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Anne Burns' Mathscapes +In her Mathscape images, Anne M. Burns combines recursive algorithms for clouds, mountains, and various imaginary plant forms into one picture. __TOC__ <br style="clear: both" />
Apollonian Snowflake +This is a combination of the [http://www.m This is a combination of the [ Apollonian Gasket] and the [ Koch Snowflake], both of which are fractals. The result will be an endless fractal made from two existing fractals. Its really a half-Apollonian Gasket because I'm only iterating the largest inscribed circle for each triangle. To start, a construction of the Koch Snowflake must be made because this will be the layout for the circles. On Geometers Sketchpad (GSP, a very useful program that I highly recommend to those who read this page) I am able to make a Koch Curve tool. This tool will let me apply the Koch Curve to any line segment. (Look at the bottom for specific instructions). Simultaneously, I add inscribed circles to my Curve tool. These circles will be my Apollonian aspect of my image. When I increase the iterations of the snowflake, the circles will iterate as well. As cool as this sounds already, adding colors will really make the snowflake ten times more awesome. make the snowflake ten times more awesome.
Apothems and Area +The image to the right shows the shortest distance from the center to the midpoint of one side in various regular polygons.
Application of the Euclidean Algorithm +This image shows a pattern of music rhythms generated by Euclidean algorithm. To find out the process of generating music rhythms or how it sounds like, go to section [[The Application of Euclidean Algorithm#Euclidean Rhythms| Euclidean Rhythms]].
Arbelos +This modern knife in the shape of an '''arbelos''' is used to make shoes.
Arbitrage +Arbitrage is the possibility of making a r Arbitrage is the possibility of making a risk-free profit without investing capital or, alternatively, as risk-less 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 risk-less 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. on because, in reality, it does not exist.
Art Gallery Theorem +The zig-zag structure of the Berlin Jewish Museum, known as the Libeskind Building, is one example of the many wacky shaped art museums located around the world. The museum's polygonal shape lends itself to an interesting problem of guard security.


Barnsley Fern +The Barnsley Fern was created by Michael Barnsley using an iterated function system.
Basis of Vector Spaces +The same object, here a circle, can be completely different when viewed in other vector spaces.
Bedsheet Problem +Take a piece of paper. Now try to fold it in half more than 7 times. Is it possible? What is the ultimate number of folds a flat piece of material can achieve? This image shows Britney Gallivan’s success at folding a sheet 12 times.
Bezier Curves +A Bezier Curve involves the use of two anchor points and a number of control points to control the form of a curve.
Blue Wash +This image is a random fractal that is created by continually dividing a rectangle into two parts and adjusting the brightness of each resulting part.
Bounding Volumes +A box bounding the Stanford Bunny mesh.
Bouquet +This is a 9-inch diameter table-top sculpture made of acrylic plastic (plexiglas). ''Bouquet'' has a very light and open feeling and gives very different impressions when viewed from different angles.
Boy's Surface +Boy's Surface was discovered in 1901 by Ge 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 3-space 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 Mercedes-Benz. ucted as well as donated by Mercedes-Benz.
Boy's Surface Vocabulary +While trying to prove that an immersion (a 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. t is a single-sided surface with no edges.
Bridge of Peace +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.
Broken Heart +A broken heart created by a variation on a fractal.
Brunnian Links +These are Borromean Rings...
Bump Mapping +Bump mapping is the process of applying a height map to a lit polygon to give a polygon the perception of depth.


Cantor Set +A Cantor set is a simple [[Field:Fractals|fractal]] that laid the foundation for modern topology. The picture at right is an artistic representation of the Cantor set.
Cardioid +A Cardioid is a pattern defined by the path of a point of the circumference of a circle that rotates around another circle.
Catalan Numbers +This greedy little worm wants to eat the p This greedy little worm wants to eat the poor apple. He can only go to the east and to the north in this 8 by 8 grid. Since there is stain on the grid, he cannot pass above the diagonal connecting the worm and the apple. How many ways could he get there? The main image shows only one way of reaching the apple. :This is a very famous grid problem in combinatorics, which could be solved by Catalan numbers. which could be solved by Catalan numbers.
Catenary +A catenary is the curve created by a theoretical representation of a hanging chain or cable held at both ends.
Change Of Coordinate Transformations +An example of various coordinate transformations applied to simple geometry.
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