Application

Application Challenge Technology

Creating Digital Landscapes

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!

By patrick honner, 13 years7 years ago

Automatic Origami

This video from New Scientist demonstrates some amazing self-unfolding origami.

https://www.newscientist.com/blogs/nstv/2011/05/micro-origami-unfolds-in-water.html

In the video, a carefully folded-up piece of paper is placed on the surface of the water. As the creases in the paper absorb the water, they start to expand, causing the shape to unfold.

As each subsequent layer unfolds and hits the water, the process repeats, until the shape is completely unfurled. It’s interesting to consider the potential applications of this process. An origami life boat, perhaps?

Yet another amazing way to have fun with folding!

By patrick honner, 13 years7 years ago

Application Sports Statistics

NBA Draft Math: Evaluating Team Success

After developing a simple metric for evaluating the success of NBA draft selections, I used that metric to investigate talent dispersion in the draft and then to compare the strength of various “draft classes”. As a third application of this metric, I will now analyze the success each NBA teamin making their draft picks.

I am using the total number of minutes played in the first two years of a player’s career as the basic quantification of draft pick value (the reasoning for this is explained in detail in NBA Draft Math, Part I).

In order to rate the success of a team, I looked at how each team’s draft pick performed relative to the average player chosen at that draft position for the NBA drafts between 2000 and 2009. I then computed the percentage difference between that team’s choice and the average player at that pick. The team’s overall rating is then the average of the percent differences for every draft pick.

The chart below summarizes the analysis for the Philadelphia 76ers.

As you can see, all but one of the 76ers draft choices performed better than the average player selected at that draft position. Overall, draft picks selected by Philadelphia performed about 34% better than average; they topped the list in this ranking.

This chart displays all NBA teams whose picks performed better than average. In addition to the 76ers, teams that performed notably well by this measure were the San Antonio Spurs, the Houston Rockets, and (surprisingly?) the New York Knicks.

The teams that performed worst in the analysis were the Boston Celtics, the Portland Trailblazers, and the Charlotte Bobcats.

Some interesting results! The basic limitations of this metric have been addressed in NBA Draft Math, Part I, but this simple approach has opened up a lot of opportunities for analysis, and naturally, improvement.

Application Geometry Photography

Math Photo: Knitting the Plane

As opposed to tiling the plane, here’s knitting the plane. Or, the fence.

As you can see, they’ve still got a ways to go!

And this isn’t the first example of mathematical knitting I’ve seen: check out this knitted Klein bottle!

By patrick honner, 14 years7 years ago

Application Sports Statistics

Rating the Ballparks

In an attempt to rate the various Major League Baseball stadiums around the country, Nate Silver looked at the user ratings from online review site Yelp. Noting that every ballpark has at least several hundred user reviews, Silver compiled the data from Yelp’s 1 to 5 rating system to create an ordering of the stadiums. Once complete, the list creates a natural starting point to investigate questions like “Is ballpark satisfaction correlated with team performance?” and “How valuable is a retractable-roof stadium?”

Silver also provides the standard deviation for the ratings for each ballpark and explains the significance. Standard deviation is a measure of the dispersion of data, so a higher deviation means more extreme ratings.

A great, fun little project! What else can we rate using available user ratings?

Read the full article here.

By patrick honner, 14 years8 years ago

Application

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