Pages Needing More Mathematical Explanations

From Math Images

[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
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	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 three-dimensional space. This object is a single-sided 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	J-F. Collonna &. J-P Bourguigno	Chryzodes are visualizations of arithmetic using chords in a circle.
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.
Ford Circles	Geometry	code.haskell.org	This is an example of a fractal image called Ford Circles which is a special case of the Apollonian gasket
Fractal Bog	Fractals	Jean-Francois Colonna	This image was obtained by means of a self-transformation 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.
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.
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. Contents 1 The following image pages are in need of explanations that incorporate more mathematical details and content.
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.
Pascal's triangle	Algebra	The Math Forum @ Drexel	The first 11 rows of Pascal's triangle are depicted on the right.
Problem of Apollonius	Geometry	Paul Nylander	This an example of a fractal that can be created by repeatedly solving the Problem of Apollonius.
Quaternion
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 cut-out 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.
Z-Squared 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...