2013 AIME 2 Problem 10

I’ve been asked about the following problem from the 2013 AIME 2 a few times, so I decided to blog a couple of solutions for it:

Given a circle of radius $\sqrt{13}$, let A be a point at a distance $4 + \sqrt{13}$ from the center C of the circle. Let B be the point on the circle nearest to point A. A line passing through the point A intersects the circle at points K and L. What is the maximum possible area for $\Delta BKL$?

Girls’ Angle Bulletin, Volume 7, Number 1

The cover shows an example of (quasi) self-similarity in nature: the Romanesco broccoli, and alludes to this issue’s Math Buffet.  Flip over the cover and meet Anne Shiu, an L. E. Dickson instructor in the Department of Mathematics at the University of Chicago and a National Science Foundation Postdoctoral Fellow.  Dr. Shiu does research in mathematical biology, which is a vast and exciting field.

Would you believe that it is possible to create 3-D images using a camera with a single lens? Antony Orth, a graduate student in the School of Engineering and Applied Sciences at Harvard, explains how in 3-D Movie Technologies.

UC Berkeley astrophysicist Aaron Lee follows up his introduction to conic sections with Cosmic Conics II, this issue’s installment of Math In Your World. As you read this, Comet ISON hurls toward the sun, where it will venture within one solar diameter of the sun’s surface at the end of November. For more on Comet ISON, visit NASA’s Comet ISON Observing Campaign.

In addition to regular columns Anna’s Math JournalCoach Barb’s Corner, and Notes from the Club (where you can read about Dr. Anna Frebel’s recent visit to the club), we have our first installment of Member’s Thoughts in quite a while. See how one of our members rediscovered some beautiful facts about the Fibonacci numbers by asking and seeking the answer to a very natural math question.

Finally, a reminder: when you subscribe to the Girls’ Angle Bulletin, you’re not just getting a subscription to a magazine. You are also gaining access to the Girls’ Angle mentors.  We urge all subscribers and members to write us with your math questions or anything else in the Bulletin or having to do with mathematics in general. We will respond. We want you to get active and do mathematics. Parts of the Bulletin are written to induce you to wonder and respond with more questions. Don’t let those questions fade away and become forgotten. Send them to us!

We continue to encourage people to subscribe to our print version, so we have removed some content from the electronic version.  Subscriptions are a great way to support Girls’ Angle while getting something concrete back in return.  We hope you subscribe!

Uncritical Thinking

A friend sent me the challenge at right that his daughter was given in school.

Hidden Math Crossword

(The contest is now closed. Congratulations to Rebecca W. and Carly R.  Rebecca will receive an Intel web computer and Carly will receive chocolate from L. A. Burdick. Thanks to all who tried this crossword. We hope it was enjoyable.)

Sometimes it takes a little work to find the math. In the completed crossword grid, find 8 singular nouns with mathematical meaning. Each of the 8 mathematical terms has at least 5 letters, appears horizontally, and is split by a single black square. Send these 8 mathematical terms along with your contact information to girlsanglepuzzler “at” gmail.com. We will randomly draw from the correct answers received by midnight on October 1, 2013 to select a “winner” and send the winner a small prize. Girls’ Angle members will be put into a separate pool and have a chance to win an Intel web computer.

Girls’ Angle Bulletin, Volume 6, Number 6

The cover features a perspective drawing of the Back Bay by master painter Joel Babb. Last issue’s Summer Fun problem sets included a set of perspective drawing problems, one of which asked for a perspective drawing of a cityscape. The cover could be considered a sample solution to that problem. Members and subscribers: We’d love to see your cityscapes too!

In this issue’s interview, meet the Louise Wolff Kahn Professor Emerita in Mathematics and History of Science and Technology at Smith College, Marjorie Senechal. In this interview, she discusses mathematics, some of her mathematical experiences, how she goes about solving math problems, how she came up for the title of her biography of Dorothy Wrinch, and much more.

UC Berkeley astrophysicist Aaron Lee contributes this, and next, month’s Math In Your World. He writes about the orbits of celestial bodies and explores the polar equation that describes them. This two-part series anticipates the arrival of Comet ISON, which may become visible to the naked eye in November.

In addition to regular columns Anna’s Math JournalErrorbusters!, and Coach Barb’s Corner, find solutions to the five Summer Fun problem sets from the previous issue. Read how to thwart meddling gnomes, learn Vieta’s formulas, explore Gauss’ generalization of Wilson’s theorem, explore two extensions of the integers, and get a firm grasp of the basics of perspective drawing.

Finally, a reminder: when you subscribe to the Girls’ Angle Bulletin, you’re not just getting a subscription to a magazine. You are also gaining access to the Girls’ Angle mentors.  We urge all subscribers and members to write us with your math questions and solutions to the Summer Fun problem sets or anything else in the Bulletin or having to do with mathematics in general. We will respond. We want you to get active and do mathematics. Parts of the Bulletin are written to induce you to wonder and respond with more questions. Don’t let those questions fade away and become forgotten. Send them to us!

We continue to encourage people to subscribe to our print version, so we have removed some content from the electronic version.  Subscriptions are a great way to support Girls’ Angle while getting something concrete back in return.  We hope you subscribe!

Why is the area under one hump of a sine curve exactly 2?

I was talking with a student recently who told me that he always found the fact that $\int_0^{\pi} \sin x \, dx = 2$ amazing. “How is it that the area under one hump of the sine curve comes out exactly 2?” He asked me if there is an easy way to see that, or is it something you just have to discover by doing the computation.

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HCSSiM!

I recently returned from teaching a workshop at HCSSiM.

It was a blast!

I tip my hat to David Kelly for creating such an awesome experience.

If you’re a high school student who loves math and wants to add your mark to the HCSSiM experience, take the Interesting Test and apply. It’s truly a once-in-a-lifetime experience.

Have a Yellow Pig!