Pages Needing More Mathematical Explanations
[Again, straighten out Image Author vs. Student Author disparity. GK]
The following image pages are in need of explanations that incorporate more mathematical details and content.
Field  Author  Description  

Arbitrage  Other  psdGraphics  
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... 
Buffon's Needle  The Buffon's Needle problem is a mathematical method of approximating the value of pi <math>(\pi = 3.1415...) </math>involving repeatedly dropping needles on a sheet of lined paper and observing how often the needle intersects a line.  
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 Euler Spiral.  
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  
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  
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. 
Law of cosines  The law of cosines is a trigonometric generalization of the Pythagorean Theorem.  
MILS 04B hlv2  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  Depicted on the right are the first 11 rows of Pascal's triangle, one of the bestknown integer patterns in the history of mathematics. Each entry in the triangle is the sum of the two numbers above it. Pascal's triangle is named after the French mathematician and philosopher Blaise Pascal (16231662), who was the first to write an organized work about the properties and applications of the triangle in his treatise, Traité du triangle arithmétique (Treatise on Arithmetical Triangle) in 1653.<ref name = "wiki:Pascal's triangle">Wikipedia (Pascal's Triangle). (n.d.). Pascal's Triangle. Retrieved from http://en.wikipedia.org/wiki/Pascal%27s_triangle</ref><ref>Pickover, Clifford A.(2009). The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics Sterling. ISBN 9781402757969</ref>
 
Pigeonhole Principle  A pigeon is looking for a spot in the grid, but each box or pigeonhole is occupied. Where should the poor pigeon on the outside go? No matter which box he chooses, he must share with another pigeon. Therefore, if we want all of the pigeons to fit into the grid, there is definitely a pigeonhole that contains more than one pigeon. This concept is commonly known as the pigeonhole principle. The pigeonhole principle itself may seem simple but it is a powerful tool in mathematics.  
Quadratic Functions in Landmarks  Algebra  Teacher's Network  The Harbour Bridge in Sydney, Australia. The bridge is in the shape of a parabola. 
Quaternion  Geometry  Quaternions are a number system that work as an extension of complex numbers by having three imaginary components  
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 Giuşcă  
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 Golden Ratio  
The Logarithms, Its Discovery and Development  Algebra  John Napier  These are two pages from John Napier's original Mirifici Logarithmorum Cannonis Descriptio (The Description of the Wonderful Canon of Logarithms) which started with the following which translates into

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... 