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Topics include elementary set theory, techniques for systematic counting, axioms for probability, conditional probability, discrete random variables, infinite geometric series, and random walks. Applications to card games like bridge and poker, to gambling, to sports, to election results, and to inference in fields like history and genealogy, national security, and theology. The emphasis is on careful application of basic principles rather than on memorizing and using formulas. Infinities. The concept of infinity is hard to grasp because it is an abstraction.

There are no tangible objects in our lives that are truly infinite in number so we really have nothing to compare it to. The only way to get an infinite number of anything is by invoking infinity elsewhere, which doesn’t really clarify matters much. 6 Must-See Math Videos That Will Inspire And Frighten. GEM1518K - Mathematics in Art & Architecture - Project Submission. “For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art.” - M.C.

Escher Contents. Moebius Transformations Revealed. Proofs Without Words Gallery. 6174 (number) 6174 is known as Kaprekar's constant[1][2][3] after the Indian mathematician D.

R. DC.pdf (application/pdf Object) The eloquence of... Maths: Free maths help, advice and ramblings. If you are the first to solve this problem I will give you complete set of the Richard Feynman Lectures on Physics (read up upon the Feynman Lectures on Physics).

Question: Take a square of arbitrary side length and construct four new squares with a side length half of the original positioned in the corners a quarter of the way down and across the two sides creating the corner. This would look like: Then in each of the new squares in the furthest corner from the first square create a new square with half the side length a quarter of the way down and across the two sides creating the corner.

Point nine recurring equals one. (This page is entirely factually accurate.

It is neither a joke nor a satire nor a collection of fallacious proofs. All these proofs are genuine and the results are true. Thanks.) Preliminary note. Troll pi explained. Here's the "Troll Pi" or "Pi equals 4" image.

Here's the breakdown, as simple as I can make it. All of the following facts are true: 3 Dimensional Fractals & Mandelbulb. 3 Dimensional Fractals and the Search for the 'true' 3D Mandelbrot Three Dimensional Fractal Mappings Years ago, many fractal enthusiasts viewed these intricate and majestic patterns and thought "Wouldn't this be incredible in 3-D?

". Dozens of methods have been developed to view fractals in an arbitrary number of dimensions. Quaternions are 3D shadows of 4D Julia Sets, which, if sliced in a plane, reveal the corresponding 2 dimensional Julia Set. Other attractive developments include 'Quasi-Fuchian" fractals and the recent popularity of the 'Mandelbulb" 3D Mandelbrot - which was exclusively discovered and implemented collaboratively by the inquisitive genius folks at Fractalforums.com.

Go there to see what is literally the cutting edge of fractal discovery on a daily basis. Euler's Solution to the Basel Problem : EvolutionBlog. I’m in the mood for some math today, so here’s an amusing little proof I recently showed to my History of Mathematics class.

We shall derive the formula \[ \frac{\pi^2}{6}=1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\dots \] Contact networks have no influence on cooperation among individuals. Researchers at Carlos III University of Madrid and the University of Zaragoza theoretically predict, in a scientific study, that contact networks have no influence on cooperation among individuals. For the past twenty years, there has been a great controversy regarding whether the structure of interactions among individuals (that is, if the existence of a certain contact network or social network) helps to foment cooperation among them in situations in which not cooperating brings benefits without generating the costs of helping.

Many theoretical studies have analyzed this subject, but the conclusions have been contradictory, since the way in which people make decisions is almost always based on a hypothesis of the models with very little basis to justify it. This work is based on the results of an experiment carried out by the researchers and on information from other previous studies, as well as on the results (as yet unpublished) obtained from their own new experiments. Benford's Law. If you’ve not heard about Benford’s Law before, you’re in for a real treat with this post. Before we get into the theory, however, indulge with me in a little thought experiment.

(Gedanken) Gedanken Experiment Actual results Huh !!? 5 and Penrose Tiling [video] Pattern master wins million-dollar mathematics prize - physics-math - 21 March 2012. 'Infinity Computer' Calculates Area Of Sierpinski Carpet Exactly. Dirac String Trick. Math Fun Facts!

This archive is designed as a resource for enriching your math courses and nurturing your interest and talent in mathematics! Each Math Fun Fact is a math puzzle or short article that contains a cool mathematics idea. You'll can learn about the mathematics of things like card shuffling to poker to computer vision to fractals to music, just to name a few. This makes great enrichment material for gifted math students or problem-solving groups.

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