Unsolved Problems. There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The Goldbach conjecture. 2. The Riemann hypothesis. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Such that , where is the totient function. 14. 15. 16. Nature by Numbers. 13 Useful Math Cheat Sheets. Posted by Antonio Cangiano in Applied Math, Math Education, Software, Tutorial on September 20th, 2008 | 37 responses Cheat sheets can be very useful and make for great posters around your room.

The following is a collection of 13 cheat sheets for several mathematical topics and programs: And since most of us like to show our math pride off when out and about as well, Amazon sells this awesome Math Cheat Sheet T-shirt with formulas on both sides (Also available for Science and Engineering). How awesome is this? Sponsor’s message: Looking for online algebra homework solutions? Ethiopian multiplication. Ethiopian multiplication You are encouraged to solve this task according to the task description, using any language you may know. What's Special About This Number? What's Special About This Number?

If you know a distinctive fact about a number not listed here, please e-mail me. primes graphs digits sums of powers bases combinatorics powers/polygonal Fibonacci geometry repdigits algebra perfect/amicable pandigital matrices divisors games/puzzles 0 is the additive identity . Alpha: Computational Knowledge Engine. Maze Generator. Maze Generator The program generates mazes using three standard algorithms: Depth-first search, Prim's algorithm, and Kruskal's algorithm.

The Show Gen option will allow you to watch the construction process. Use the scrollbar below the option to control the generation speed. Similarly, the Show Solve option will display the process of solving the maze, and it too has a scrollbar for speed control.The Backtracks option controls the display of dead-end paths, where the solver backs up.The Cycle button will loop the program indefinitely, generating and solving mazes using the current settings. NOTE: This applet will not run properly using Microsoft's Internet Explorer 4 browser if Explorer's Java JIT compiler is turned on. Phi 1.618.

Ø PHI: The Golden Ratio or Golden Section (In Nature, Art, Science and Religion) The Golden Section is a unique Ratio (or relationship between parts) that seems to be preferred by Nature as the best geometry for growth, energy conservation, elegance and has some fundamental relationships to the platonic solids and the Mandelbrot set.

It was formally discovered by the Greeks and incorporated into their art and architecture, but it has been shown to occur even in prehistoric art, possibly as a function of Man's natural affinity for it's beauty. The rectangle at left has a vertical edge length of 1 the horizontal or width of the rectangle is 1.618 If we make a line inside and form a square (far left) it creates another 'golden rectangle' (at right) this subdivision continues inward in a spiral fashion tracing the form of a perfect PHI spiral seen in galaxies, seashells .... Even your hand, arm, ear, teeth, etc are in PHI Proportions! Introduction to Algorithms. Since 2008, Academic Earth has worked diligently to compile an ever-growing collection of online college courses, made available free of charge, from some of the most respected universities.

We proudly build on the precedent set forth by MIT OpenCourseware, believing that everyone deserves access to a world-class education. To facilitate this goal, we have curated links to over 750 online courses and 8,500 individual online lectures, giving students of all ages unparalleled access to college courses they may otherwise never experience. Whether supplementing existing coursework, or learning for the sake of learning, anyone with an internet connection has the freedom to learn at their own pace from world-renowned experts, without the burden of rising tuition costs. To access this collection of free online college courses, simply select your area of interest from the menu below. From Art and Design to Social Science, Academic Earth is sure to have the course you’re looking for.

Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal. Opening Pandora's Box For the Second Time ur story starts with a guy named Rudy Rucker, an American mathematician, computer scientist and science fiction author (and in fact one of the founders of the cyberpunk science-fiction movement).

Around 20 years ago, along with other approaches, he first imagined the concept behind the potential 3D Mandelbulb (barring a small mistake in the formula, which nevertheless still can produce very interesting results - see later), and also wrote a short story about the 3D Mandelbrot in 1987 entitled "As Above, So Below" (also see his blog entry and notebook). Back then of course, the hardware was barely up to the task of rendering the 2D Mandelbrot, let alone the 3D version - which would require billions of calculations to see the results, making research in the area a painstaking process to say the least. So the idea slumbered for 20 years until around 2007. Zooming in reveals some interesting detail, but nothing truly fantastic. Full size shown here.