Challenge

Challenge Probability

Random Walks (and Bike Rides)

For the second consecutive day, I unexpectedly crossed paths with an acquaintance. In both cases, the encounter occured outside my daily routines, the person was someone I know only minimally, and we were both en route to different destinations when we happened to notice each other.

There are a lot of interesting results associated with objects moving around randomly in a given space, but as is usually the case with mathematics, the situations are idealized to eliminate some of the complicating real-world issues. Imagine a dot moving back and forth on the number line, or randomly around the Cartesian plane, for example.

I’m not really sure how unlikely it is for me to have two serendipitous encounters on back-to-back days, but the following questions are probably significant: how dense is the population? How many people do I know? How attentive am I? How popular is my destination? There are probably many more other important and complicating factors.

In any event, it’s certainly unlikely that it will happen again today.

By patrick honner, 14 years11 years ago

Challenge Geometry

Related Rates on the Street

I feel like I’ve had this experience many times in my life: I’m biking down the road, or walking along at a brisk pace, and out of the corner of my eye I catch a glimpse of a person I think I know. As I turn back to take another look, a well-positioned telephone pole or lamp post gets in between me and the unknown.

Somehow, the geometry and physics of the situation perfectly conspire to always keep the pole between me and the mystery person.

Click on the image below for a demonstration

A thorough analysis of the problem would be interesting, taking into consideration the different initial velocities, the different positions, the radius of the pole, different paths, and the like.

By patrick honner, 14 years9 years ago

Challenge NYT

Math Quiz: NYT Learning Network

Through Math for America, I have been contributing to the New York Times Learning Network. Here is my latest contribution:

http://learning.blogs.nytimes.com/2010/07/29/test-yourself-july-29-2010/

This problem is based on New York Yankees pitcher Mariano Rivera as his remarkable record as a closer.

By patrick honner, 14 years9 years ago

Challenge NYT

Math Quiz: New York Times Learning Network

Through Math for America, I have been contributing to the New York Times Learning Network. Here is my latest contribution:

http://learning.blogs.nytimes.com/2010/07/28/test-yourself-july-28-2010/

This problem is based on the amount of oil leaking into the Gulf of Mexico as a result of the British Petroleum accident.

By patrick honner, 14 years11 years ago

Challenge Sports

Fluctuating Batting Averages

When Miguel Cabrera came up to the plate in the fifth inning of last night’s Tigers-Rays game, he was 0-for-1 in the game and his up-to-the-minute batting average was announced as .349. I found this strange because, when the game started, Cabrera’s batting average was .350.

A player’s batting average is equal to (total hits) / (total at-bats). Thus the effect of one more at-bat without a hit dropped his average by .001, or 1/1000 (Note: rounding probably plays an important role here).

I wondered if this information uniquely determined both Cabrera’s hits and at-bats this season. Or maybe some combination of mathematics, baseball knowledge, and guessing could help me get those numbers. I did get the numbers–unfortunately, they were wrong.

An interesting question here is “What is the smallest possible number of hits such that one more hitless at-bat results in one’s rounded batting average dropping by .001?”

By patrick honner, 14 years11 years ago

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