Mr Honner

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.

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, 15 yearsOctober 15, 2010 ago

Appreciation Numbers

Octomatics — The New New Math

It’s hard to tell how serious these people are about creating a new number system, but the effort is worthy of a little appreciation: introducing Octomatics!

www.infoverse.org/octomatics/

Octomatics offers a new numeral systems that enjoys a visual addition method and a smaller multiplication table. They’ve also defined a new clock, a new calendar, and they’ve prototyped a new calculator!

Truth be told, I’ve always secretly desired a new clock and calendar system–one that wasn’t so archaic and contrived. I’m not getting my hopes up, though; Octomatics looks less like a paradigm shift and more like Esperanto to me.

By patrick honner, 15 yearsOctober 14, 2010 ago

Challenge NYT

Math Quiz: NYT Learning Network

Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:

http://learning.blogs.nytimes.com/2010/10/13/test-yourself-math-oct-13-2010/

This problem was based on a new airplane seat design–the Skyrider–that was discussed in an earlier post

By patrick honner, 15 yearsOctober 13, 2010 ago

Geometry

Today in Triangle Appreciation

As it’s 10/12/10, I thought it would be the appropriate day to appreciate the 10-10-12 triangle!

Of course, it’s nice that the 10-10-12 triangle is isosceles. But what’s really cool is what happens when you drop the altitude from the top vertex!

It’s well known that in an isosceles triangle, the median and the altitude from the vertex are the same–this means that not only does this segment make a right angle (it’s the altitude), but it also divides the opposite side at its midpoint (it’s the median). So that segment creates two right triangles with hypotenuse 10 and side 6. Of course, the other side must be eight, since

$6^2 + 8^2 = 10^2$

Thank you, Pythagorean Theorem. So the 10-10-12 triangle is just two right triangles pasted together.

It’s not quite equilateral, but the 10-10-12 triangle is still pretty cool.

More Triangle Appreciation

Reality Sports

Octomatics — The New New Math

Math Quiz: NYT Learning Network

Today in Triangle Appreciation

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