## SMMG - January 2008

 Saturday January 19, 2008 Location: WEL 1.316 (On the UT campus) Group Leader: Dr. Fernando Rodriguez Villegas Topic: Logarithms and Random Numbers Title: Making Up Numbers: The Art of the Cheat Poster: Click here for the poster.

The first Saturday Morning Math Group of the year 2008 was a tremendous success! Dr. Fernando Rodriguez Villegas came and entertained an audience of approximately 200 with his talk "Making Up Numbers: The Art of the Cheat." Dr. Villegas talked about some of the history behind logarithms, how the use of the logarithmic scale helped Kepler discover his celebrated Third Law of planetary motion, and how tattered pages in books of logarithm tables "accidentally" led to the discovery of Benford's Law. We learned that naturally-occurring random numbers tend to have 1 as their leading digit a whopping 30% of the time - not 11.1% as one might expect - and we saw how one can use this principle to detect people who are cheating on their tax returns!

## Math Circle - February 2008

 Saturday February 9, 2008 Location: WEL 1.316 (On the UT campus) Group Leader: Sam Baethge Topic: Geometry Title: "Similarity, Ratios, and Areas" Preview Problem Set: Click here for Page 1, and here for Page 2. Challenge Problem Set: Unfortunately, we cannot post the Challenge Problem Set from this month due to copyright considerations. However, we will post some follow-up questions here soon.

The first meeting of The Austin Math Circle was a tremendous success! Sam Baethge, a retired high school teacher and math team coach, talked to an audience of approximately 50 students and parents about how we can use simple ideas such as similarity, ratios, and area comparisons to prove beautiful theorems from Euclidean geometry such as Ceva's Theorem and Menelaus' Theorem. Sam then treated our audience to an assortment of contest problems and challenged our students to find clever solutions to these questions using the geometric principles we discussed.

## SMMG - February 2008

 Saturday February 23, 2008 Location: WEL 1.316 (On the UT campus) Group Leader: Dr. Henry Segerman Topic: Combinatorics and Graphs Title: The Mathematics of Juggling Poster: Click here for the poster.

The February meeting of the Saturday Morning Math Group was a blast! Dr. Henry Segerman entertained an audience of approximately 150 with his talk "The Mathematics of Juggling." Dr. Segerman talked about how we can use combinatorics and graph theory to analyze - and even generate - juggling patterns. He also talked about how to juggle with three hands (hint: depending on the pattern, it's easier than it sounds), a non-periodic juggling scheme that involves infinitely many balls, and what it might look like if we were able to juggle anti-matter. He also fielded some juggling-related questions at the end of the talk, such as "What is the most unusual thing you've juggled?" (Answer: flaming torches) and "What is the greatest number of objects you can juggle at once?" (Answer: Dr. Segerman's personal record is seven). Due to safety considerations, we were not able to get our speaker to juggle seven flaming torches at once, but the tricks he did show us were very entertaining.

For the problem set Dr. Segerman gave during his talk, click here.

## Math Circle - March 2008

 Saturday March 8, 2008 Location: WEL 1.316 (On the UT campus) Group Leader: Brian Katz Topic: Graph Theory Preview Problem Set: Click here for Page 1, and here for Page 2. Challenge Problem Set: Will be posted after the meeting.

The March meeting of the Austin Math Circle was a lot of fun! Our very own Brian Katz came and gave a talk about some elementary (but very clever!) theorems of graph theory, including a criterion for the existence of an Euler circuit, and some theorems about planar graphs. At the end of his talk, Brian hinted at a connection between regular planar graphs and the beloved Platonic solids, and invited students to explore this beautiful correspondence on their own after the talk. Brian's presentation was very engaging, with numerous opportunities for students to explore problems, make conjectures, and prove their findings.

## SMMG - March 2008

 Saturday March 22, 2008 Location: WEL 1.316 (On the UT campus) Group Leader: Dr. Ted Mahavier (Lamar University) Topic: Optimization Title: Q: What Do Mathematicians Play With? A: Spiders, Coke Cans, and Money Poster: Click here for the poster.

The March meeting of SMMG was a blast! Dr. Ted Mahavier of Lamar University entertained an audience of about 150 with his talk about what it means to be a mathematician, and what mathematicians like to think about. We took a look at some interesting problems, such as how one should save money so that he/she can retire a millionaire, the shortest path from one point on a box to another, and the best possible size of a Coke can. During the break, Dr. Mahavier gave the students two problems to work on and gave prizes from Mathnerds.com to the students who gave the best solutions.

## Math Circle - April 2008

 Saturday April 12, 2008 Location: WEL 1.316 (On the UT campus) Group Leader: Dr. Edward Early (St. Edward's University) Topic: Combinatorics and Number Theory Title: Posets and Mobius Functions Preview Problem Set: Click here.

The April meeting of the Math Circle meeting was a lot of fun! Dr. Edward Early of St. Edward's University came and talked about posets, Mobius functions, and some interesting applications in number theory and combinatorics. Dr. Early introduced the idea of a partial order on a set, showed how we can capture order structure in a picture called a Hasse diagram, and explained how one can define a Mobius function on a graded poset. At the end of the talk, we even saw a mysterious connection between Mobius functions and the number of regions formed by cutting a plane with several lines.

This was the last Austin Math Circle meeting of the semester. We're grateful to all the faculty, grad students, and guest speakers who made it possible for us to kick off this new program. Because of the Math Circle, students were introduced to mathematical topics (such as graph theory and posets) that they would not have seen in their math classes in school.