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## October 2 – The Mathematics of Magic Squares

Radu Sorici is a senior at UTD with a double major: Mathematics and Computer Science.   He has been a participant in the international math competitions. Radu works closely with Dr. Andreescu on several projects, including AwesomeMath and the online journal Mathematical Reflections.

Magic Squares are a well-known but endlessly fascinating form of number puzzle.  This should be a very accessible lecture for all students.

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## Linear Perspective Follow Up

Dr. Yotov sends his appreciation for the large and attentive group we had last Saturday.  He also forwarded this link to more resourcess:

Here is a wonderful link to materials on Geometry and Arts:  <http://myweb.cwpost.liu.edu/aburns/sigmaa-arts/index.html>

Dr. Yotov’s talk had all of the great elements of a Math Circle lecture.  He began with a very visual and accessible discussion of one point perspective.  The lecture then built upon this concept to introduce the additional complexities of two-point, three-point and even four-point perspective!  By the end of the talk Dr. Yotov bridged from these ideas to the very challenging but useful concepts of projective geometry.

One of the highlights at the end of the lecture was a look at forced perspective art.  The examples by Julian Beever are only possible by applying the mathematics discovered during the Renaissance and explained to us by Dr. Yotov.

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## September 25 – Mirroslav Yotov

For our next Math Circle we are very pleased to have Dr. Mirroslav Yotov who will speak about “Linear perspective or how Geometry helps in drawing realistic pictures

Have you ever had troubles in drawing a picture and making the painting look natural? Well, I have! And now I know that simple rules from Geometry can help resolve this problem. It was actually the great painters of Renaissances who developed the part of Geometry, called Projective Geometry, in order to put an order in the painting process! Many masterpieces in visual arts, including movies, were made following these rules. I will share with you my excitement of what I know from Geometry, and how it is applied to the visual arts. The presentation will be accessible to people who know about straight lines, circles, planes, and spheres.

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## Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry

Our September 18th speaker, Dr. Branislav Kisacanin,  is an accomplished author.  His book, Mathematical Problems and Proofs, has enjoyed very favorable reviews on Amazon:

This is a very interesting book. If you have mastered the bare essentials of set theory (through the upside down A for “for all” and the backwards E for “there exists”), AND either 1) the bare essentials of combinatorics (through Pascal’s triangle), or 2) the bare essentials of number theory (through the definition of the Moebius function and the statement of the Chinese Remainder theorem), or 3) the bare essentials of geometry (through the law of cosines), AND if you are very talented in mathematics, then this book is a “MUST READ”. It matters not whether you are a high school student or a professional mathematician. You will find new and fruitful insights and quite a few interesting problems in this book. For the beginner, there are several tantalizing (but somewhat oversimplified) references to advanced topics such as Paul Cohen’s proof of the independence of the continuum hypotheses and Wiles’ proof of Fermat’s last theorem. For the professional there are footnotes with references to little known and suprising results obtained in the 20th century. But, unlike the claims in the “editorial review”, this book neither prepares you to read the literaure nor is it a store house of exercises which will help you take your problem solving abilities to the next level. The “editorial review” is “off”, but the book is “right on”. Only the title is unfortunate. Where it will help the career mathematician is in the “beer hall” or “coffee house” or “tea time” discussions with other mathematicians. It is just chock full of beautiful little “gems” which can be shared with one’s friends. This is the kind of beautiful stuff that makes mathematics truly interesting and exciting and though I have searched for a book like this for the last 35 years, this is by far the best in its class which I have found. Dr. John Aiken, Jan 5, 2003.

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## September 18th – Analysis of Number Sequences

The 2010-2011 season of Metroplex Math Circle will have a strong start with our first lecture by Dr. Branislav Kisačanin.

Dr. Kisačanin is a computer scientist at Texas Instruments working in the field of computer vision. In his spare time he likes to use computer vision for fun project such as his Tetris-playing robot. He loved math and physics competitions and nowadays likes to challenge his wife, kids, and friends with math problems and puzzles. Dr.Kisačanin wrote a book about selected mathematical gems:Mathematical Problems and Proofs.

Dr. Kisačanin has chosen Number Sequences as his first topic.  These sequences are critical parts of the tool kit of any middle school problem solver but also offer unexplored mysteries for professional mathematicians.  Following are some of the topics Dr. Kisačanin may cover in the course of his talk:

Triangular numbers

• Derive the formula and the relation to square numbers both algebraically and geometrically
• Sum of n squares (Gregory’s vanishing triangle, induction)
• Sum of n cubes (connection back to triangular numbers)
• Excercise: Sum of n odd numbers (again alg + geom)
• OPTIONAL: Sums of higher powers (telescoping)

Fibonacci numbers

Binomial coefficients

• Coefficients in (a+b)^n
• Combinations
• Pascal’s Triangle
• Excercise: each row sums to 2^n, finding triangular and Fibonacci numbers, …

Other sequences and open problems

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## MMC Speaker Builds Tetris Playing Robot

We have had many firsts at MMC from our talented and varied speakers, but I think on September 18th we will hear from the very first MMC lecturer to have built a robot to play Tetris leveraging his advanced work in vision algorithms.

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## Fermat’s Last Theorem

Here is a terrific video talking about two of the greatest mathematical problem solvers, Fermat and Andrew Wiles.    It is great insight into the life of Wiles, the genius who solved Fermat’s Last Theorem.

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## Metroplex Math Circle 2010-2011

I’m very pleased to announce that the Metroplex Math Circle will soon begin its 2010-2011 season of world class lecturers and challenging problems that have already changed the lives of many outstanding students.

Over the next couple of weeks I will be posting information about our first two lectures scheduled for September 18th and 25th.  To receive up to date information about these and future lectures please consider joining either our Yahoo Group E-Mail list or our Facebook Group.

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