plant 1 
Fractals 
Jos Leys 
A fractal that looks organic in origin, much like a fern or other plant. Fractals reiterate infinitely, and real ferns seem to grow in the same sort of iterative pattern. 
TestTestTest 
Algebra 
test 
Testing 
The Logarithms, Its Discovery and Development 
Algebra 
John Napier 

The Regular Hendecachoron 
Geometry 
Carlo Sequin 
This object has 11 vertices (shown as spheres), 55 edges (shown as thin cylindrical beams), and 55 triangular faces (shown as cutout frames). Different colors indicate triangles belonging to different cells. 
Three Cottages Problem 
Other 
Unknown 
The three cottage problem is a problem in graph theory. 
Tone 
Dynamic Systems 
Tyler Sammann 
This image shows the keyboard of a piano, which is a tonal instrument. 
Tunnel 
Fractals 
Jos Leys 
A fractal image originating from a Mandelbrot set that Jos Leys created using Ultrafractal. 
Visualization of Social Networks 
Statistics 
Social Graph 
Friend network of a particular Facebook account. The pink indicates a "mob" of tightly interconnected friends, such as high school or college friends. 
ZSquared Necklace 
Geometry 
Tom Banchoff 
Each subject is the graph of a function of a complex variable, first the complex squaring operation and then the cubing function... 