October 2010

Geometry

The Final Word in Triangle Appreciation

As has been previously noted, October has been a nice month for triangle appreciation. Today, 10/19/10, offers us one more polygon to ponder.

Consider the 10-19-10 triangle.

It’s a fairly ordinary triangle, as triangles go. It’s a little short compared to the other triangles we’ve looked at recently, but there’s nothing wrong with that.

What’s special about the 10-19-10 triangle is that it’s our last chance this month to enjoy triangularity. Tomorrow, the Triangle Inequality steps in. You can’t have a 10-20-10 triangle, because once the third side hits 20, you need all of the 10s to get from point A to point B. There’s no wiggle room for the triangle’s interior.

Although I must admit, I do find much to admire in this degenerate triangle.

Resources Teaching

The First Word Calculator

This is a pretty awesome widget from the folks at Wolfram Alpha: a word calculator!

http://blog.wolframalpha.com/2010/10/15/celebrating-dictionary-day-with-new-word-data/

It does the basic things you’d expect, like give you definitions, pronunciations, synonyms, and the like. But it also gives you cool things like word frequency (“frequency” is the 3209th most common word) and hyphenations (me-di-e-val has 8 letters and 4 syllables)

And, when I typed my name in, I learned that 599,125 people are named Patrick, and our most common age is 46.

WolframAlpha’s mission is to make the world’s information computable–not just searchable. I guess the lesson here is that everything is computable in some way.

By patrick honner, 14 years9 years ago

Geometry History

Benoit Mandelbrot

Benoit Mandelbrot died this week at the age of 85, leaving a giant mark on the worlds of mathematics and science. Mandelbrot coined the term fractal, writing the seminal book on the topic in 1982–The Fractal Geometry of Nature. By rejecting the generally accepted, if never actually articulated, notion that things were smooth, Mandelbrot challenged everyone’s notion of shape, distance, and dimension.

As is often the case, Mandelbrot was considered crazy at first, but he dies with almost legendary status. We will likely be talking about fractals and Mandelbrot sets hundreds if not thousands of years from now, the way we talk about the Pythagorean Theorem and Euler’s Number today.

And as is also often the case, Mandelbrot’s brilliant and revolutionary ideas can be traced to a simple question that he chose to think of differently: how long is the coast of Britain?

The answer, he was surprised to discover, depends on how closely one looks. On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.

“Here is a question, a staple of grade-school geometry that, if you think about it, is impossible,” Dr. Mandelbrot told The New York Times earlier this year in an interview. “The length of the coastline, in a sense, is infinite.”

From Mandelbrot’s NYT’s obituary.

By patrick honner, 14 years9 years ago

Appreciation Geometry

More Triangle Appreciation

It’s been a great week for special triangles.

Six days ago was a rare Equilateral Triangle day, four days ago we appreciated the 10-12-10 triangle, and today, 10/16/10, gives us another triangle to admire.

It’s actually very closely related to the 10-12-10 triangle, which we saw is just two right triangles pasted together.

Just cut along the dotted altitude:

Now rotate the two pieces:

Stick them back together along their common side of length 6:

Now flip, and voila! Another triangle made by gluing two congruent right triangles together!

I’m running out of good triangles, so we may not appreciate another until December 10th.

Application Sports

Reality Sports

This is an interesting post about testing the “reality” of video games:

http://dubiousquality.blogspot.com/2010/10/back-now-with-100-more-broken.html

After running numerous computer v. computer matchups in Madden football (at various coaching settings), statistical averages from the video games were compared to real NFL averages. For example, total points were 4.4% lower in the computer games; there were 11.3% fewer interceptions, but 10.4% more fumbles. Based on his analysis, the author concludes that the game-play is not realistic enough.

The majority of the post is actually a rant about the abundance of advertising in this particular video game. By that measure, I’d say the game is very realistic.

By patrick honner, 14 years9 years ago

Follow Mr Honner