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bulgarianacademyIn this talk we discuss a new geometric characterization of the so called Napoleon n-gons characterized by the property that the centers of the regular n-gons erected outwardly on its sides are vertices of a regular n-gon. As a consequence, we obtain a new proof of the well-known theorem of Barlotti-Greber that an n-gon is Napoleon if and only if it is affine-regular. Moreover, we generalize this theorem by obtaining an analytic characterization of the n-gons leading to a regular n-gon after iterating the above construction k  times.
The talk is based on a joint work with Prof. T. Andreescu, University of Texas at Dallas and
Prof. V. Georgiev, University of Pisa, Italy accepted for publication in American Mathematical Monthly.

Later in the session, you will learn more about the High School Students Institut of Mathematics and Informatics established in 2000 by the Union of Bulgarian Mathematicians on the occasion of the World Year of Mathematics.


poshenIt’s easy to generate large numbers for their own sake.  A more interesting question is whether huge numbers ever arise naturally from simple-looking situations.  In this talk, we will explore two examples of this phenomenon.  The first will be a surprise from the International Mathematical Olympiad.  The second concerns Szemeredi’s Regularity Lemma, a result of central significance in graph theory.
This talk will be accessible to a general audience.  Only understanding of arithmetic is required: addition, subtraction, multiplication, division, and exponentiation.  Nevertheless, only about 50 (out of 500+) International Math Olympiad contestants correctly solved the corresponding problem during the IMO contest, and so the talk will be of interest to students spanning the full range of experience.
About the speaker:
As a math professor at Carnegie Mellon University, Po-Shen Lo conducts research on a variety of topics that lie at the intersection of combinatorics (the study of discrete systems), probability theory, and computer science.  Po-Shen also works to connect the worlds of research and school math, as the national lead coach of the USA International Math Olympiad team.  He was a member of the 1999 USA IMO team, which was led by Titu Andreescu.  To further develop the talent base in the USA (and the world), he recently teamed up with a number of math/science contest stars to create an open web platform (expii.com), which empowers the world to collaboratively create interactive expositions on math and science topics.

MMC LogoPlease join us for a fun look at permutation patterns.  We will count some special classes of permutations.  For example, there are “132-avoiding” permutations, which are those (like 546231) that never have three entries in order smallest-largest-middle.  Among the n! permutations of size n, how many are 132-avoiding?  And how many are 123-avoiding?  That question is just the beginning.  Next, we can count the number of permutations with 3 “descents”—downsteps between consecutive entries—again, like 546231—or the number of permutations with 3 “excedences”—cases of pi(i)>i—again, like 546231.  There is a connection, which is another beginning.  All this can be unified, and we’ll try to do that using “triangular functions.”


amc8e02Come join us this Saturday for a fun session of AMC 8 level problems and beyond.  November 18, 2014 (Tuesday) is the AMC 8 test, so come study with Dr. Titu Andreescu, former director of the American Mathematics Competition for 5 years, former coach of the US IMO team, and of course, the director of Metroplex Math Circle and AwesomeMath.

If you have a child who would like to participate in the AMC 8 tests, but his/her school does not offer the opportunity, you can register with Kathy Cordeiro after math circle ($10 registration fee).

Remember, we are now meeting in room 2.312 of the ECSS building.

AMC_8_And_Beyond_MMC

Answers_to_AMC_8_Session


imre

Please join us for another exciting math circle where we are pleased to welcome Dr. Imre Leader.  Dr. Leader is a professor of Pure Mathematics at the University of Cambridge, an IMO medalist, and a 10 times national champion of Othello!

He will give a presentation this Saturday on Van Der Waerden’s Theorem which “is a theorem in the branch of mathematics called Ramsey theory. Van der Waerden’s theorem states that for any given positive integers r and k, there is some number N such that if the integers {1, 2, …, N} are colored, each with one of r different colors, then there are at least k integers in arithmetic progression all of the same color. The least such N is the Van der Waerden number W(rk). It is named after the Dutch mathematician B. L. van der Waerden.[1]

Here is a question to get you thinking, “Suppose that we are given a long string of beads. The beads come in two colors, red or blue, but there may be no `pattern’ to the sequence of colors. Can we guarantee to find three equally-spaced beads of the same color? For example, if the 4th, 6th and 8th beads were blue then this would count.”

This topic will be accessible for even young students as long as they understand power notation, e.g. 3^10.

REMINDER:  We are meeting in room 2.312 of the ECSS building


fibonacci

(Image credit: Wikipedia)

Come join us in learning about  number sequences! We will start with a story about Leonardo Pisano, better known as Fibonacci, his often forgotten fundamental contributions to mathematics (do you know what they are?), and his ubiquitous sequence of Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, …

We will also learn about other important sequences, such as perfect numbers, Mersenne primes, Fermat primes, and see how they are often related to each other in sometimes unexpected ways. They even make surprising appearances in other mathematical disciplines, for example Fermat primes play a key role in what Gauss discovered about construction of regular polygons.
If this sounds interesting, then this lecture is for you, regardless of your grade level. Parents are welcome too and everybody can ask questions! In our audience we mostly see students from grades 6-12, but it is not rare to see much younger aspiring mathematicians and scientists, including future winners of ISEF and other major competitions!
To hear about all that and much more, come join us at this free, no-registration-needed, event at UTD, on Saturday, Sept. 20, 2014, 2-4 PM, in the ECSS building, room 2.312 (note, this is a different room) For more information about how to find us, please see: http://metroplexmathcircle.wordpress.com/about/directions-and-times/
Our speaker, Dr. Branislav Kisačanin, is a frequent speaker at the Metroplex Math Circle and a faculty member at the AwesomeMath Summer Camps and at the new AwesomeMath Academy. He is also involved in science fair competitions at all levels, school to ISEF. He is a practicing computer scientist with great interest in teaching and writing about math, physics, and computer science.
 

Please join us for this kick off event for Math Circle!  Naoki Sato will give an enlightening talk about Game Theory as described below:

 Nim_qc

When playing a two-player game, what is the best move? What is the best overall strategy? And is there a way to determine who can win? In this talk, we will be exploring the basics of combinatorial game theory, starting with simple two-player games, such as Nim. Along the way, we will see how we can determine winning positions, and we will give techniques for analyzing other types of games.

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