## Monday, May 25, 2009

### Thanks to our student coaches!

The photo above shows many Albany Area Math Circle veterans celebrating at our year-end picnic after a terrific year of working with younger students as middle school math circle mentors, MATHCOUNTS coaches, and running summer math camps for middle schoolers. (You can click on the thumbnail for a better view.)

Students pictured are from left to right:

Eric Wang (Shenendahoah HS junior, Acadia/Gowana/Koda MS MATHCOUNTS coach)

Dave Bieber (Niskayuna HS junior, Van Antwerp MS MATHCOUNTS coach, founder and leader summer middle school math camp)

Matthew Babbitt (homeschool 8th grader from Fort Edward, heeg MATHCOUNTS coach, middle school math circle mentor)

Schuyler Smith (homeschool sophomore from Ballston Lake, middle school math circle mentor)

Jay White (homeschool sophomore from Schenectady, heeg MATHCOUNTS coach)

Dana McLaughlin (Guilderland HS sophomore, middle school math circle mentor)

Andrew Ardito (homeschool junior from Coxsackie, AAMC captain, mentor/group-leader middle school math circle)

Zagreb Mukerjee (Guilderland HS senior, heeg MATHCOUNTS coach, middle school math circle lead mentor)

Bea Malsky (Guilderland HS sophomore, middle school math circle mentor)

Markus Salasoo (Niskayuna HS senior, summer math camp co-founder, middle school math circle mentor)

Liz Simon (Guilderland HS senior, lead mentor middle school math circle)

Jason Xu (Niskayuna High School sophomore, middle school math circle mentor)

Anagha Tolpadi (Niskayuna High School junior, Iroquois MS MATHCOUNTS coach, middle school math circle mentor)

Lindsay White (homeschool senior from Schenectady, heeg MATHCOUNTS coach)

Felix Sun (Shenendahoah HS sophomore, Acadia/Gowana/Koda MS MATHCOUNTS coach, middle school math circle lead mentor)

Not pictured:

Haejin Hwang (Guilderland HS sophomore, middle school math circle mentor)

Noah Rubin (Guilderland HS sophomore, middle school math circle mentor)

Wyatt Smith (homeschool freshman from Ballston Lake, middle school math circle mentor)

Luke Trouwborst (homeschool junior from Schenectady, heegMATHCOUNTS coach)

Thanks to all of you who have generously shared your talents and your enthusiasm for challenging mathematics with so many terrific younger students this year!

### Farewell to our seniors!

Wilson Cheung is graduating from Scotia-Glenville High School and will study at SUNY Geneseo next year. Although Wilson only discovered our math circle and joined us during his senior year, he made contributions to AAMC's success at the Princeton Math Contest (PUMaC) and to AAMC team Octahedra at the Harvard-MIT Math Tournament (HMMT).

Zagreb Mukerjee is graduating from Guilderland High School and will study at Harvard next year. Zagreb has been a member of Albany Area Math Circle since his sophomore year, participating in many AAMC adventures at HMMT and NYSML as well as the Upstate NY ARML team. He is a "renaissance person," who has won many notable honors in the humanities as well as in math. Zagreb participated in the League of Women Voter's LeaderSpark and Students Inside Albany leadership training programs, and he has put those leadership skills to great use as a MATHCOUNTS coach of the heeg team as well as in leading the new middle school math circle initiative that started up last fall at the Clifton Park library.

Markus Salasoo is graduating from Niskayuna High School and will study at Cornell next year. Markus has participated on Albany Area Math Circle teams at NYSML and HMMT during his four years in high school, and was himself originally on an Iroquois MATHCOUNTS team coached by an AAMC alum. Last summer, Markus worked with fellow AAMC member Dave Bieber to launch a very successful middle school math camp, which they plan to run again this summer.

Liz Simon is graduating from Guilderland High School and will study at MIT next year. Liz has been a member of Albany Area Math Circle since her sophomore year and has excelled at inspiring and encouraging younger students to share her enthusiasm for tackling "extreme math" challenges. She has been a leader of her high school math club as well as a lead mentor for our new middle school math circle initiative. Liz has done an outstanding job of working with the most extraordinarily talented group of middle school girls that our math circle has ever seen.

