Pages Needing More Mathematical Explanations
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[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  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... 