Through Math for America, I am part of an on-going collaboration with the New York Times Learning
https://learning.blogs.nytimes.com/2011/07/20/test-yourself-math-july-20-2011/
This math problem is based on the difference in earning potential between high school and college graduates. It adds up!
As a car-less person in a car-driven world, I occasionally need to rent a car to move sofas, bring home large plants, or just get away from all my car-less neighbors for the weekend. A long history of distrust of car-related business people (sales, repair) makes me approach my car-rental interactions with cynicism. Here’s yet another reason that cynicism is justified.
Car rental agencies offer a Pre-Pay for Gas option when you pick up your vehicle. “Pay now, and you won’t have to worry about filling the tank when you return the car. It’s less hassle for you! ” says the salesperson. “You even get a discounted rate on gas!” It’s not emphasized initially, but you won’t be charged what it costs to fill the tank when you return the car; you will be charged for a full tank of gas, regardless of how much gas is in the tank.
This is actually a good deal for you if you can arrange your travel in such a way as to roll into the lot on an empty tank of gas. But if you pre-pay and then return the car with half a tank of fuel? You just gave the rental agency 8 gallons X $4 per gallon = $32 worth of gas. That’s a nice little bonus for them!
And for the record, the sort of meticulous, obsessive planning required to return a rental car on empty tends to detract from the fun of your road-trip. Not for me, necessarily, but potentially for your passengers.
Tim Chartier, a professor of mathematics at Davidson college, has put together some great resources on using mathematical algorithms and free computer software to create random-looking 2D and 3D landscapes.
In the following paper posted at the MAA’s Digital Library, Chartier outlines the basic ideas of fractal geometry and random number generation, and creates a simple computer program that will generate random-looking coastlines and mountain ranges:
http://mathdl.maa.org/mathDL/23/?pa=content&sa=viewDocument&nodeId=1795
And in a follow-up blog post, Chartier takes the process one step further by turning his 2D fractal island into a planet, using free ray-tracing software.
http://forum.davidson.edu/mathmovement/2011/07/10/a-random-planet/
After explaining how to produce the planet, Chartier challenges the reader to create and submit their own!
It’s easy to see some of the applications of this idea in computer animation and graphics, as well as perhaps in simulations. A simple, innovative, and fun idea to explore!
This beach umbrella casts a fairly octogonal shadow! If I knew more about astronomy, I suppose I could have used this shadow to compute the time of day.
Related Posts
This is a nice profile on Dan Feyer, the winner of the 2010 American Crossword Puzzle Tournament.
http://www.nytimes.com/2010/12/07/science/07profile.html
Feyer, who is a music director in New York City, excelled at math as well as music in school. This combination of talents, math and music, is not uncommon, and both of these skills sets seem to appear with great frequency among crossword puzzle enthusiasts.
Indeed, as the article points out, Jon Delfin, a 7-time winner of the tournament, is also a musician, and many other winners and crossword constructors are math and computer science types. As one puzzler points out, the connection between math, music, and crossword puzzles is pattern finding. In addition, the three fields also rely on the manipulation of symbols that often contain no inherent meaning themselves.
This all makes perfect sense to me. I am an avid crossword puzzle solver, I have competed in the tournament many times, and I have even constructed several puzzles of my own, including this one that incorporates many mathematical ideas:
https://mrhonner.com/2011/06/02/crossword-puzzle-a-touch-of-math-2/
Unfortunately, constructing a good crossword puzzle takes as much time and effort as constructing a good math test!