Yipu Wang is graduating from Guilderland High School and will study at Cornell next year. Yipu has been a member of Albany Area Math Circle throughout high school, contributing to many team successes at NYSML, HMMT, and PUMaC, as well as earning outstanding individual honors as a two-time USA Math Olympiad participant and reaching the top level of the USA Physics Olympiad qualification test series. Yipu has also won statewide honors for his talents with the violin.

Lindsay White is graduating from her homeschooling high school program and will study at Philadelphia Biblical University next year. Lindsay has been a member of our math circle for the past three years and has participated in many AAMC mathematical expeditions to HMMT and NYSML. Lindsay's radiant smile, spirited determination, and cheerful demeanor have encouraged everyone around her to persist in working on difficult problems. She also participated in the League of Women Voter's LeaderSpark program and has put those leadership skills to work in coaching heeg MATHCOUNTS students throughout her time in high school.

We will very much miss all of our seniors, but we can take comfort in the fact that they have collectively inspired and encouraged so many younger students who will be the spirit of Albany Area Math Circle for many years to come.

Zagreb Mukerjee is graduating from Guilderland High School and will study at Harvard next year. Zagreb has been a member of Albany Area Math Circle since his sophomore year, participating in many AAMC adventures at HMMT and NYSML as well as the Upstate NY ARML team. He is a "renaissance person," who has won many notable honors in the humanities as well as in math. Zagreb participated in the League of Women Voter's LeaderSpark and Students Inside Albany leadership training programs, and he has put those leadership skills to great use as a MATHCOUNTS coach of the heeg team as well as in leading the new middle school math circle initiative that started up last fall at the Clifton Park library.

Markus Salasoo is graduating from Niskayuna High School and will study at Cornell next year. Markus has participated on Albany Area Math Circle teams at NYSML and HMMT during his four years in high school, and was himself originally on an Iroquois MATHCOUNTS team coached by an AAMC alum. Last summer, Markus worked with fellow AAMC member Dave Bieber to launch a very successful middle school math camp, which they plan to run again this summer.

Liz Simon is graduating from Guilderland High School and will study at MIT next year. Liz has been a member of Albany Area Math Circle since her sophomore year and has excelled at inspiring and encouraging younger students to share her enthusiasm for tackling "extreme math" challenges. She has been a leader of her high school math club as well as a lead mentor for our new middle school math circle initiative. Liz has done an outstanding job of working with the most extraordinarily talented group of middle school girls that our math circle has ever seen.

Yipu Wang is graduating from Guilderland High School and will study at Cornell next year. Yipu has been a member of Albany Area Math Circle throughout high school, contributing to many team successes at NYSML, HMMT, and PUMaC, as well as earning outstanding individual honors as a two-time USA Math Olympiad participant and reaching the top level of the USA Physics Olympiad qualification test series. Yipu has also won statewide honors for his talents with the violin.

Lindsay White is graduating from her homeschooling high school program and will study at Philadelphia Biblical University next year. Lindsay has been a member of our math circle for the past three years and has participated in many AAMC mathematical expeditions to HMMT and NYSML. Lindsay's radiant smile, spirited determination, and cheerful demeanor have encouraged everyone around her to persist in working on difficult problems. She also participated in the League of Women Voter's LeaderSpark program and has put those leadership skills to work in coaching heeg MATHCOUNTS students throughout her time in high school.

We will very much miss all of our seniors, but we can take comfort in the fact that they have collectively inspired and encouraged so many younger students who will be the spirit of Albany Area Math Circle for many years to come.

## Wednesday, May 13, 2009

### Physics blind spots

Via Uncertain Principles, here's some fascinating evidence about a physics blindspot.

## Monday, May 4, 2009

### Number sense!

How Many Millions are in a Trillion? from Econ4U on Vimeo.

