A Chiral Aperiodic Monotile

An update to the aperiodic tile. This update shows that a shape that tiles the plane aperiodically without reflections is possible. The original one did not.

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Mathematicians have finally discovered an elusive ‘einstein’ tile

A 13-sided shape known as “the hat” has mathematicians tipping their caps.

It’s the first true example of an “einstein,” a single shape that forms a special tiling of a plane: Like bathroom floor tile, it can cover an entire surface with no gaps or overlaps but only with a pattern that never repeats.

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Math 'Genius' Maryam Mirzakhani Dies At Age 40

Maryam Mirzakhani, an Iranian-born mathematician who was the first woman to win the coveted Fields Medal, died Saturday in a US hospital after a battle with cancer. She was 40.

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With Discovery, 3 Scientists Chip Away At An Unsolvable Math Problem

There are now 15 known convex pentagons, or nonregular pentagons with the angles pointing outward, that can "tile the plane."

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No 'Simple Theory of Everything'

The "exceptionally simple theory of everything," proposed by a surfing physicist in 2007, does not hold water, says Emory mathematician Skip Garibaldi.

Garibaldi, a rock climber in his spare time, did the math to disprove the theory, which involves a mysterious structure known as E8. The resulting paper, co-authored by physicist Jacques Distler of the University of Texas, will appear in an upcoming issue of Communications in Mathematical Physics.

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Cinderella

Experience Geometry on your desktop and on the web. Easily create startling geometric constructions! Starting from simple triangle relations, continuing with trigonometric theorems up to fractals and transformation groups Cinderella lets you create and manipulate visualizations in an intuitive, yet powerful way.

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Geometry Constructions->LaTeX Converter (GCLC)

GCLC (from "Geometry Constructions->LaTeX converter") is a tool for visualizing and teaching geometry, and for producing mathematical illustrations. Its basic purpose is converting descriptions of mathematical objects (written in the GCL language) into digital figures. GCLC provides easy-to-use support for many geometrical constructions, isometric transformations, conics, and parametric curves. The basic idea behind GCLC is that constructions are formal procedures, rather than drawings. Thus, in GCLC, producing mathematical illustrations is based on "describing figures" rather than of "drawing figures".

Polyhedra.org

Polyhedra.org is a collection of interactive models based on the canvas element.

Möbius Transformations Revealed

Möbius Transformations Revealed is a short video by Douglas Arnold and Jonathan Rogness which depicts the beauty of Möbius transformations and shows how moving to a higher dimension reveals their essential unity. It was one of the winners in the 2007 Science and Visualization Challenge and was featured along with the other winning entries in the September 28, 2007 issue of journal Science.

Surfer dude stuns physicists with theory of everything

An impoverished surfer has drawn up a new theory of the universe, seen by some as the Holy Grail of physics, which has received rave reviews from scientists.

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His paper can be downloaded here.

A previous article can be found here.

Islamic Star Patterns

Islamic star patterns arose in the centuries after the birth of Islam, and spread quickly as Islamic rule grew outward from the Middle East to encompass western Europe, northern Africa, and southern Asia. This form of ornamentation peaked in the first half of the second millennium. The practice then tapered off as the borders of the Muslim world began to shrink. Today, historical artifacts can be found in countries from Spain to Uzbekistan, with important concentrations in Spain, Turkey, Iran, and Morocco.

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Arabic Geometry

Catnaps.org has an interesting article on Arabic geometrical patterns.

The Human Geometry

The Human Geometry Project celebrates mathematical art, music, dance and literature through exploration of the human form. And for more risqué pictures, visit Naked Geometry.

Gato (Graph Animation Toolbox)

Gato - the Graph Animation Toolbox - is a software which visualizes algorithms on graphs. Graphs are mathematical objects consisting of vertices and edges connecting pairs of vertices: think of cities as vertices and interstates as edges connecting two cities. Algorithms might find a shortest path - the fastest route - or a minimal spanning tree or solve one of other interesting problems on graphs: maximal-flow, weighted and non-weighted matching and min-cost flow. Visualisation means linking cause - the statements of an algorithm - immediately to an effect - changes to the graph the algorithm has as its input - by terms of blinking, changing colors and other visual effects.

E-Tutor Graphing Calculator

E-Tutor has a nice, online, graphing calculator for visualizing equations.

Graph Layout Engine (GLEE)

GLEE is a .NET tool for graph layout and viewing. It has been developed in Microsoft Research by Lev Nachmanson. GLEE is built on principles of the Sugiyama scheme; it produces so called layered, or hierarchical, layouts. This kind of a layout naturally applies to graphs with some flow of information. The graph could represent a control flow graph of a program, a state machine, a C++ class hierarchy, etc.

WZGrapher Function Grapher

WZGrapher is an easy-to-use and small-footprinted Function Graphing and Calculation Program written in C language, with capabilities to plot both cartesian and polar functions. WZGrapher can also be used to graph numerical solution curves of integrals, to solve numerically and graph ordinary differential equations up to the fifth order, and to calculate value tables (also of ODEs) including the first derivative values.

Group Explorer

Group Explorer is mathematical visualization software for the abstract algebra classroom. It helps the user visualize group theory, builds students' intuition, and enables experimentation with groups.

Mathematical Illustrations

Mathematical Illustrations is a book on mathematical PostScript programming and geometry. The website contains plenty of examples for downloading.

WIRIS CAS Web Calculator

WIRIS CAS is an on-line platform for mathematical calculations designed for education. It is in fact a CAS that also includes a DGS inside. You can access a powerful calculation toolbar through an HTML page that includes integrals and limits calculation, function graphing in 2D or 3D or symbolic matrices manipulation. It covers all mathematical topics from High School to University level (Calculus, Algebra, …).