The 21% correct response figure cited at the end of the video comes from a multiple choice survey given to a thousand American adults. A monkey throwing darts at the five answer choices they provided in the multiple choice version of their poll would hit the correct answer 20% of the time, so a 21% correct response rate is discouraging.

Search for Intelligent Life points out another video describing the public's bewilderment in the face of large numbers:

Edith Stokey and Richard Zeckhauser have a simple and sensible suggestion for getting a handle on large numbers: long division.

A useful number to keep in mind for back-of-the-envelope calculations is that the US population is roughly 300 million.

So the next time you read that the federal government is considering spending a billion dollars on something, you can think that's over $3 per American. And when the federal government considers spending a trillion dollars on something, that's over $3K per person.

## Saturday, May 2, 2009

### Hyperbolic geometry that links crochet and coral

This fascinating TED talk video describes the connections between coral reefs, crochet, and hyperbolic geometry.

If you don't know about hyperbolic geometry, you're not alone (and you're in for a treat.) The TED video gives a nice introduction to the basic idea of hyperbolic geometry, contrasting it to the more familiar Euclidian geometry taught in high school as well as the somewhat less familiar spherical geometry.

For more information about hyperbolic space, check out Williams College math professor Colin Adams' fast-talking alter ego "Mel Slugbate" and his pitch selling real estate in hyperbolic space. You can see a video of Mel's sales pitch as well as his overhead slides on this MSRI webpage.

It turns out that it's remarkably difficult to create 3-d physical models of hyperbolic space using the usual rigid materials (e.g., paper) traditionally employed by geometers. Moreover, such materials are fragile and difficult to manipulate for exploration. However, Cornell mathematician Daina Taimina has discovered that crochet is an ideal medium for constructing sturdy and beautiful models of hyperbolic space, such the hyperbolic plane shown above.

You can see some of her beautiful models and some simple directions here. She has also recently published a book Crocheting Adventures with Hyperbolic Planes with more information.

### Silly standardized test question puzzler

Tanya Khovanova posed an interesting puzzle from VI Arnold:

This one is worth thinking about.

The Russian students to whom Professor Arnold posed this problem were probably members of math circles, which originated in Eastern Europe and Russia and encourage outside-the-box thinking rather than cookbook approaches to problems.

Why couldn't the Russian students solve this apparently straightforward and simple problem?

Scroll down this page for the explanation.

The Russian students realized that the triangle specified in the problem can't exist. The altitude to the hypotenuse of a right triangle can never be more than half the length of the hypotenuse. In fact, the altitude to the hypotenuse of a right triangle will always be exactly half the length of the hypotenuse. This fact is easy to see if you recall that every right triangle can be inscribed in a semicircle.

It's troubling to think that the American standardized testing company allowed this nonsensical problem to stay on their test for ten years!

I have a tiny book written by Vladimir Arnold Problems for Kids from 5 to 15. A free online version of this book is available in Russian. The book contains 79 problems, and problem Number 6 criticizes American math education. Here is the translation:

(From an American standardized test) A hypotenuse of a right triangle is 10 inches, and the altitude having the hypotenuse as its base is 6 inches. Find the area of the triangle. American students solved this problem successfully for 10 years, by providing the “correct” answer: 30 inches squared. However, when Russian students from Moscow tried to solve it, none of them “succeeded”. Why?

This one is worth thinking about.

The Russian students to whom Professor Arnold posed this problem were probably members of math circles, which originated in Eastern Europe and Russia and encourage outside-the-box thinking rather than cookbook approaches to problems.

Why couldn't the Russian students solve this apparently straightforward and simple problem?

Scroll down this page for the explanation.

The Russian students realized that the triangle specified in the problem can't exist. The altitude to the hypotenuse of a right triangle can never be more than half the length of the hypotenuse. In fact, the altitude to the hypotenuse of a right triangle will always be exactly half the length of the hypotenuse. This fact is easy to see if you recall that every right triangle can be inscribed in a semicircle.

It's troubling to think that the American standardized testing company allowed this nonsensical problem to stay on their test for ten years!

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